From 8b5a486a6a2cd7b5c9b07053fe9857e399e65f63 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Wed, 6 Apr 2022 20:32:40 +0200 Subject: FIrst Commit Name added --- buch/papers/fm/main.tex | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 1e75235..de3e10a 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -3,10 +3,13 @@ % % (c) 2020 Hochschule Rapperswil % +% !TeX root = /.../...buch.tex +%\begin {document} \chapter{Thema\label{chapter:fm}} \lhead{Thema} \begin{refsection} -\chapterauthor{Hans Muster} + +\chapterauthor{Joshua Bär} Ein paar Hinweise für die korrekte Formatierung des Textes \begin{itemize} @@ -34,3 +37,5 @@ Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren \printbibliography[heading=subbibliography] \end{refsection} + +%\end {document} -- cgit v1.2.1 From 2bba3b1d52604c9f671763927ec592a72b09088e Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Sun, 15 May 2022 15:36:08 +0200 Subject: a few animations --- buch/papers/fm/Python animation/Bessel-FM.ipynb | 193 ++++++++++++++++++++++++ buch/papers/fm/Python animation/Bessel-FM.py | 42 ++++++ buch/papers/fm/RS presentation/RS.tex | 162 ++++++++++++++++++++ 3 files changed, 397 insertions(+) create mode 100644 buch/papers/fm/Python animation/Bessel-FM.ipynb create mode 100644 buch/papers/fm/Python animation/Bessel-FM.py create mode 100644 buch/papers/fm/RS presentation/RS.tex (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb new file mode 100644 index 0000000..9d0835a --- /dev/null +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -0,0 +1,193 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 74, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "operands could not be broadcast together with shapes (3,) (600,) ", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/Python animation/Bessel-FM.ipynb Cell 1'\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 13\u001b[0m x \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mlinspace(\u001b[39m0.01\u001b[39m, N\u001b[39m*\u001b[39mT, N)\n\u001b[1;32m 14\u001b[0m beta \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mlinspace(\u001b[39m0.1\u001b[39m,\u001b[39m10\u001b[39m, \u001b[39m3\u001b[39m)\n\u001b[0;32m---> 15\u001b[0m y_old \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39msin(\u001b[39m100.0\u001b[39m \u001b[39m*\u001b[39m \u001b[39m2.0\u001b[39m\u001b[39m*\u001b[39mnp\u001b[39m.\u001b[39mpi\u001b[39m*\u001b[39mx\u001b[39m+\u001b[39mbeta\u001b[39m*\u001b[39;49mnp\u001b[39m.\u001b[39;49msin(\u001b[39m50.0\u001b[39;49m \u001b[39m*\u001b[39;49m \u001b[39m2.0\u001b[39;49m\u001b[39m*\u001b[39;49mnp\u001b[39m.\u001b[39;49mpi\u001b[39m*\u001b[39;49mx))\n\u001b[1;32m 16\u001b[0m y \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m\u001b[39m*\u001b[39mx;\n\u001b[1;32m 17\u001b[0m xf \u001b[39m=\u001b[39m fftfreq(N, \u001b[39m1\u001b[39m \u001b[39m/\u001b[39m \u001b[39m400\u001b[39m)\n", + "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,) (600,) " + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy import signal\n", + "from scipy.fft import fft, ifft, fftfreq\n", + "import scipy.special as sc\n", + "import scipy.fftpack\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.widgets import Slider\n", + "\n", + "# Number of samplepoints\n", + "N = 600\n", + "# sample spacing\n", + "T = 1.0 / 800.0\n", + "x = np.linspace(0.01, N*T, N)\n", + "beta = 1.0\n", + "y_old = np.sin(100.0 * 2.0*np.pi*x+beta*np.sin(50.0 * 2.0*np.pi*x))\n", + "y = 0*x;\n", + "xf = fftfreq(N, 1 / 400)\n", + "for k in range (-5, 5):\n", + " y = sc.jv(k,beta)*np.sin((100.0+k*50) * 2.0*np.pi*x)\n", + " yf = fft(y)\n", + " plt.plot(xf, np.abs(yf))\n", + "\n", + "axamp = plt.axes(np.linspace(0.1, 3, 10))\n", + "beta_slider = Slider(\n", + "ax=axamp,\n", + "label=\"Amplitude\",\n", + "valmin=0,\n", + "valmax=10,\n", + "valinit=beta,\n", + "orientation=\"vertical\"\n", + ")\n", + "plt.show()\n", + "\n", + "yf_old = fft(y_old)\n", + "plt.plot(xf, np.abs(yf_old))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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gNOXrz6ql5+ATVyzkf71xiIFTY7TUp8v960REqtK8H8w+H3fc1MnJ0Tzf69k3e2UREZlWVQfFh5e0cH1nG4//373k9RxtEZFzUtVBAfDljy9n/9FT/OOu9yrdFBGRWKr6oPiNrkUsaa3nb/7prUo3RUQklqo+KFLJBL9746W8tOd9dhzUw4xERM5W1QcFwLrrl5FNJ3j8n/ZWuikiIrFTE0HR2pDhX31kKT967SD9gyOVbo6ISKzURFAAfPmmTkZzBf77lncq3RQRkVipmaBYsaiJX12xkCdfepvRXKHSzRERiY2aCQqA3/vEcg6fGOGv/8+blW6KiEhs1FRQfPLKDm699mK+9pN/ZuvbmgNKRKQUNRUUZsaf/8sPs7gly70bt3F8eKzSTRIRmfdqKigAmrNpvr7uOg4NDPOnP9xOMBu6iIicSc0FBcBHL72Ae29ewY9ePcj/2BbJc5RERGKrJoMC4O5PXcHqzgv40x9u5+3+oUo3R0Rk3qrZoEgmjIfXXUcyYfze469waOBUpZskIjIv1WxQACxprefbX1rFe8dHuO1bL7Knb7DSTRIRmXdqOigAPnZZOxvvuoHhsTy3/7cX2X5AEweKiBSr+aCA4AFH3/vKjWTTSdY/+hJb9vRXukkiIvOGgiJ0WccCvveVG7mwuY4vbXiZDT9/i4KeiicioqAodnFrPd/7yk3cdHk7Dzyzk9/6a41biIgoKKa4oDHDhn9zPf/19mv5f++d4Jav/4xv/3SPnrktIjVLQTENM+Nff3QpP/7DX+NXVyzkwc27+Pw3fsaz2w/pcpSI1BwFxQwWNWf59pdW8ZfrVzKSK/CVv/sFn/vGz9j8hgJDRGqHxWmuo1WrVnlPT09FfncuX+B/vn6Qv/xJL3uODHHlogX89scu5TevW0JLQ7oibRIRmY2ZbXX3Ved1DAXF2ckXnGdeP8ijP93DjoPHyaQSrLnmIr54/TJuvKydRMIq2j4RkWIKigrbfmCATT37+OG2AxwfznFhUx2/3rWIz3Qt4qbL26lLJSvdRBGpcQqKeWJ4LM8/7HyPZ7cf4n/v7uPkaJ7GTJJfu6qDmy5fyA2XtXN5RyNm6m2ISLTmIihSc9WYWpZNJ7n12ou59dqLGR7L8+Kb/fzDzvd44ZeH2fzGuwBc2FTHDZe1c31nG9cua+Xqi5rJpHQvgYjMfwqKOZZNJ/nU1RfyqasvxN3Z23+Sl/b08+Kb/by4p5/u1w4CkEkm+NDFzVy7tIUPLW7m6ouauHJRE411+k8iIvOLPpXKyMxYvrCR5QsbWb/6EtydgwPDvLbvGK/tO8ar+47x/a37GRrNT+xzaXsDl3csoLO9kc6FDcFreyNL2upJaqBcRCpAQREhM2NJaz1LWuv53K8sBqBQcA4cO8WuQ8f55bsn2P3uCd7sG+TFN/s5NTYZIOmksaytgc6FjVza3sDStgYWt2S5qCXL4pYsHQvqSCV1KUtE5p6CosISCWPZBQ0su6CB37jmoolyd+fwiRH2Hhlib/8Qe/tPhsvBpayTRb0QgITBhU1ZFrVkWdwcBEhHUx0LF2Rob6yjfUGGhQuC14aM/rOLSOn0iTFPmRmLmrMsas7yscvaT9vm7gycGuPQwDDvDgyHr6eC1+PD9PYN8vPeIwyO5KY9dn06SfuCDO0L6mitT9My3U/DB8saMknduSVSgxQUMWRmtDZkaG3I8KHFzWesNzyWp39olCMnRugfGuHI4Cj9g6P0D44E5YMjHD05yt7+IQZOjXH81BgzzUySShgt9Wmasika64KfBROvSRozp5c11iWLtqfIppPUZ5LUp4OfulRCX1AUiQEFRRXLppMTYyKlKBScwdEcAyfHJoJjYJqf48M5hkaCn8Mnhhk6kmcwXJ96SWz2NiaCAAl/isPktG1hWV0YMHWpBJlUgkwyfE0lqEslTyurS53+Wlw3k0yodyRSIgWFTEgkjOZsmuZsmmXneIx8wTk5mmNoZDI8hkZyDI7kGM4VGB7Nc2os/BnNM5zLF5UVODWaZyQXbDt6cpRTY5Pbh8cKpw3wn69MKkFdUXikkwlSSSOdCF5TyQSZpJEK19PJBKmETdRLJRKkkzZlOThOOjG+bKROWz7zsVJJI2FB/WQiXJ5SdtqPGYnElG1hmchcKikozGwN8HUgCXzH3f/zlO11wN8CHwX6gS+6+95w2/3AnUAe+H13f66UY0o8JRNGUzZNU7Y8EyW6O6P5AqO58CdfYGSsMFE2kht/zU9sLy6f3CfPSNFxRnIFcvkCYwUPXvPOWL5ALu/kCgVOjQWvufHygp+2PF53fL2SzCBpp4dHMmmnl00Jl1LLzIyEQSLcbuFywoJ/aIwvB9sm607+nF4vEQZb4gzHmbqfWRiG0+xr4e8drz9RN1G0XLwtMb4MMFmeMDCC41m4nEiEr+NlZhjT1x9vy3h9xss4fZslOK0sEfZwbbr6Fe79zhoUZpYEHgE+A+wHXjGzbnffWVTtTuCou19hZuuAh4AvmlkXsA64BrgY+EczuzLcZ7ZjinyAmVGXSs7rebTcfTJIwnCZGkJTQ2csX6BQgFyhQMGDfQvhcfIF/0BZoTC5LV9w8j5ZNrHNnXw+fJ1ynOKy/JTjFK+P5goTZQV3CgWCV3cKHiy7M7G9eLngwXsx3jYP6+eLtxV8xnExmRQEzOnhcXr4hGFjHwyf81VKj2I10Ovue4LG2kZgLVD8ob4W+E/h8tPAX1kQgWuBje4+ArxlZr3h8SjhmCKxZGakk0Y6CfXM30CbTzwMj+LAGQ8VLxQHTNG2ovAZ39eLAiw/JZwmthXG18N9wt8/8epMBFkQYkVlTIach+vF9f20OpPLFIVjcJzp6xfCufcm6o2H8Rnqj7e7MPF3TB5j/L3aNgf/fUoJiiXAvqL1/cDHzlTH3XNmNgC0h+UvTdl3Sbg82zFFpEYEl4bQ7ANl8OdzcIx5/1VeM7vLzHrMrKevr6/SzRERqTmlBMUBOO0mmKVh2bR1zCwFtBAMap9p31KOCYC7P+ruq9x9VUdHRwnNFRGRuVRKULwCrDCz5WaWIRic7p5Spxu4I1y+DXjegwdddAPrzKzOzJYDK4CXSzymiIjMA7OOUYRjDvcAzxHcyrrB3XeY2QNAj7t3A48BT4aD1e8TfPAT1ttEMEidA+529zzAdMec+z9PRETOl55wJyJSxebiCXfzfjBbREQqS0EhIiIzUlCIiMiMFBQiIjKjWA1mm9kJYHel2zFPLASOVLoR84Deh0l6LybpvZh0lbs3nc8B4jbN+O7zHb2vFmbWo/dC70MxvReT9F5MMrPzvlVUl55ERGRGCgoREZlR3ILi0Uo3YB7RexHQ+zBJ78UkvReTzvu9iNVgtoiIRC9uPQoREYmYgkJERGYUi6AwszVmttvMes3svkq3J0pmtszMXjCznWa2w8zuDcsvMLMfm9k/h69tlW5rVMwsaWbbzOyZcH25mW0Jz4+nwqnrq56ZtZrZ02b2SzPbZWY31up5YWb/Pvz/Y7uZfdfMsrVyXpjZBjM7bGbbi8qmPQ8s8I3wPXndzD5Syu+Y90FhZkngEeAWoAtYb2ZdlW1VpHLAH7l7F3ADcHf4998H/MTdVwA/Cddrxb3ArqL1h4CH3f0K4ChwZ0VaFb2vA8+6+9XAtQTvSc2dF2a2BPh9YJW7f5jg0QXrqJ3z4nFgzZSyM50HtxA8F2gFcBfwrVJ+wbwPCmA10Ovue9x9FNgIrK1wmyLj7ofc/Rfh8gmCD4MlBO/BE2G1J4DfrEgDI2ZmS4HPA98J1w34NPB0WKUm3gszawH+BcGzYHD3UXc/Ro2eFwRfHq4Pn7DZAByiRs4Ld/8pwXOAip3pPFgL/K0HXgJazWzxbL8jDkGxBNhXtL4/LKs5ZtYJrAS2AIvc/VC46V1gUaXaFbGvAX8MFML1duCYu+fC9Vo5P5YDfcDfhJfhvmNmjdTgeeHuB4D/ArxDEBADwFZq87wYd6bz4Jw+T+MQFAKY2QLg+8AfuPvx4m3hY2er/j5nM/sCcNjdt1a6LfNACvgI8C13XwkMMeUyUw2dF20E/1JeDlwMNPLBSzE1ay7OgzgExQFgWdH60rCsZphZmiAk/t7dfxAWvzfeZQxfD1eqfRH6OHCrme0luAT5aYLr9K3hJQeonfNjP7Df3beE608TBEctnhe/Drzl7n3uPgb8gOBcqcXzYtyZzoNz+jyNQ1C8AqwI72DIEAxSdVe4TZEJr8E/Buxy978o2tQN3BEu3wH8KOq2Rc3d73f3pe7eSXAePO/uvw28ANwWVquV9+JdYJ+ZXRUW3UzwbPqaOy8ILjndYGYN4f8v4+9FzZ0XRc50HnQDXwrvfroBGCi6RHVGsfhmtpl9juDadBLY4O4PVrZF0TGzTwA/A95g8rr8nxCMU2wCLgHeBn7L3acOaFUtM/sk8B/c/QtmdhlBD+MCYBvwO+4+UsHmRcLMriMY1M8Ae4AvE/zjr+bOCzP7M+CLBHcJbgP+LcG196o/L8zsu8AnCaZWfw/4j8APmeY8CIP0rwguzZ0Evuzus84uG4ugEBGRyonDpScREakgBYWIiMxIQSEiIjNSUIiIyIwUFCIiMiMFhYiIzEhBISIiM/r/lXwoXNBP92cAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Number of samplepoints\n", + "N = 600\n", + "# sample spacing\n", + "T = 1.0 / 800.0\n", + "x = np.linspace(0.0, N*T, N)\n", + "y = sc.jv(3,x)#np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)\n", + "yf = scipy.fftpack.fft(y)\n", + "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(xf, 2.0/N * np.abs(yf[:N//2]))\n", + "ax.set(\n", + " xlim=(0, 100)\n", + ")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "for n in range (5):\n", + " x = np.linspace(0,15,1000)\n", + " y = sc.jv(n,x)\n", + " plt.plot(x, y, '-')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from scipy import special\n", + "\n", + "def drumhead_height(n, k, distance, angle, t):\n", + " kth_zero = special.jn_zeros(n, k)[-1]\n", + " return np.cos(t) * np.cos(n*angle) * special.jn(n, distance*kth_zero)\n", + "\n", + "theta = np.r_[0:2*np.pi:50j]\n", + "radius = np.r_[0:1:50j]\n", + "x = np.array([r * np.cos(theta) for r in radius])\n", + "y = np.array([r * np.sin(theta) for r in radius])\n", + "z = np.array([drumhead_height(1, 1, r, theta, 0.5) for r in radius])\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig = plt.figure()\n", + "ax = fig.add_axes(rect=(0, 0.05, 0.95, 0.95), projection='3d')\n", + "ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap='RdBu_r', vmin=-0.5, vmax=0.5)\n", + "ax.set_xlabel('X')\n", + "ax.set_ylabel('Y')\n", + "ax.set_xticks(np.arange(-1, 1.1, 0.5))\n", + "ax.set_yticks(np.arange(-1, 1.1, 0.5))\n", + "ax.set_zlabel('Z')\n", + "\n", + "plt.show()" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" + }, + "kernelspec": { + "display_name": "Python 3.8.10 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/buch/papers/fm/Python animation/Bessel-FM.py b/buch/papers/fm/Python animation/Bessel-FM.py new file mode 100644 index 0000000..cf30e16 --- /dev/null +++ b/buch/papers/fm/Python animation/Bessel-FM.py @@ -0,0 +1,42 @@ +import numpy as np +from scipy import signal +from scipy.fft import fft, ifft, fftfreq +import scipy.special as sc +import scipy.fftpack +import matplotlib.pyplot as plt +from matplotlib.widgets import Slider + +# Number of samplepoints +N = 600 +# sample spacing +T = 1.0 / 800.0 +x = np.linspace(0.01, N*T, N) +beta = 1.0 +y_old = np.sin(100.0 * 2.0*np.pi*x+beta*np.sin(50.0 * 2.0*np.pi*x)) +y = 0*x; +xf = fftfreq(N, 1 / 400) +for k in range (-5, 5): + y = sc.jv(k,beta)*np.sin((100.0+k*50) * 2.0*np.pi*x) + yf = fft(y) + plt.plot(xf, np.abs(yf)) + +axbeta =plt.axes([0.25, 0.1, 0.65, 0.03]) +beta_slider = Slider( +ax=axbeta, +label="Beta", +valmin=0.1, +valmax=3, +valinit=beta, +) + +def update(val): + line.set_ydata(fm(beta_slider.val)) + fig.canvas.draw_idle() + + +beta_slider.on_changed(update) +plt.show() + +yf_old = fft(y_old) +plt.plot(xf, np.abs(yf_old)) +plt.show() \ No newline at end of file diff --git a/buch/papers/fm/RS presentation/RS.tex b/buch/papers/fm/RS presentation/RS.tex new file mode 100644 index 0000000..8e3de17 --- /dev/null +++ b/buch/papers/fm/RS presentation/RS.tex @@ -0,0 +1,162 @@ +\documentclass[11pt,aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{lmodern} +\usepackage[ngerman]{babel} +\usepackage{tikz} +\usetheme{Hannover} + +\begin{document} + \author{Joshua Bär} + \title{FM - Bessel} + \subtitle{} + \logo{} + \institute{OST Ostschweizer Fachhochschule} + \date{16.5.2022} + \subject{Mathematisches Seminar} + %\setbeamercovered{transparent} + \setbeamercovered{invisible} + \setbeamertemplate{navigation symbols}{} + \begin{frame}[plain] + \maketitle + \end{frame} +%------------------------------------------------------------------------------- +\section{Einführung} + \begin{frame} + \frametitle{Frequenzmodulation} + \begin{itemize} + \visible<1->{\item Für Übertragung von Daten} + \visible<2->{\item Amplituden unabhängig} + \end{itemize} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \frametitle{Parameter} + \begin{center} + \begin{tabular}{ c c c } + \hline + Nutzlas & Fehler & Versenden \\ + \hline + 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\ + 4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\ +\visible<1->{3}& +\visible<1->{3}& +\visible<1->{9 Werte eines Polynoms vom Grad 2} \\ + &&\\ +\visible<1->{$k$} & +\visible<1->{$t$} & +\visible<1->{$k+2t$ Werte eines Polynoms vom Grad $k-1$} \\ + \hline + &&\\ + &&\\ + \multicolumn{3}{l} { + \visible<1>{Ausserdem können bis zu $2t$ Fehler erkannt werden!} + } + \end{tabular} + \end{center} + \end{frame} + +%------------------------------------------------------------------------------- + +\section{Diskrete Fourier Transformation} + \begin{frame} + \frametitle{Idee} + \begin{itemize} + \item Fourier-transformieren + \item Übertragung + \item Rücktransformieren + \end{itemize} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \begin{figure} + \only<1>{ + \includegraphics[width=0.9\linewidth]{images/fig1.pdf} + } + \only<2>{ + \includegraphics[width=0.9\linewidth]{images/fig2.pdf} + } + \only<3>{ + \includegraphics[width=0.9\linewidth]{images/fig3.pdf} + } + \only<4>{ + \includegraphics[width=0.9\linewidth]{images/fig4.pdf} + } + \only<5>{ + \includegraphics[width=0.9\linewidth]{images/fig5.pdf} + } + \only<6>{ + \includegraphics[width=0.9\linewidth]{images/fig6.pdf} + } + \only<7>{ + \includegraphics[width=0.9\linewidth]{images/fig7.pdf} + } + \end{figure} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \frametitle{Diskrete Fourier Transformation} + \begin{itemize} + \item Diskrete Fourier-Transformation gegeben durch: + \visible<1->{ + \[ + \label{ft_discrete} + \hat{c}_{k} + = \frac{1}{N} \sum_{n=0}^{N-1} + {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn} + \]} + \visible<2->{ + \item Ersetzte + \[ + w = e^{-\frac{2\pi j}{N} k} + \]} + \visible<3->{ + \item Wenn $N$ konstant: + \[ + \hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N) + \]} + \end{itemize} + \end{frame} + +%------------------------------------------------------------------------------- + +%------------------------------------------------------------------------------- + \begin{frame} + \frametitle{Ein Beispiel} + + \begin{itemize} + + \onslide<1->{\item endlicher Körper $q = 11$} + + \onslide<2->{ist eine Primzahl} + + \onslide<3->{beinhaltet die Zahlen $\mathbb{F}_{11} = \{0,1,2,3,4,5,6,7,8,9,10\}$} + + \vspace{10pt} + + \onslide<4->{\item Nachrichtenblock $=$ Nutzlast $+$ Fehlerkorrekturstellen} + + \onslide<5->{$n = q - 1 = 10$ Zahlen} + + \vspace{10pt} + + \onslide<6->{\item Max.~Fehler $t = 2$} + + \onslide<7->{maximale Anzahl von Fehler, die wir noch korrigieren können} + + \vspace{10pt} + + \onslide<8->{\item Nutzlast $k = n -2t = 6$ Zahlen} + + \onslide<9->{Fehlerkorrkturstellen $2t = 4$ Zahlen} + + \onslide<10->{Nachricht $m = [0,0,0,0,4,7,2,5,8,1]$} + + \onslide<11->{als Polynom $m(X) = 4X^5 + 7X^4 + 2X^3 + 5X^2 + 8X + 1$} + + \end{itemize} + + \end{frame} + + +\end{document} -- cgit v1.2.1 From 5187a5a947c0283e9f3d7fbc2acef96278109939 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Fri, 20 May 2022 18:14:40 +0200 Subject: presentation FM-Bessel --- buch/papers/fm/.vscode/settings.json | 3 + buch/papers/fm/Python animation/Bessel-FM.ipynb | 164 ++++++++++------ buch/papers/fm/RS presentation/FM_presentation.pdf | Bin 0 -> 357597 bytes buch/papers/fm/RS presentation/FM_presentation.tex | 125 ++++++++++++ ...quency modulation (FM) and Bessel functions.pdf | Bin 0 -> 159598 bytes buch/papers/fm/RS presentation/README.txt | 1 + buch/papers/fm/RS presentation/RS.tex | 209 +++++++++------------ buch/papers/fm/RS presentation/images/100HZ.png | Bin 0 -> 8601 bytes buch/papers/fm/RS presentation/images/200HZ.png | Bin 0 -> 8502 bytes buch/papers/fm/RS presentation/images/300HZ.png | Bin 0 -> 9059 bytes buch/papers/fm/RS presentation/images/400HZ.png | Bin 0 -> 9949 bytes buch/papers/fm/RS 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create mode 100644 buch/papers/fm/RS presentation/images/400HZ.png create mode 100644 buch/papers/fm/RS presentation/images/bessel.png create mode 100644 buch/papers/fm/RS presentation/images/bessel2.png create mode 100644 buch/papers/fm/RS presentation/images/bessel_beta1.png create mode 100644 buch/papers/fm/RS presentation/images/bessel_frequenz.png create mode 100644 buch/papers/fm/RS presentation/images/beta_0.001.png create mode 100644 buch/papers/fm/RS presentation/images/beta_0.1.png create mode 100644 buch/papers/fm/RS presentation/images/beta_0.5.png create mode 100644 buch/papers/fm/RS presentation/images/beta_1.png create mode 100644 buch/papers/fm/RS presentation/images/beta_2.png create mode 100644 buch/papers/fm/RS presentation/images/beta_3.png create mode 100644 buch/papers/fm/RS presentation/images/fm_10Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_20hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_30Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_3Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_40Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_5Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_7Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_frequenz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_in_time.png (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/.vscode/settings.json b/buch/papers/fm/.vscode/settings.json new file mode 100644 index 0000000..5125289 --- /dev/null +++ b/buch/papers/fm/.vscode/settings.json @@ -0,0 +1,3 @@ +{ + "notebook.cellFocusIndicator": "border" +} \ No newline at end of file diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb index 9d0835a..bfbb83d 100644 --- a/buch/papers/fm/Python animation/Bessel-FM.ipynb +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -2,21 +2,9 @@ "cells": [ { "cell_type": "code", - "execution_count": 74, + "execution_count": 117, "metadata": {}, - "outputs": [ - { - "ename": "ValueError", - "evalue": "operands could not be broadcast together with shapes (3,) (600,) ", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/Python animation/Bessel-FM.ipynb Cell 1'\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 13\u001b[0m x \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mlinspace(\u001b[39m0.01\u001b[39m, N\u001b[39m*\u001b[39mT, N)\n\u001b[1;32m 14\u001b[0m beta \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mlinspace(\u001b[39m0.1\u001b[39m,\u001b[39m10\u001b[39m, \u001b[39m3\u001b[39m)\n\u001b[0;32m---> 15\u001b[0m y_old \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39msin(\u001b[39m100.0\u001b[39m \u001b[39m*\u001b[39m \u001b[39m2.0\u001b[39m\u001b[39m*\u001b[39mnp\u001b[39m.\u001b[39mpi\u001b[39m*\u001b[39mx\u001b[39m+\u001b[39mbeta\u001b[39m*\u001b[39;49mnp\u001b[39m.\u001b[39;49msin(\u001b[39m50.0\u001b[39;49m \u001b[39m*\u001b[39;49m \u001b[39m2.0\u001b[39;49m\u001b[39m*\u001b[39;49mnp\u001b[39m.\u001b[39;49mpi\u001b[39m*\u001b[39;49mx))\n\u001b[1;32m 16\u001b[0m y \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m\u001b[39m*\u001b[39mx;\n\u001b[1;32m 17\u001b[0m xf \u001b[39m=\u001b[39m fftfreq(N, \u001b[39m1\u001b[39m \u001b[39m/\u001b[39m \u001b[39m400\u001b[39m)\n", - "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,) (600,) " - ] - } - ], + "outputs": [], "source": [ "import numpy as np\n", "from scipy import signal\n", @@ -25,45 +13,71 @@ "import scipy.fftpack\n", "import matplotlib.pyplot as plt\n", "from matplotlib.widgets import Slider\n", - "\n", + "def fm(beta):\n", + " # Number of samplepoints\n", + " N = 600\n", + " # sample spacing\n", + " T = 1.0 / 1000.0\n", + " fc = 100.0\n", + " fm = 30.0\n", + " x = np.linspace(0.01, N*T, N)\n", + " #beta = 1.0\n", + " y_old = np.sin(fc * 2.0*np.pi*x+beta*np.sin(fm * 2.0*np.pi*x))\n", + " y = 0*x;\n", + " xf = fftfreq(N, 1 / 400)\n", + " for k in range (-4, 4):\n", + " y = sc.jv(k,beta)*np.sin((fc+k*fm) * 2.0*np.pi*x)\n", + " yf = fft(y)/(fc*np.pi)\n", + " plt.plot(xf, np.abs(yf))\n", + " plt.xlim(-150, 150)\n", + " plt.show()\n", + " #yf_old = fft(y_old)\n", + " #plt.plot(xf, np.abs(yf_old))\n", + " #plt.show()\n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ "# Number of samplepoints\n", - "N = 600\n", + "N = 800\n", "# sample spacing\n", - "T = 1.0 / 800.0\n", + "T = 1.0 / 1000.0\n", "x = np.linspace(0.01, N*T, N)\n", - "beta = 1.0\n", - "y_old = np.sin(100.0 * 2.0*np.pi*x+beta*np.sin(50.0 * 2.0*np.pi*x))\n", - "y = 0*x;\n", - "xf = fftfreq(N, 1 / 400)\n", - "for k in range (-5, 5):\n", - " y = sc.jv(k,beta)*np.sin((100.0+k*50) * 2.0*np.pi*x)\n", - " yf = fft(y)\n", - " plt.plot(xf, np.abs(yf))\n", "\n", - "axamp = plt.axes(np.linspace(0.1, 3, 10))\n", - "beta_slider = Slider(\n", - "ax=axamp,\n", - "label=\"Amplitude\",\n", - "valmin=0,\n", - "valmax=10,\n", - "valinit=beta,\n", - "orientation=\"vertical\"\n", - ")\n", - "plt.show()\n", - "\n", - "yf_old = fft(y_old)\n", + "y_old = np.sin(100* 2.0*np.pi*x+1*np.sin(15* 2.0*np.pi*x))\n", + "yf_old = fft(y_old)/(100*np.pi)\n", + "xf = fftfreq(N, 1 / 1000)\n", "plt.plot(xf, np.abs(yf_old))\n", - "plt.show()\n" + "#plt.xlim(-150, 150)\n", + "plt.show()" ] }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 118, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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"text/plain": [ "
" ] @@ -75,32 +89,17 @@ } ], "source": [ - "\n", - "# Number of samplepoints\n", - "N = 600\n", - "# sample spacing\n", - "T = 1.0 / 800.0\n", - "x = np.linspace(0.0, N*T, N)\n", - "y = sc.jv(3,x)#np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)\n", - "yf = scipy.fftpack.fft(y)\n", - "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.plot(xf, 2.0/N * np.abs(yf[:N//2]))\n", - "ax.set(\n", - " xlim=(0, 100)\n", - ")\n", - "plt.show()\n" + "fm(1)" ] }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 122, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -109,20 +108,35 @@ "needs_background": "light" }, "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.7651976865579666\n" + ] } ], "source": [ "\n", - "for n in range (5):\n", - " x = np.linspace(0,15,1000)\n", + "for n in range (-4,4):\n", + " x = np.linspace(0,11,1000)\n", " y = sc.jv(n,x)\n", " plt.plot(x, y, '-')\n", - "plt.show()" + "plt.plot([1,1],[sc.jv(0,1),sc.jv(-1,1)],)\n", + "plt.xlim(0,10)\n", + "plt.grid(True)\n", + "plt.ylabel('Bessel J_n(b)')\n", + "plt.xlabel('b')\n", + "plt.plot(x, y)\n", + "plt.show()\n", + "\n", + "print(sc.jv(0,1))" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 85, "metadata": {}, "outputs": [ { @@ -163,6 +177,32 @@ "\n", "plt.show()" ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "x = np.linspace(0,0.1,1000)\n", + "y = np.sin(100 * 2.0*np.pi*x+1.5*np.sin(30 * 2.0*np.pi*x))\n", + "plt.plot(x, y, '-')\n", + "plt.show()" + ] } ], "metadata": { diff --git a/buch/papers/fm/RS presentation/FM_presentation.pdf b/buch/papers/fm/RS presentation/FM_presentation.pdf new file mode 100644 index 0000000..496e35e Binary files /dev/null and b/buch/papers/fm/RS presentation/FM_presentation.pdf differ diff --git a/buch/papers/fm/RS presentation/FM_presentation.tex b/buch/papers/fm/RS presentation/FM_presentation.tex new file mode 100644 index 0000000..92cb501 --- /dev/null +++ b/buch/papers/fm/RS presentation/FM_presentation.tex @@ -0,0 +1,125 @@ +%% !TeX root = RS.tex + +\documentclass[11pt,aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{lmodern} +\usepackage[ngerman]{babel} +\usepackage{tikz} +\usetheme{Hannover} + +\begin{document} + \author{Joshua Bär} + \title{FM - Bessel} + \subtitle{} + \logo{} + \institute{OST Ostschweizer Fachhochschule} + \date{16.5.2022} + \subject{Mathematisches Seminar} + %\setbeamercovered{transparent} + \setbeamercovered{invisible} + \setbeamertemplate{navigation symbols}{} + \begin{frame}[plain] + \maketitle + \end{frame} +%------------------------------------------------------------------------------- +\section{Einführung} + \begin{frame} + \frametitle{Frequenzmodulation} + + \visible<1->{ + \begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt)) + \end{equation}} + + \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}} + \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}} + \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}} + + + \end{frame} +%------------------------------------------------------------------------------- +\section{Proof} +\begin{frame} + \frametitle{Bessel} + + \visible<1->{\begin{align} + \cos(\beta\sin\varphi) + &= + J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + \sin(\beta\sin\varphi) + &= + J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + J_{-n}(\beta) &= (-1)^n J_n(\beta) + \end{align}} + \visible<2->{\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \end{align}} +\end{frame} + +%------------------------------------------------------------------------------- +\begin{frame} + \frametitle{Prof->Done} + \begin{align} + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) + \end{align} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \begin{figure} + \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}} + \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}} + \end{figure} + \end{frame} +%------------------------------------------------------------------------------- +\section{Input Parameter} + \begin{frame} + \frametitle{Träger-Frequenz Parameter} + \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} + \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}} + \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}} + \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}} + \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}} + \end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Modulations-Frequenz Parameter} +\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} +\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}} +\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}} +\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}} +\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}} +\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}} +\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Beta Parameter} + \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t)\end{equation}} + \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}} + \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}} + \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}} + \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}} + \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}} + \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}} + \only<7>{\includegraphics[scale=0.7]{images/bessel.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} + \includegraphics[scale=0.5]{images/beta_1.png} + \includegraphics[scale=0.5]{images/bessel.png} +\end{frame} +\end{document} diff --git a/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf new file mode 100644 index 0000000..a6e701c Binary files /dev/null and b/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf differ diff --git a/buch/papers/fm/RS presentation/README.txt b/buch/papers/fm/RS presentation/README.txt new file mode 100644 index 0000000..4d0620f --- /dev/null +++ b/buch/papers/fm/RS presentation/README.txt @@ -0,0 +1 @@ +Dies ist die Presentation des Reed-Solomon-Code \ No newline at end of file diff --git a/buch/papers/fm/RS presentation/RS.tex b/buch/papers/fm/RS presentation/RS.tex index 8e3de17..8a67619 100644 --- a/buch/papers/fm/RS presentation/RS.tex +++ b/buch/papers/fm/RS presentation/RS.tex @@ -1,3 +1,5 @@ +%% !TeX root = RS.tex + \documentclass[11pt,aspectratio=169]{beamer} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} @@ -13,7 +15,7 @@ \logo{} \institute{OST Ostschweizer Fachhochschule} \date{16.5.2022} - \subject{Mathematisches Seminar} + \subject{Mathematisches Seminar- Spezielle Funktionen} %\setbeamercovered{transparent} \setbeamercovered{invisible} \setbeamertemplate{navigation symbols}{} @@ -24,139 +26,98 @@ \section{Einführung} \begin{frame} \frametitle{Frequenzmodulation} - \begin{itemize} - \visible<1->{\item Für Übertragung von Daten} - \visible<2->{\item Amplituden unabhängig} - \end{itemize} + + \visible<1->{\begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt))\end{equation}} + + \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}} + \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}} + \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}} + + \end{frame} %------------------------------------------------------------------------------- - \begin{frame} - \frametitle{Parameter} - \begin{center} - \begin{tabular}{ c c c } - \hline - Nutzlas & Fehler & Versenden \\ - \hline - 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\ - 4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\ -\visible<1->{3}& -\visible<1->{3}& -\visible<1->{9 Werte eines Polynoms vom Grad 2} \\ - &&\\ -\visible<1->{$k$} & -\visible<1->{$t$} & -\visible<1->{$k+2t$ Werte eines Polynoms vom Grad $k-1$} \\ - \hline - &&\\ - &&\\ - \multicolumn{3}{l} { - \visible<1>{Ausserdem können bis zu $2t$ Fehler erkannt werden!} - } - \end{tabular} - \end{center} - \end{frame} +\section{Proof} +\begin{frame} + \frametitle{Bessel} -%------------------------------------------------------------------------------- + \visible<1->{\begin{align} + \cos(\beta\sin\varphi) + &= + J_0(\beat) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + \sin(\beta\sin\varphi) + &= + J_0(\beat) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + J_{-n}(\beat) &= (-1)^n J_n(\beta) + \end{align}} + \visible<2->{\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \end{align}} +\end{frame} -\section{Diskrete Fourier Transformation} - \begin{frame} - \frametitle{Idee} - \begin{itemize} - \item Fourier-transformieren - \item Übertragung - \item Rücktransformieren - \end{itemize} +%------------------------------------------------------------------------------- +\begin{frame} + \frametitle{Prof->Done} + \begin{align} + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omgea_m)t) + \end{align} \end{frame} %------------------------------------------------------------------------------- \begin{frame} - \begin{figure} - \only<1>{ - \includegraphics[width=0.9\linewidth]{images/fig1.pdf} - } - \only<2>{ - \includegraphics[width=0.9\linewidth]{images/fig2.pdf} - } - \only<3>{ - \includegraphics[width=0.9\linewidth]{images/fig3.pdf} - } - \only<4>{ - \includegraphics[width=0.9\linewidth]{images/fig4.pdf} - } - \only<5>{ - \includegraphics[width=0.9\linewidth]{images/fig5.pdf} - } - \only<6>{ - \includegraphics[width=0.9\linewidth]{images/fig6.pdf} - } - \only<7>{ - \includegraphics[width=0.9\linewidth]{images/fig7.pdf} - } + \begin{figure} + \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}} + \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}} \end{figure} \end{frame} %------------------------------------------------------------------------------- +\section{Input Parameter} \begin{frame} - \frametitle{Diskrete Fourier Transformation} - \begin{itemize} - \item Diskrete Fourier-Transformation gegeben durch: - \visible<1->{ - \[ - \label{ft_discrete} - \hat{c}_{k} - = \frac{1}{N} \sum_{n=0}^{N-1} - {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn} - \]} - \visible<2->{ - \item Ersetzte - \[ - w = e^{-\frac{2\pi j}{N} k} - \]} - \visible<3->{ - \item Wenn $N$ konstant: - \[ - \hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N) - \]} - \end{itemize} - \end{frame} - -%------------------------------------------------------------------------------- - -%------------------------------------------------------------------------------- - \begin{frame} - \frametitle{Ein Beispiel} - - \begin{itemize} - - \onslide<1->{\item endlicher Körper $q = 11$} - - \onslide<2->{ist eine Primzahl} - - \onslide<3->{beinhaltet die Zahlen $\mathbb{F}_{11} = \{0,1,2,3,4,5,6,7,8,9,10\}$} - - \vspace{10pt} - - \onslide<4->{\item Nachrichtenblock $=$ Nutzlast $+$ Fehlerkorrekturstellen} - - \onslide<5->{$n = q - 1 = 10$ Zahlen} - - \vspace{10pt} - - \onslide<6->{\item Max.~Fehler $t = 2$} - - \onslide<7->{maximale Anzahl von Fehler, die wir noch korrigieren können} - - \vspace{10pt} - - \onslide<8->{\item Nutzlast $k = n -2t = 6$ Zahlen} - - \onslide<9->{Fehlerkorrkturstellen $2t = 4$ Zahlen} - - \onslide<10->{Nachricht $m = [0,0,0,0,4,7,2,5,8,1]$} - - \onslide<11->{als Polynom $m(X) = 4X^5 + 7X^4 + 2X^3 + 5X^2 + 8X + 1$} - - \end{itemize} - + \frametitle{Träger-Frequenz Parameter} + \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} + \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}} + \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}} + \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}} + \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}} \end{frame} - - +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Modulations-Frequenz Parameter} +\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} +\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}} +\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}} +\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}} +\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}} +\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}} +\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Beta Parameter} + \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omgea_m)t)\end{equation}} + \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}} + \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}} + \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}} + \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}} + \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}} + \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}} + \only<7>{\includegraphics[scale=0.7]{images/bessel.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} + \includegraphics[scale=0.5]{images/beta_1.png} + \includegraphics[scale=0.5]{images/bessel.png} +\end{frame} \end{document} diff --git a/buch/papers/fm/RS presentation/images/100HZ.png b/buch/papers/fm/RS 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\chapter{Thema\label{chapter:fm}} \lhead{Thema} -- cgit v1.2.1 From 4a5bb7d7fa8ae99e2982ff30873b15a41a4f2a73 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 18 Jul 2022 14:35:43 +0200 Subject: Kapitel unterteilung --- buch/papers/fm/01_AM-FM.tex | 22 +++++++++++++ buch/papers/fm/02_frequenzyspectrum.tex | 55 +++++++++++++++++++++++++++++++++ buch/papers/fm/03_bessel.tex | 40 ++++++++++++++++++++++++ buch/papers/fm/04_fazit.tex | 40 ++++++++++++++++++++++++ buch/papers/fm/main.tex | 46 ++++++++++++++------------- buch/papers/fm/teil0.tex | 22 ------------- buch/papers/fm/teil1.tex | 55 --------------------------------- buch/papers/fm/teil2.tex | 40 ------------------------ buch/papers/fm/teil3.tex | 40 ------------------------ 9 files changed, 181 insertions(+), 179 deletions(-) create mode 100644 buch/papers/fm/01_AM-FM.tex create mode 100644 buch/papers/fm/02_frequenzyspectrum.tex create mode 100644 buch/papers/fm/03_bessel.tex create mode 100644 buch/papers/fm/04_fazit.tex delete mode 100644 buch/papers/fm/teil0.tex delete mode 100644 buch/papers/fm/teil1.tex delete mode 100644 buch/papers/fm/teil2.tex delete mode 100644 buch/papers/fm/teil3.tex (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex new file mode 100644 index 0000000..55697df --- /dev/null +++ b/buch/papers/fm/01_AM-FM.tex @@ -0,0 +1,22 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 0\label{fm:section:teil0}} +\rhead{Teil 0} +Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +erat, sed diam voluptua \cite{fm:bibtex}. +At vero eos et accusam et justo duo dolores et ea rebum. +Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum +dolor sit amet. + +Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +erat, sed diam voluptua. +At vero eos et accusam et justo duo dolores et ea rebum. Stet clita +kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit +amet. + + diff --git a/buch/papers/fm/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex new file mode 100644 index 0000000..6f9edf1 --- /dev/null +++ b/buch/papers/fm/02_frequenzyspectrum.tex @@ -0,0 +1,55 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 1 +\label{fm:section:teil1}} +\rhead{Problemstellung} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. +Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit +aut fugit, sed quia consequuntur magni dolores eos qui ratione +voluptatem sequi nesciunt +\begin{equation} +\int_a^b x^2\, dx += +\left[ \frac13 x^3 \right]_a^b += +\frac{b^3-a^3}3. +\label{fm:equation1} +\end{equation} +Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, +consectetur, adipisci velit, sed quia non numquam eius modi tempora +incidunt ut labore et dolore magnam aliquam quaerat voluptatem. + +Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis +suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? +Quis autem vel eum iure reprehenderit qui in ea voluptate velit +esse quam nihil molestiae consequatur, vel illum qui dolorem eum +fugiat quo voluptas nulla pariatur? + +\subsection{De finibus bonorum et malorum +\label{fm:subsection:finibus}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. + +Et harum quidem rerum facilis est et expedita distinctio +\ref{fm:section:loesung}. +Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil +impedit quo minus id quod maxime placeat facere possimus, omnis +voluptas assumenda est, omnis dolor repellendus +\ref{fm:section:folgerung}. +Temporibus autem quibusdam et aut officiis debitis aut rerum +necessitatibus saepe eveniet ut et voluptates repudiandae sint et +molestiae non recusandae. +Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis +voluptatibus maiores alias consequatur aut perferendis doloribus +asperiores repellat. + + diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex new file mode 100644 index 0000000..6ab6fa0 --- /dev/null +++ b/buch/papers/fm/03_bessel.tex @@ -0,0 +1,40 @@ +% +% teil2.tex -- Beispiel-File für teil2 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 2 +\label{fm:section:teil2}} +\rhead{Teil 2} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +velit, sed quia non numquam eius modi tempora incidunt ut labore +et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +reprehenderit qui in ea voluptate velit esse quam nihil molestiae +consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +pariatur? + +\subsection{De finibus bonorum et malorum +\label{fm:subsection:bonorum}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +est et expedita distinctio. Nam libero tempore, cum soluta nobis +est eligendi optio cumque nihil impedit quo minus id quod maxime +placeat facere possimus, omnis voluptas assumenda est, omnis dolor +repellendus. Temporibus autem quibusdam et aut officiis debitis aut +rerum necessitatibus saepe eveniet ut et voluptates repudiandae +sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +sapiente delectus, ut aut reiciendis voluptatibus maiores alias +consequatur aut perferendis doloribus asperiores repellat. + + diff --git a/buch/papers/fm/04_fazit.tex b/buch/papers/fm/04_fazit.tex new file mode 100644 index 0000000..3bcfc4d --- /dev/null +++ b/buch/papers/fm/04_fazit.tex @@ -0,0 +1,40 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 3 +\label{fm:section:teil3}} +\rhead{Teil 3} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +velit, sed quia non numquam eius modi tempora incidunt ut labore +et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +reprehenderit qui in ea voluptate velit esse quam nihil molestiae +consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +pariatur? + +\subsection{De finibus bonorum et malorum +\label{fm:subsection:malorum}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +est et expedita distinctio. Nam libero tempore, cum soluta nobis +est eligendi optio cumque nihil impedit quo minus id quod maxime +placeat facere possimus, omnis voluptas assumenda est, omnis dolor +repellendus. Temporibus autem quibusdam et aut officiis debitis aut +rerum necessitatibus saepe eveniet ut et voluptates repudiandae +sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +sapiente delectus, ut aut reiciendis voluptatibus maiores alias +consequatur aut perferendis doloribus asperiores repellat. + + diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 00fb34b..1f8ebde 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -11,29 +11,31 @@ \chapterauthor{Joshua Bär} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} +Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Frequenz Modulatrion (FM)(acronym?). -\input{papers/fm/teil0.tex} -\input{papers/fm/teil1.tex} -\input{papers/fm/teil2.tex} -\input{papers/fm/teil3.tex} +%Ein paar Hinweise für die korrekte Formatierung des Textes +%\begin{itemize} +%\item +%Absätze werden gebildet, indem man eine Leerzeile einfügt. +%Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. +%\item +%Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende +%Optionen werden gelöscht. +%Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. +%\item +%Beginnen Sie jeden Satz auf einer neuen Zeile. +%Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen +%in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt +%anzuwenden. +%\item +%Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren +%Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. +%\end{itemize} + +\input{papers/fm/01_AM-FM.tex} +\input{papers/fm/02_frequenzyspectrum.tex} +\input{papers/fm/03_bessel.tex} +\input{papers/fm/04_fazit.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/fm/teil0.tex b/buch/papers/fm/teil0.tex deleted file mode 100644 index 55697df..0000000 --- a/buch/papers/fm/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{fm:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{fm:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/fm/teil1.tex b/buch/papers/fm/teil1.tex deleted file mode 100644 index 6f9edf1..0000000 --- a/buch/papers/fm/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{fm:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{fm:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{fm:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{fm:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/fm/teil2.tex b/buch/papers/fm/teil2.tex deleted file mode 100644 index 6ab6fa0..0000000 --- a/buch/papers/fm/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{fm:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/fm/teil3.tex b/buch/papers/fm/teil3.tex deleted file mode 100644 index 3bcfc4d..0000000 --- a/buch/papers/fm/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{fm:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - -- cgit v1.2.1 From 24235f4b1ac1d6b837fc7740a69d8906ff2376eb Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 18 Jul 2022 14:44:14 +0200 Subject: save --- buch/papers/fm/01_AM-FM.tex | 25 ++++----- buch/papers/fm/02_frequenzyspectrum.tex | 94 ++++++++++++++++----------------- buch/papers/fm/03_bessel.tex | 50 +++++++----------- 3 files changed, 78 insertions(+), 91 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index 55697df..58dd6e7 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -3,20 +3,17 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{fm:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{fm:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. +\section{AM - FM\label{fm:section:teil0}} +\rhead{AM- FM} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. +TODO: +Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] + +%Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +%nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +%erat, sed diam voluptua \cite{fm:bibtex}. +%At vero eos et accusam et justo duo dolores et ea rebum. +%Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum +%dolor sit amet. diff --git a/buch/papers/fm/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex index 6f9edf1..1c6044d 100644 --- a/buch/papers/fm/02_frequenzyspectrum.tex +++ b/buch/papers/fm/02_frequenzyspectrum.tex @@ -3,53 +3,53 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 1 +\section{AM-FM im Frequenzspektrum \label{fm:section:teil1}} \rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{fm:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{fm:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{fm:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - +Hier Beschreiben ich das Frequenzspektrum und wie AM und FM aussehen und generiert werden. +%Sed ut perspiciatis unde omnis iste natus error sit voluptatem +%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +%quae ab illo inventore veritatis et quasi architecto beatae vitae +%dicta sunt explicabo. +%Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit +%aut fugit, sed quia consequuntur magni dolores eos qui ratione +%voluptatem sequi nesciunt +%\begin{equation} +%\int_a^b x^2\, dx +%= +%\left[ \frac13 x^3 \right]_a^b +%= +%\frac{b^3-a^3}3. +%\label{fm:equation1} +%\end{equation} +%Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, +%consectetur, adipisci velit, sed quia non numquam eius modi tempora +%incidunt ut labore et dolore magnam aliquam quaerat voluptatem. +% +%Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis +%suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? +%Quis autem vel eum iure reprehenderit qui in ea voluptate velit +%esse quam nihil molestiae consequatur, vel illum qui dolorem eum +%fugiat quo voluptas nulla pariatur? +% +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:finibus}} +%At vero eos et accusamus et iusto odio dignissimos ducimus qui +%blanditiis praesentium voluptatum deleniti atque corrupti quos +%dolores et quas molestias excepturi sint occaecati cupiditate non +%provident, similique sunt in culpa qui officia deserunt mollitia +%animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. +% +%Et harum quidem rerum facilis est et expedita distinctio +%\ref{fm:section:loesung}. +%Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil +%impedit quo minus id quod maxime placeat facere possimus, omnis +%voluptas assumenda est, omnis dolor repellendus +%\ref{fm:section:folgerung}. +%Temporibus autem quibusdam et aut officiis debitis aut rerum +%necessitatibus saepe eveniet ut et voluptates repudiandae sint et +%molestiae non recusandae. +%Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis +%voluptatibus maiores alias consequatur aut perferendis doloribus +%asperiores repellat. diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index 6ab6fa0..fdaa0d1 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -3,38 +3,28 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 2 +\section{FM und Besselfunktion \label{fm:section:teil2}} \rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? -\subsection{De finibus bonorum et malorum -\label{fm:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +Hier wird beschrieben wie die Bessel Funktion der FM im Frequenzspektrum hilft, wieso diese gebrauch wird und ihre Vorteile. +%Sed ut perspiciatis unde omnis iste natus error sit voluptatem +%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +%quae ab illo inventore veritatis et quasi architecto beatae vitae +%dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +%aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +%eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +%est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +%velit, sed quia non numquam eius modi tempora incidunt ut labore +%et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +%veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +%nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +%reprehenderit qui in ea voluptate velit esse quam nihil molestiae +%consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +%pariatur? +% +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:bonorum}} + -- cgit v1.2.1 From 49524d47d4705bf9b49568625976ad1f2ef67aff Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 18 Jul 2022 16:30:50 +0200 Subject: save --- buch/papers/fm/01_AM-FM.tex | 2 ++ buch/papers/fm/04_fazit.tex | 66 ++++++++++++++++++++++----------------------- buch/papers/fm/main.tex | 7 +++-- 3 files changed, 40 insertions(+), 35 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index 58dd6e7..6f1c942 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -9,6 +9,8 @@ TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] + + %Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam %nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam %erat, sed diam voluptua \cite{fm:bibtex}. diff --git a/buch/papers/fm/04_fazit.tex b/buch/papers/fm/04_fazit.tex index 3bcfc4d..8c6c002 100644 --- a/buch/papers/fm/04_fazit.tex +++ b/buch/papers/fm/04_fazit.tex @@ -3,38 +3,38 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 3 -\label{fm:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +\section{Fazit +\label{fm:section:fazit}} +\rhead{Zusamenfassend} +%Sed ut perspiciatis unde omnis iste natus error sit voluptatem +%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +%quae ab illo inventore veritatis et quasi architecto beatae vitae +%dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +%aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +%eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +%est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +%velit, sed quia non numquam eius modi tempora incidunt ut labore +%et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +%veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +%nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +%reprehenderit qui in ea voluptate velit esse quam nihil molestiae +%consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +%pariatur? +% +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:malorum}} +%At vero eos et accusamus et iusto odio dignissimos ducimus qui +%blanditiis praesentium voluptatum deleniti atque corrupti quos +%dolores et quas molestias excepturi sint occaecati cupiditate non +%provident, similique sunt in culpa qui officia deserunt mollitia +%animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +%est et expedita distinctio. Nam libero tempore, cum soluta nobis +%est eligendi optio cumque nihil impedit quo minus id quod maxime +%placeat facere possimus, omnis voluptas assumenda est, omnis dolor +%repellendus. Temporibus autem quibusdam et aut officiis debitis aut +%rerum necessitatibus saepe eveniet ut et voluptates repudiandae +%sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +%sapiente delectus, ut aut reiciendis voluptatibus maiores alias +%consequatur aut perferendis doloribus asperiores repellat. diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 1f8ebde..393daa5 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -5,14 +5,17 @@ % % !TeX root = buch.tex %\begin {document} -\chapter{Thema\label{chapter:fm}} -\lhead{Thema} +\chapter{FM\label{chapter:fm}} +\lhead{FM} \begin{refsection} \chapterauthor{Joshua Bär} Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Frequenz Modulatrion (FM)(acronym?). +Mit hilfe einer Modulation kann ein Übertragungs Signal \(m(t)\) auf einen Trägerfrequenz \( f_c \) kombiniert werden. +Das Ziel ist es dieses modulierte Signal dan im Empfangsspektrum wieder demodulieren und so informationen im Signal \( m(t) \)zu Übertragen. + %Ein paar Hinweise für die korrekte Formatierung des Textes %\begin{itemize} %\item -- cgit v1.2.1 From 1001d7e685fbf99051c5cfe26abc800aa1ae1c2f Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 18 Jul 2022 17:15:22 +0200 Subject: save --- buch/papers/fm/01_AM-FM.tex | 2 +- buch/papers/fm/Makefile | 32 ++++++++++++++++++++++++++++++-- buch/papers/fm/main.tex | 4 ++-- buch/papers/fm/standalone.tex | 30 ++++++++++++++++++++++++++++++ 4 files changed, 63 insertions(+), 5 deletions(-) create mode 100644 buch/papers/fm/standalone.tex (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index 6f1c942..a267322 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -13,7 +13,7 @@ Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequ %Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam %nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -%erat, sed diam voluptua \cite{fm:bibtex}. +erat, sed diam voluptua \cite{fm:bibtex}. %At vero eos et accusam et justo duo dolores et ea rebum. %Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum %dolor sit amet. diff --git a/buch/papers/fm/Makefile b/buch/papers/fm/Makefile index f43d497..fb42942 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -4,6 +4,34 @@ # (c) 2020 Prof Dr Andreas Mueller # -images: - @echo "no images to be created in fm" +SOURCES := \ + 01_AM-FM.tex \ + 02_frequenzyspectrum.tex \ + main.tex \ + 03_bessel.tex \ + 04_fazit.tex +#TIKZFIGURES := \ + tikz/atoms-grid-still.tex \ + +#FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) + +.PHONY: images +#images: $(FIGURES) + +#figures/%.pdf: tikz/%.tex +# mkdir -p figures +# pdflatex --output-directory=figures $< + +.PHONY: standalone +standalone: standalone.tex $(SOURCES) #$(FIGURES) + mkdir -p standalone + cd ../..; \ + pdflatex \ + --halt-on-error \ + --shell-escape \ + --output-directory=papers/fm/standalone \ + papers/fm/standalone.tex; + cd standalone; \ + bibtex standalone; \ + makeindex standalone; \ No newline at end of file diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 393daa5..be66a2f 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -13,8 +13,8 @@ Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Frequenz Modulatrion (FM)(acronym?). -Mit hilfe einer Modulation kann ein Übertragungs Signal \(m(t)\) auf einen Trägerfrequenz \( f_c \) kombiniert werden. -Das Ziel ist es dieses modulierte Signal dan im Empfangsspektrum wieder demodulieren und so informationen im Signal \( m(t) \)zu Übertragen. +%Mit hilfe einer Modulation kann ein Übertragungs Signal \(m(t)\) auf einen Trägerfrequenz \( f_c \) kombiniert werden. +%Das Ziel ist es dieses modulierte Signal dan im Empfangsspektrum wieder demodulieren und so informationen im Signal \( m(t) \)zu Übertragen. %Ein paar Hinweise für die korrekte Formatierung des Textes %\begin{itemize} diff --git a/buch/papers/fm/standalone.tex b/buch/papers/fm/standalone.tex new file mode 100644 index 0000000..51a5c8c --- /dev/null +++ b/buch/papers/fm/standalone.tex @@ -0,0 +1,30 @@ +\documentclass{book} + +\input{common/packages.tex} + +% additional packages used by the individual papers, add a line for +% each paper +\input{papers/common/addpackages.tex} + +% workaround for biblatex bug +\makeatletter +\def\blx@maxline{77} +\makeatother +\addbibresource{chapters/references.bib} + +% Bibresources for each article +\input{papers/common/addbibresources.tex} + +% make sure the last index starts on an odd page +\AtEndDocument{\clearpage\ifodd\value{page}\else\null\clearpage\fi} +\makeindex + +%\pgfplotsset{compat=1.12} +\setlength{\headheight}{15pt} % fix headheight warning +\DeclareGraphicsRule{*}{mps}{*}{} + +\begin{document} + \input{common/macros.tex} + \def\chapterauthor#1{{\large #1}\bigskip\bigskip} + \input{papers/fm/main.tex} +\end{document} -- cgit v1.2.1 From b72c171ecac28671740a594f89a02fd3bc4d0e96 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 19 Jul 2022 07:44:42 +0200 Subject: dependencies fixed --- buch/papers/fm/Makefile.inc | 6 +----- 1 file changed, 1 insertion(+), 5 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index 0f144b6..dcdecd2 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,9 +6,5 @@ dependencies-fm = \ papers/fm/packages.tex \ papers/fm/main.tex \ - papers/fm/references.bib \ - papers/fm/teil0.tex \ - papers/fm/teil1.tex \ - papers/fm/teil2.tex \ - papers/fm/teil3.tex + papers/fm/references.bib -- cgit v1.2.1 From 36f9ca108e2cc08f68d7095b5e09b59bff90f98c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 19 Jul 2022 07:52:32 +0200 Subject: makefile fix --- buch/papers/fm/Makefile.inc | 4 ++++ 1 file changed, 4 insertions(+) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index dcdecd2..e5cd9f6 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,5 +6,9 @@ dependencies-fm = \ papers/fm/packages.tex \ papers/fm/main.tex \ + papers/fm/01_AM-FM.tex \ + papers/fm/02_frequenzyspectrum.tex \ + papers/fm/03_bessel.tex \ + papers/fm/04_fazit.tex \ papers/fm/references.bib -- cgit v1.2.1 From e694c3a02296d4a0b551ad0be3f980a91a0e05f2 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 19 Jul 2022 13:53:55 +0200 Subject: save --- buch/papers/fm/01_AM-FM.tex | 6 ++++++ buch/papers/fm/main.tex | 47 ++++++++++++++++++------------------------- buch/papers/fm/standalone.tex | 1 + 3 files changed, 27 insertions(+), 27 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index a267322..f1c59a9 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -6,6 +6,12 @@ \section{AM - FM\label{fm:section:teil0}} \rhead{AM- FM} +Das sinusförmige Trägersignal hat die übliche Form: +\(x-c(t) = A_c \cdot cos(\omega_ct+\psi)\). +Wobei die konstanten Amplitude \(A_c\) und Phase \(\psi\) vom Nachrichtensignal \(m(t)\) verändert wird. +Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), +steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. +\newblockpunct TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index be66a2f..24c645f 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -3,37 +3,30 @@ % % (c) 2020 Hochschule Rapperswil % -% !TeX root = buch.tex -%\begin {document} -\chapter{FM\label{chapter:fm}} + +\chapter{FM \(\with\)Bessel\label{chapter:fm}} \lhead{FM} \begin{refsection} \chapterauthor{Joshua Bär} -Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Frequenz Modulatrion (FM)(acronym?). - -%Mit hilfe einer Modulation kann ein Übertragungs Signal \(m(t)\) auf einen Trägerfrequenz \( f_c \) kombiniert werden. -%Das Ziel ist es dieses modulierte Signal dan im Empfangsspektrum wieder demodulieren und so informationen im Signal \( m(t) \)zu Übertragen. - -%Ein paar Hinweise für die korrekte Formatierung des Textes -%\begin{itemize} -%\item -%Absätze werden gebildet, indem man eine Leerzeile einfügt. -%Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -%\item -%Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -%Optionen werden gelöscht. -%Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -%\item -%Beginnen Sie jeden Satz auf einer neuen Zeile. -%Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -%in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -%anzuwenden. -%\item -%Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -%Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -%\end{itemize} +Die Frequenzmodulation ist eine Modulation die man auch schon im alten Radio findet. +Falls du dich an die Zeit erinnerst, konnte man zwischen \textit{FM-AM} Umschalten, +dies bedeutete so viel wie: \textit{F}requenz-\textit{M}odulation und \textit{A}mplituden-\textit{M}odulation. +Durch die Modulation wird ein Nachrichtensignal \(m(t)\) auf ein Trägersignal (z.B. ein Sinus- oder Rechtecksignal) abgebildet (kombiniert). +Durch dieses Auftragen vom Nachrichtensignal \(m(t)\) kann das modulierte Signal in einem gewünschten Frequenzbereich übertragen werden. +Der ursprünglich Frequenzbereich des Nachrichtensignal \(m(t)\) erstreckt sich typischerweise von 0 HZ bis zur Bandbreite \(B_m\). +\newline +Beim Empfänger wird dann durch Demodulation das ursprüngliche Nachrichtensignal \(m(t)\) so originalgetreu wie möglich zurückgewonnen. +\newline +Beim Trägersignal \(x_c(t)\) handelt es sich um ein informationsloses Hilfssignal. +Durch die Modulation mit dem Nachrichtensignal \(m(t)\) wird es zum modulierten zu übertragenden Signal. +Für alle Erklärungen wird ein sinusförmiges Trägersignal benutzt, jedoch kann auch ein Rechtecksignal, +welches Digital einfach umzusetzten ist, +genauso als Trägersignal genutzt werden kann. +Zuerst wird erklärt was \textit{FM-AM} ist, danach wie sich diese im Frequenzspektrum verhalten. +Erst dann erklär ich dir wie die Besselfunktion mit der Frequenzmodulation( acro?) zusammenhängt. +Nun zur Modulation im nächsten Abschnitt. \input{papers/fm/01_AM-FM.tex} \input{papers/fm/02_frequenzyspectrum.tex} @@ -43,4 +36,4 @@ Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Freque \printbibliography[heading=subbibliography] \end{refsection} -%\end {document} + diff --git a/buch/papers/fm/standalone.tex b/buch/papers/fm/standalone.tex index 51a5c8c..c161ed5 100644 --- a/buch/papers/fm/standalone.tex +++ b/buch/papers/fm/standalone.tex @@ -1,5 +1,6 @@ \documentclass{book} +\def\IncludeBookCover{0} \input{common/packages.tex} % additional packages used by the individual papers, add a line for -- cgit v1.2.1 From 6c23215c9ad1209bee5d1d2704579b4761341b71 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 19 Jul 2022 14:36:41 +0200 Subject: add gitignore --- buch/papers/fm/.gitignore | 1 + buch/papers/fm/01_AM-FM.tex | 5 +++-- buch/papers/fm/Makefile | 6 +++--- buch/papers/fm/main.tex | 6 +++--- 4 files changed, 10 insertions(+), 8 deletions(-) create mode 100644 buch/papers/fm/.gitignore (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/.gitignore b/buch/papers/fm/.gitignore new file mode 100644 index 0000000..eae2913 --- /dev/null +++ b/buch/papers/fm/.gitignore @@ -0,0 +1 @@ +standalone \ No newline at end of file diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index f1c59a9..b9d6167 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -7,11 +7,12 @@ \rhead{AM- FM} Das sinusförmige Trägersignal hat die übliche Form: -\(x-c(t) = A_c \cdot cos(\omega_ct+\psi)\). -Wobei die konstanten Amplitude \(A_c\) und Phase \(\psi\) vom Nachrichtensignal \(m(t)\) verändert wird. +\(x_c(t) = A_c \cdot cos(\omega_ct+\varphi)\). +Wobei die konstanten Amplitude \(A_c\) und Phase \(\varphi\) vom Nachrichtensignal \(m(t)\) verändert wird. Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. \newblockpunct + TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] diff --git a/buch/papers/fm/Makefile b/buch/papers/fm/Makefile index fb42942..c84963f 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -7,16 +7,16 @@ SOURCES := \ 01_AM-FM.tex \ 02_frequenzyspectrum.tex \ - main.tex \ 03_bessel.tex \ - 04_fazit.tex + 04_fazit.tex \ + main.tex #TIKZFIGURES := \ tikz/atoms-grid-still.tex \ #FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) -.PHONY: images +#.PHONY: images #images: $(FIGURES) #figures/%.pdf: tikz/%.tex diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 24c645f..56a7ac5 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -4,18 +4,18 @@ % (c) 2020 Hochschule Rapperswil % -\chapter{FM \(\with\)Bessel\label{chapter:fm}} +\chapter{FM Bessel\label{chapter:fm}} \lhead{FM} \begin{refsection} \chapterauthor{Joshua Bär} - +%$\with$ Die Frequenzmodulation ist eine Modulation die man auch schon im alten Radio findet. Falls du dich an die Zeit erinnerst, konnte man zwischen \textit{FM-AM} Umschalten, dies bedeutete so viel wie: \textit{F}requenz-\textit{M}odulation und \textit{A}mplituden-\textit{M}odulation. Durch die Modulation wird ein Nachrichtensignal \(m(t)\) auf ein Trägersignal (z.B. ein Sinus- oder Rechtecksignal) abgebildet (kombiniert). Durch dieses Auftragen vom Nachrichtensignal \(m(t)\) kann das modulierte Signal in einem gewünschten Frequenzbereich übertragen werden. -Der ursprünglich Frequenzbereich des Nachrichtensignal \(m(t)\) erstreckt sich typischerweise von 0 HZ bis zur Bandbreite \(B_m\). +Der ursprünglich Frequenzbereich des Nachrichtensignal \(m(t)\) erstreckt sich typischerweise von 0 Hz bis zur Bandbreite \(B_m\). \newline Beim Empfänger wird dann durch Demodulation das ursprüngliche Nachrichtensignal \(m(t)\) so originalgetreu wie möglich zurückgewonnen. \newline -- cgit v1.2.1 From a01266d1d515ffbb6d5a965cea415b65b092a64b Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 19 Jul 2022 18:01:20 +0200 Subject: not finished --- buch/papers/fm/01_AM-FM.tex | 12 ++++++++++-- buch/papers/fm/main.tex | 5 +++-- 2 files changed, 13 insertions(+), 4 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index b9d6167..ef55d55 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -7,12 +7,20 @@ \rhead{AM- FM} Das sinusförmige Trägersignal hat die übliche Form: -\(x_c(t) = A_c \cdot cos(\omega_ct+\varphi)\). +\(x_c(t) = A_c \cdot cos(\omega_c(t)+\varphi)\). Wobei die konstanten Amplitude \(A_c\) und Phase \(\varphi\) vom Nachrichtensignal \(m(t)\) verändert wird. Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. \newblockpunct - +Jedoch ist das für die Vilfalt der Modulationsarten keine Einschrenkung. +Ein Nachrichtensignal kann auch über die Momentanfrequenz (instantenous frequency) \(\omega_i\) eines trägers verändert werden. +Mathematisch wird dann daraus +\[ + \omega_i = \omega_c + \frac{d \varphi(t)}{dt} +\] +mit der Ableitung der Phase. +\newline +\newline TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 56a7ac5..fcf4d1a 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -1,15 +1,16 @@ +% !TeX root = ../../buch.tex % % main.tex -- Paper zum Thema % % (c) 2020 Hochschule Rapperswil % -\chapter{FM Bessel\label{chapter:fm}} +\chapter{FM Bessel\label{chapter:fm}} \lhead{FM} \begin{refsection} \chapterauthor{Joshua Bär} -%$\with$ + Die Frequenzmodulation ist eine Modulation die man auch schon im alten Radio findet. Falls du dich an die Zeit erinnerst, konnte man zwischen \textit{FM-AM} Umschalten, dies bedeutete so viel wie: \textit{F}requenz-\textit{M}odulation und \textit{A}mplituden-\textit{M}odulation. -- cgit v1.2.1 From 02fad480aad27d6d2fa1192eeab5c6654557b884 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 26 Jul 2022 09:31:35 +0200 Subject: svae between --- buch/papers/fm/01_AM-FM.tex | 37 ++++++++++++++++++++++--------------- buch/papers/fm/main.tex | 2 +- buch/papers/fm/references.bib | 11 +++++++++++ 3 files changed, 34 insertions(+), 16 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index ef55d55..2267d39 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -7,30 +7,37 @@ \rhead{AM- FM} Das sinusförmige Trägersignal hat die übliche Form: -\(x_c(t) = A_c \cdot cos(\omega_c(t)+\varphi)\). +\(x_c(t) = A_c \cdot \cos(\omega_c(t)+\varphi)\). Wobei die konstanten Amplitude \(A_c\) und Phase \(\varphi\) vom Nachrichtensignal \(m(t)\) verändert wird. Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. \newblockpunct -Jedoch ist das für die Vilfalt der Modulationsarten keine Einschrenkung. +Jedoch ist das für die Vielfalt der Modulationsarten keine Einschrenkung. Ein Nachrichtensignal kann auch über die Momentanfrequenz (instantenous frequency) \(\omega_i\) eines trägers verändert werden. Mathematisch wird dann daraus \[ \omega_i = \omega_c + \frac{d \varphi(t)}{dt} \] -mit der Ableitung der Phase. +mit der Ableitung der Phase\cite{fm:NAT}. +Mit diesen drei parameter ergeben sich auch drei modulationsarten, die Amplitudenmodulation welche \(A_c\) benutzt, +die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): \newline \newline -TODO: -Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] - - - -%Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -%nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{fm:bibtex}. -%At vero eos et accusam et justo duo dolores et ea rebum. -%Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -%dolor sit amet. - +To do: Bilder jeder Modulationsart +\subsection{AM - Amplitudenmodulation} +Das Ziel ist FM zu verstehen doch dazu wird zuerst AM erklärt welches einwenig einfacher zu verstehen ist und erst dann übertragen wir die Ideeen in FM. +Nun zur Amplitudenmodulation verwenden wir das bevorzugte Trägersignal +\[ + x_c(t) = A_c \cdot \cos(\omega_ct). +\] +Dies bringt den grossen Vorteil das, dass modulierend Signal sämtliche Anteile im Frequenzspektrum inanspruch nimmt +und das Trägersignal nur zwei komplexe Schwingungen besitzt. +Dies sieht man besonders in der Eulerischen Formel +\[ + x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. +\] +Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. +\newline +TODO: +Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[\cos( \cos x)\] diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index fcf4d1a..6af3386 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -27,7 +27,7 @@ welches Digital einfach umzusetzten ist, genauso als Trägersignal genutzt werden kann. Zuerst wird erklärt was \textit{FM-AM} ist, danach wie sich diese im Frequenzspektrum verhalten. Erst dann erklär ich dir wie die Besselfunktion mit der Frequenzmodulation( acro?) zusammenhängt. -Nun zur Modulation im nächsten Abschnitt. +Nun zur Modulation im nächsten Abschnitt.\cite{fm:NAT} \input{papers/fm/01_AM-FM.tex} \input{papers/fm/02_frequenzyspectrum.tex} diff --git a/buch/papers/fm/references.bib b/buch/papers/fm/references.bib index 76eb265..21b910b 100644 --- a/buch/papers/fm/references.bib +++ b/buch/papers/fm/references.bib @@ -23,6 +23,17 @@ volume = {2} } +@book{fm:NAT, + title = {Nachrichtentechnik 1 + 2}, + author = {Thomas Kneubühler}, + publisher = {None}, + year = {2021}, + isbn = {}, + inseries = {Script for students}, + volume = {} +} + + @article{fm:mendezmueller, author = { Tabea Méndez and Andreas Müller }, title = { Noncommutative harmonic analysis and image registration }, -- cgit v1.2.1 From a5b1d13fd6d9d5df3d7289093e57cf67ae5cb81c Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 26 Jul 2022 15:04:22 +0200 Subject: Kapitel TODOs --- buch/papers/fm/01_AM-FM.tex | 4 +++ buch/papers/fm/02_frequenzyspectrum.tex | 2 ++ buch/papers/fm/03_bessel.tex | 24 ++++++---------- buch/papers/fm/04_fazit.tex | 32 ++------------------- buch/papers/fm/FM presentation/A2-14.pdf | Bin 0 -> 259673 bytes buch/papers/fm/FM presentation/FM_presentation.pdf | Bin 0 -> 357597 bytes ...quency modulation (FM) and Bessel functions.pdf | Bin 0 -> 159598 bytes ...l2022_Book_H\303\266hereMathematikImAlltag.pdf" | Bin 0 -> 4118379 bytes 8 files changed, 17 insertions(+), 45 deletions(-) create mode 100644 buch/papers/fm/FM presentation/A2-14.pdf create mode 100644 buch/papers/fm/FM presentation/FM_presentation.pdf create mode 100644 buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf create mode 100644 "buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index 2267d39..163c792 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -38,6 +38,10 @@ Dies sieht man besonders in der Eulerischen Formel x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. \] Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. +Nun wird der parameter \(A_c\) durch das Moduierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. +\newline \newline TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[\cos( \cos x)\] +so wird beschrieben das daraus eigentlich \(x_c(t) = A_c \cdot \cos(\omega_i)\) wird und somit \(x_c(t) = A_c \cdot \cos(\omega_c + \frac{d \varphi(t)}{dt})\). +Da \(\sin \) abgeleitet \(\cos \) ergibt, so wird aus dem \(m(t)\) ein \( \frac{d \varphi(t)}{dt}\) in der momentan frequenz. \[ \Rightarrow \cos( \cos x) \] diff --git a/buch/papers/fm/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex index 1c6044d..80e1c65 100644 --- a/buch/papers/fm/02_frequenzyspectrum.tex +++ b/buch/papers/fm/02_frequenzyspectrum.tex @@ -7,7 +7,9 @@ \label{fm:section:teil1}} \rhead{Problemstellung} +TODO Hier Beschreiben ich das Frequenzspektrum und wie AM und FM aussehen und generiert werden. +Somit auch die Herleitung des Frequenzspektrum. %Sed ut perspiciatis unde omnis iste natus error sit voluptatem %accusantium doloremque laudantium, totam rem aperiam, eaque ipsa %quae ab illo inventore veritatis et quasi architecto beatae vitae diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index fdaa0d1..aed084e 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -7,22 +7,16 @@ \label{fm:section:teil2}} \rhead{Teil 2} + +TODO Hier wird beschrieben wie die Bessel Funktion der FM im Frequenzspektrum hilft, wieso diese gebrauch wird und ihre Vorteile. -%Sed ut perspiciatis unde omnis iste natus error sit voluptatem -%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -%quae ab illo inventore veritatis et quasi architecto beatae vitae -%dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -%aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -%eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -%est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -%velit, sed quia non numquam eius modi tempora incidunt ut labore -%et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -%veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -%nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -%reprehenderit qui in ea voluptate velit esse quam nihil molestiae -%consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -%pariatur? -% +\begin{itemize} + \item Zuerest einmal die Herleitung von FM zu der Besselfunktion + \item Im Frequenzspektrum darstellen mit Farben, ersichtlich machen. + \item Parameter tuing der Trägerfrequenz, Modulierende frequenz und Beta. +\end{itemize} + + %\subsection{De finibus bonorum et malorum %\label{fm:subsection:bonorum}} diff --git a/buch/papers/fm/04_fazit.tex b/buch/papers/fm/04_fazit.tex index 8c6c002..8d5eca4 100644 --- a/buch/papers/fm/04_fazit.tex +++ b/buch/papers/fm/04_fazit.tex @@ -6,35 +6,7 @@ \section{Fazit \label{fm:section:fazit}} \rhead{Zusamenfassend} -%Sed ut perspiciatis unde omnis iste natus error sit voluptatem -%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -%quae ab illo inventore veritatis et quasi architecto beatae vitae -%dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -%aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -%eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -%est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -%velit, sed quia non numquam eius modi tempora incidunt ut labore -%et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -%veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -%nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -%reprehenderit qui in ea voluptate velit esse quam nihil molestiae -%consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -%pariatur? -% -%\subsection{De finibus bonorum et malorum -%\label{fm:subsection:malorum}} -%At vero eos et accusamus et iusto odio dignissimos ducimus qui -%blanditiis praesentium voluptatum deleniti atque corrupti quos -%dolores et quas molestias excepturi sint occaecati cupiditate non -%provident, similique sunt in culpa qui officia deserunt mollitia -%animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -%est et expedita distinctio. Nam libero tempore, cum soluta nobis -%est eligendi optio cumque nihil impedit quo minus id quod maxime -%placeat facere possimus, omnis voluptas assumenda est, omnis dolor -%repellendus. Temporibus autem quibusdam et aut officiis debitis aut -%rerum necessitatibus saepe eveniet ut et voluptates repudiandae -%sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -%sapiente delectus, ut aut reiciendis voluptatibus maiores alias -%consequatur aut perferendis doloribus asperiores repellat. + +TODO Anwendungen erklären und Sinn des Ganzen. diff --git a/buch/papers/fm/FM presentation/A2-14.pdf b/buch/papers/fm/FM presentation/A2-14.pdf new file mode 100644 index 0000000..7348cca Binary files /dev/null and b/buch/papers/fm/FM presentation/A2-14.pdf differ diff --git a/buch/papers/fm/FM presentation/FM_presentation.pdf b/buch/papers/fm/FM presentation/FM_presentation.pdf new file mode 100644 index 0000000..496e35e Binary files /dev/null and b/buch/papers/fm/FM presentation/FM_presentation.pdf differ diff --git a/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf new file mode 100644 index 0000000..a6e701c Binary files /dev/null and b/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel 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Ostschweizer Fachhochschule} + \date{16.5.2022} + \subject{Mathematisches Seminar - Spezielle Funktionen} + %\setbeamercovered{transparent} + \setbeamercovered{invisible} + \setbeamertemplate{navigation symbols}{} + \begin{frame}[plain] + \maketitle + \end{frame} +%------------------------------------------------------------------------------- +\section{Einführung} + \begin{frame} + \frametitle{Frequenzmodulation} + + \visible<1->{ + \begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt)) + \end{equation}} + + \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}} + \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}} + \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}} + + + \end{frame} +%------------------------------------------------------------------------------- +\section{Proof} +\begin{frame} + \frametitle{Bessel} + + \visible<1->{\begin{align} + \cos(\beta\sin\varphi) + &= + J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + \sin(\beta\sin\varphi) + &= + J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + J_{-n}(\beta) &= (-1)^n J_n(\beta) + \end{align}} + \visible<2->{\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \end{align}} +\end{frame} + +%------------------------------------------------------------------------------- +\begin{frame} + \frametitle{Prof->Done} + \begin{align} + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) + \end{align} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \begin{figure} + \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}} + \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}} + \end{figure} + \end{frame} +%------------------------------------------------------------------------------- +\section{Input Parameter} + \begin{frame} + \frametitle{Träger-Frequenz Parameter} + \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} + \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}} + \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}} + \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}} + \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}} + \end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Modulations-Frequenz Parameter} +\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} +\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}} +\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}} +\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}} +\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}} +\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}} +\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Beta Parameter} + \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t)\end{equation}} + \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}} + \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}} + \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}} + \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}} + \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}} + \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}} + \only<7>{\includegraphics[scale=0.7]{images/bessel.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} + \includegraphics[scale=0.5]{images/beta_1.png} + \includegraphics[scale=0.5]{images/bessel.png} +\end{frame} +\end{document} diff --git a/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf deleted file mode 100644 index a6e701c..0000000 Binary files a/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf and /dev/null differ diff --git a/buch/papers/fm/FM presentation/README.txt b/buch/papers/fm/FM presentation/README.txt new file mode 100644 index 0000000..65f390d --- /dev/null +++ b/buch/papers/fm/FM presentation/README.txt @@ -0,0 +1 @@ +Dies ist die Presentation des FM - Bessel \ No newline at end of file diff --git "a/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" "b/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" deleted file mode 100644 index 2a0bddd..0000000 Binary files "a/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" and 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a/buch/papers/fm/RS presentation/FM_presentation.pdf and /dev/null differ diff --git a/buch/papers/fm/RS presentation/FM_presentation.tex b/buch/papers/fm/RS presentation/FM_presentation.tex deleted file mode 100644 index 92cb501..0000000 --- a/buch/papers/fm/RS presentation/FM_presentation.tex +++ /dev/null @@ -1,125 +0,0 @@ -%% !TeX root = RS.tex - -\documentclass[11pt,aspectratio=169]{beamer} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{lmodern} -\usepackage[ngerman]{babel} -\usepackage{tikz} -\usetheme{Hannover} - -\begin{document} - \author{Joshua Bär} - \title{FM - Bessel} - \subtitle{} - \logo{} - \institute{OST Ostschweizer Fachhochschule} - \date{16.5.2022} - \subject{Mathematisches Seminar} - %\setbeamercovered{transparent} - \setbeamercovered{invisible} - \setbeamertemplate{navigation symbols}{} - \begin{frame}[plain] - \maketitle - \end{frame} -%------------------------------------------------------------------------------- -\section{Einführung} - \begin{frame} - \frametitle{Frequenzmodulation} - - \visible<1->{ - \begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt)) - \end{equation}} - - \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}} - \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}} - \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}} - - - \end{frame} -%------------------------------------------------------------------------------- -\section{Proof} -\begin{frame} - \frametitle{Bessel} - - \visible<1->{\begin{align} - \cos(\beta\sin\varphi) - &= - J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) - \\ - \sin(\beta\sin\varphi) - &= - J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) - \\ - J_{-n}(\beta) &= (-1)^n J_n(\beta) - \end{align}} - \visible<2->{\begin{align} - \cos(A + B) - &= - \cos(A)\cos(B)-\sin(A)\sin(B) - \\ - 2\cos (A)\cos (B) - &= - \cos(A-B)+\cos(A+B) - \\ - 2\sin(A)\sin(B) - &= - \cos(A-B)-\cos(A+B) - \end{align}} -\end{frame} - -%------------------------------------------------------------------------------- -\begin{frame} - \frametitle{Prof->Done} - \begin{align} - \cos(\omega_ct+\beta\sin(\omega_mt)) - &= - \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) - \end{align} - \end{frame} -%------------------------------------------------------------------------------- - \begin{frame} - \begin{figure} - \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}} - \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}} - \end{figure} - \end{frame} -%------------------------------------------------------------------------------- -\section{Input Parameter} - \begin{frame} - \frametitle{Träger-Frequenz Parameter} - \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} - \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}} - \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}} - \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}} - \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}} - \end{frame} -%------------------------------------------------------------------------------- -\begin{frame} -\frametitle{Modulations-Frequenz Parameter} -\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} -\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}} -\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}} -\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}} -\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}} -\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}} -\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}} -\end{frame} -%------------------------------------------------------------------------------- -\begin{frame} -\frametitle{Beta Parameter} - \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t)\end{equation}} - \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}} - \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}} - \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}} - \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}} - \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}} - \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}} - \only<7>{\includegraphics[scale=0.7]{images/bessel.png}} -\end{frame} -%------------------------------------------------------------------------------- -\begin{frame} - \includegraphics[scale=0.5]{images/beta_1.png} - \includegraphics[scale=0.5]{images/bessel.png} -\end{frame} -\end{document} diff --git a/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf deleted file mode 100644 index a6e701c..0000000 Binary files a/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf and /dev/null differ diff --git a/buch/papers/fm/RS presentation/README.txt b/buch/papers/fm/RS presentation/README.txt deleted file mode 100644 index 4d0620f..0000000 --- a/buch/papers/fm/RS presentation/README.txt +++ /dev/null @@ -1 +0,0 @@ -Dies ist die Presentation des Reed-Solomon-Code \ No newline at end of file diff --git a/buch/papers/fm/RS presentation/RS.tex b/buch/papers/fm/RS presentation/RS.tex deleted file mode 100644 index 8a67619..0000000 --- a/buch/papers/fm/RS presentation/RS.tex +++ /dev/null @@ -1,123 +0,0 @@ -%% !TeX root = RS.tex - -\documentclass[11pt,aspectratio=169]{beamer} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{lmodern} -\usepackage[ngerman]{babel} -\usepackage{tikz} -\usetheme{Hannover} - -\begin{document} - \author{Joshua Bär} - \title{FM - Bessel} - \subtitle{} - \logo{} - \institute{OST Ostschweizer Fachhochschule} - \date{16.5.2022} - \subject{Mathematisches Seminar- Spezielle Funktionen} - %\setbeamercovered{transparent} - \setbeamercovered{invisible} - \setbeamertemplate{navigation symbols}{} - \begin{frame}[plain] - \maketitle - \end{frame} -%------------------------------------------------------------------------------- -\section{Einführung} - \begin{frame} - \frametitle{Frequenzmodulation} - - \visible<1->{\begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt))\end{equation}} - - \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}} - \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}} - \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}} - - - \end{frame} -%------------------------------------------------------------------------------- -\section{Proof} -\begin{frame} - \frametitle{Bessel} - - \visible<1->{\begin{align} - \cos(\beta\sin\varphi) - &= - J_0(\beat) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) - \\ - \sin(\beta\sin\varphi) - &= - J_0(\beat) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) - \\ - J_{-n}(\beat) &= (-1)^n J_n(\beta) - \end{align}} - \visible<2->{\begin{align} - \cos(A + B) - &= - \cos(A)\cos(B)-\sin(A)\sin(B) - \\ - 2\cos (A)\cos (B) - &= - \cos(A-B)+\cos(A+B) - \\ - 2\sin(A)\sin(B) - &= - \cos(A-B)-\cos(A+B) - \end{align}} -\end{frame} - -%------------------------------------------------------------------------------- -\begin{frame} - \frametitle{Prof->Done} - \begin{align} - \cos(\omega_ct+\beta\sin(\omega_mt)) - &= - \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omgea_m)t) - \end{align} - \end{frame} -%------------------------------------------------------------------------------- - \begin{frame} - \begin{figure} - \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}} - \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}} - \end{figure} - \end{frame} -%------------------------------------------------------------------------------- -\section{Input Parameter} - \begin{frame} - \frametitle{Träger-Frequenz Parameter} - \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} - \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}} - \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}} - \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}} - \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}} - \end{frame} -%------------------------------------------------------------------------------- -\begin{frame} -\frametitle{Modulations-Frequenz Parameter} -\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} -\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}} -\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}} -\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}} -\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}} -\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}} -\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}} -\end{frame} -%------------------------------------------------------------------------------- -\begin{frame} -\frametitle{Beta Parameter} - \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omgea_m)t)\end{equation}} - \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}} - \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}} - \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}} - \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}} - \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}} - \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}} - \only<7>{\includegraphics[scale=0.7]{images/bessel.png}} -\end{frame} -%------------------------------------------------------------------------------- -\begin{frame} - \includegraphics[scale=0.5]{images/beta_1.png} - \includegraphics[scale=0.5]{images/bessel.png} -\end{frame} -\end{document} diff --git a/buch/papers/fm/RS presentation/images/100HZ.png b/buch/papers/fm/RS presentation/images/100HZ.png deleted file mode 100644 index 371b9bf..0000000 Binary files a/buch/papers/fm/RS presentation/images/100HZ.png and 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presentation/images/fm_7Hz.png and /dev/null differ diff --git a/buch/papers/fm/RS presentation/images/fm_frequenz.png b/buch/papers/fm/RS presentation/images/fm_frequenz.png deleted file mode 100644 index 26bfd86..0000000 Binary files a/buch/papers/fm/RS presentation/images/fm_frequenz.png and /dev/null differ diff --git a/buch/papers/fm/RS presentation/images/fm_in_time.png b/buch/papers/fm/RS presentation/images/fm_in_time.png deleted file mode 100644 index 068eafc..0000000 Binary files a/buch/papers/fm/RS presentation/images/fm_in_time.png and /dev/null differ -- cgit v1.2.1 From e7f4d8d568bf62c76f4bf0ffdc0fe009134c184d Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Wed, 27 Jul 2022 17:45:10 +0200 Subject: Herleitung Kapitel Bessel --- buch/papers/fm/03_bessel.tex | 123 +++++++++++++++++++++++++++++++++++++++++-- buch/papers/fm/Makefile | 8 +-- buch/papers/fm/packages.tex | 2 +- 3 files changed, 126 insertions(+), 7 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index aed084e..7a0e20e 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -4,9 +4,126 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{FM und Besselfunktion -\label{fm:section:teil2}} -\rhead{Teil 2} - +\label{fm:section:proof}} +\rhead{Herleitung} +Die momentane Trägerkreisfrequenz \(\omega_i\) wie schon in (ref) beschrieben ist, bringt die Vorigen Kapittel beschreiben. (Ableitung \(\frac{d \varphi(t)}{dt}\) mit sich). +Diese wiederum kann durch \(\beta\sin(\omega_mt)\) ausgedrückt werden, wobei es das Modulierende Signal \(m(t)\) ist. +Somit haben wir unser \(x_c\) welches +\[ +\cos(\omega_c t+\beta\sin(\omega_mt)) +\] +ist. +\subsection{Herleitung} +Das Ziel ist es Unser moduliertes Signal mit der Besselfunktion so auszudrücken: +\begin{align} + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) + \label{fm:eq:proof} +\end{align} +Doch dazu brauchen wir die Hilfe der Additionsthoerme +\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \label{fm:eq:addth1} + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \label{fm:eq:addth2} + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \label{fm:eq:addth3} +\end{align} +und die drei Besselfunktions indentitäten, +\begin{align} + \cos(\beta\sin\phi) + &= + J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\phi) + \label{fm:eq:besselid1} + \\ + \sin(\beta\sin\phi) + &= + J_0(\beta) + 2\sum_{k=1}^\infty J_{2k+1}(\beta) \cos((2k+1)\phi) + \label{fm:eq:besselid2} + \\ + J_{-n}(\beta) &= (-1)^n J_n(\beta) + \label{fm:eq:besselid3} +\end{align} +welche man im Kapitel (ref), ref, ref findet. +\newline +Mit dem \refname{fm:eq:addth1} wird aus dem modulierten Signal +\[ +\cos(\omega_c t + \beta\sin(\omega_mt)) +\] +das Signal +\[ + \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_c)\sin(\beta\sin(\omega_m t)). + \label{fm:eq:start} +\] +Zu beginn wird der erste Teil +\[ + \cos(\omega_c)\cos(\beta\sin(\omega_mt)) +\] +mit hilfe der Bessel indentität \ref{fm:eq:besselid1} zum +\[ + J_0(\beta)\cos(\omega_c) + \sum_{k=1}^\infty J_{2k}(\beta) 2\cos(\omega_c t)\cos(2k\omega_m t) +\] +\newline +TODO 2 und \(\cos( )\) in lime. +wobei mit dem \colorbox{lime}{Additionstheorem} \ref{fm:eq:addth2} zum +\[ + J_0(\beta)\dot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} +\] +wird. +Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term +\[ + \sum_{n\, gerade} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) + \label{fm:eq:gerade} +\] +\newline +nun zum zweiten Teil des Term \ref{fm:eq:start} +\[ + \sin(\omega_c)\sin(\beta\sin(\omega_m t)). +\] +Dieser wird mit der \ref{fm:eq:besselid2} Bessel indentität zu +\[ + J_0(\beta) \dot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) 2\sin(\omega_c t)\cos((2k+1)\omega_m t). +\] +Auch hier wird ein Additionstheorem \ref{fm:eq:addth3} gebraucht um aus dem Sumanden diesen Term +\[ + J_0(\beta) \dot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{Teil1} - \cos((\omega_c+(2k+1)\omega_m) t) \} +\]zu gewinnen. +Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. +Zusätzlich dabei noch die letzte Bessel indentität \ref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1 J_n(\beta)\). +Somit wird Teil1 zum negativen Term und die Summe vereinfacht sich zu +\[ + \sum_{n\, ungerade} -1 J_{n}(\beta) \cos((\omega_c + n\omega_m) t). + \label{fm:eq:ungerade} +\] +Substituiert man nun noch \(n \text{mit} -n \) so fällt das \(-1\) weg. +Beide Teile \ref{fm:eq:gerade} Gerade und \ref{fm:eq:ungerade} Ungerade ergeben zusammen +\[ + \cos(\omega_ct+\beta\sin(\omega_mt)) + = + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t). +\] +Somit ist \ref{fm:eq:proof} bewiesen. +\newpage +\subsection{Bessel und Frequenzspektrum} +Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. +\begin{figure} + \centering + \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} + \caption{Bessle Funktion \(J_{k}(\beta)\)} + \label{fig:bessel} +\end{figure} +TODO Grafik einfügen, +\newline +Nun einmal das Modulierte FM signal im Frequenzspektrum mit den einzelen Summen dargestellt TODO Hier wird beschrieben wie die Bessel Funktion der FM im Frequenzspektrum hilft, wieso diese gebrauch wird und ihre Vorteile. diff --git a/buch/papers/fm/Makefile b/buch/papers/fm/Makefile index c84963f..aee954f 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -16,15 +16,17 @@ SOURCES := \ #FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) -#.PHONY: images -#images: $(FIGURES) +all: images standalone + +.PHONY: images +images: $(FIGURES) #figures/%.pdf: tikz/%.tex # mkdir -p figures # pdflatex --output-directory=figures $< .PHONY: standalone -standalone: standalone.tex $(SOURCES) #$(FIGURES) +standalone: standalone.tex $(SOURCES) $(FIGURES) mkdir -p standalone cd ../..; \ pdflatex \ diff --git a/buch/papers/fm/packages.tex b/buch/papers/fm/packages.tex index 4cba2b6..f0ca8cc 100644 --- a/buch/papers/fm/packages.tex +++ b/buch/papers/fm/packages.tex @@ -7,4 +7,4 @@ % if your paper needs special packages, add package commands as in the % following example %\usepackage{packagename} - +\usepackage{xcolor} -- cgit v1.2.1 From 166573a69495056cfeaf76624373a74326374170 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Wed, 27 Jul 2022 19:28:06 +0200 Subject: Reorganized Kapitel --- buch/papers/fm/00_modulation.tex | 28 ++++++++++++++++ buch/papers/fm/01_AM-FM.tex | 47 --------------------------- buch/papers/fm/01_AM.tex | 29 +++++++++++++++++ buch/papers/fm/02_FM.tex | 56 ++++++++++++++++++++++++++++++++ buch/papers/fm/02_frequenzyspectrum.tex | 57 --------------------------------- buch/papers/fm/Makefile | 5 +-- buch/papers/fm/Makefile.inc | 5 +-- buch/papers/fm/main.tex | 6 ++-- 8 files changed, 123 insertions(+), 110 deletions(-) create mode 100644 buch/papers/fm/00_modulation.tex delete mode 100644 buch/papers/fm/01_AM-FM.tex create mode 100644 buch/papers/fm/01_AM.tex create mode 100644 buch/papers/fm/02_FM.tex delete mode 100644 buch/papers/fm/02_frequenzyspectrum.tex (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/00_modulation.tex b/buch/papers/fm/00_modulation.tex new file mode 100644 index 0000000..dc99b40 --- /dev/null +++ b/buch/papers/fm/00_modulation.tex @@ -0,0 +1,28 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\subsection{Modulationsarten\label{fm:section:modulation}} + +Das sinusförmige Trägersignal hat die übliche Form: +\(x_c(t) = A_c \cdot \cos(\omega_c(t)+\varphi)\). +Wobei die konstanten Amplitude \(A_c\) und Phase \(\varphi\) vom Nachrichtensignal \(m(t)\) verändert wird. +Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), +steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. +\newblockpunct +Jedoch ist das für die Vielfalt der Modulationsarten keine Einschrenkung. +Ein Nachrichtensignal kann auch über die Momentanfrequenz (instantenous frequency) \(\omega_i\) eines trägers verändert werden. +Mathematisch wird dann daraus +\[ + \omega_i = \omega_c + \frac{d \varphi(t)}{dt} +\] +mit der Ableitung der Phase\cite{fm:NAT}. +Mit diesen drei parameter ergeben sich auch drei modulationsarten, die Amplitudenmodulation welche \(A_c\) benutzt, +die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): +\newline +\newline +To do: Bilder jeder Modulationsart + + + diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex deleted file mode 100644 index 163c792..0000000 --- a/buch/papers/fm/01_AM-FM.tex +++ /dev/null @@ -1,47 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{AM - FM\label{fm:section:teil0}} -\rhead{AM- FM} - -Das sinusförmige Trägersignal hat die übliche Form: -\(x_c(t) = A_c \cdot \cos(\omega_c(t)+\varphi)\). -Wobei die konstanten Amplitude \(A_c\) und Phase \(\varphi\) vom Nachrichtensignal \(m(t)\) verändert wird. -Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), -steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. -\newblockpunct -Jedoch ist das für die Vielfalt der Modulationsarten keine Einschrenkung. -Ein Nachrichtensignal kann auch über die Momentanfrequenz (instantenous frequency) \(\omega_i\) eines trägers verändert werden. -Mathematisch wird dann daraus -\[ - \omega_i = \omega_c + \frac{d \varphi(t)}{dt} -\] -mit der Ableitung der Phase\cite{fm:NAT}. -Mit diesen drei parameter ergeben sich auch drei modulationsarten, die Amplitudenmodulation welche \(A_c\) benutzt, -die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): -\newline -\newline -To do: Bilder jeder Modulationsart - -\subsection{AM - Amplitudenmodulation} -Das Ziel ist FM zu verstehen doch dazu wird zuerst AM erklärt welches einwenig einfacher zu verstehen ist und erst dann übertragen wir die Ideeen in FM. -Nun zur Amplitudenmodulation verwenden wir das bevorzugte Trägersignal -\[ - x_c(t) = A_c \cdot \cos(\omega_ct). -\] -Dies bringt den grossen Vorteil das, dass modulierend Signal sämtliche Anteile im Frequenzspektrum inanspruch nimmt -und das Trägersignal nur zwei komplexe Schwingungen besitzt. -Dies sieht man besonders in der Eulerischen Formel -\[ - x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. -\] -Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. -Nun wird der parameter \(A_c\) durch das Moduierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. -\newline -\newline -TODO: -Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[\cos( \cos x)\] -so wird beschrieben das daraus eigentlich \(x_c(t) = A_c \cdot \cos(\omega_i)\) wird und somit \(x_c(t) = A_c \cdot \cos(\omega_c + \frac{d \varphi(t)}{dt})\). -Da \(\sin \) abgeleitet \(\cos \) ergibt, so wird aus dem \(m(t)\) ein \( \frac{d \varphi(t)}{dt}\) in der momentan frequenz. \[ \Rightarrow \cos( \cos x) \] diff --git a/buch/papers/fm/01_AM.tex b/buch/papers/fm/01_AM.tex new file mode 100644 index 0000000..921fcf2 --- /dev/null +++ b/buch/papers/fm/01_AM.tex @@ -0,0 +1,29 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Amplitudenmodulation\label{fm:section:teil0}} +\rhead{AM} + +Das Ziel ist FM zu verstehen doch dazu wird zuerst AM erklärt welches einwenig einfacher zu verstehen ist und erst dann übertragen wir die Ideen in FM. +Nun zur Amplitudenmodulation verwenden wir das bevorzugte Trägersignal +\[ + x_c(t) = A_c \cdot \cos(\omega_ct). +\] +Dies bringt den grossen Vorteil das, dass modulierend Signal sämtliche Anteile im Frequenzspektrum inanspruch nimmt +und das Trägersignal nur zwei komplexe Schwingungen besitzt. +Dies sieht man besonders in der Eulerischen Formel +\[ + x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. +\] +Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. +Nun wird der parameter \(A_c\) durch das Moduierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. +\newline +\newline +TODO: +Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[\cos( \cos x)\] +so wird beschrieben das daraus eigentlich \(x_c(t) = A_c \cdot \cos(\omega_i)\) wird und somit \(x_c(t) = A_c \cdot \cos(\omega_c + \frac{d \varphi(t)}{dt})\). +Da \(\sin \) abgeleitet \(\cos \) ergibt, so wird aus dem \(m(t)\) ein \( \frac{d \varphi(t)}{dt}\) in der momentan frequenz. \[ \Rightarrow \cos( \cos x) \] + +\subsection{Frequenzspektrum} \ No newline at end of file diff --git a/buch/papers/fm/02_FM.tex b/buch/papers/fm/02_FM.tex new file mode 100644 index 0000000..fedfaaa --- /dev/null +++ b/buch/papers/fm/02_FM.tex @@ -0,0 +1,56 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{FM +\label{fm:section:teil1}} +\rhead{FM} +\subsection{Frequenzspektrum} +TODO +Hier Beschreiben ich FM und FM im Frequenzspektrum. +%Sed ut perspiciatis unde omnis iste natus error sit voluptatem +%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +%quae ab illo inventore veritatis et quasi architecto beatae vitae +%dicta sunt explicabo. +%Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit +%aut fugit, sed quia consequuntur magni dolores eos qui ratione +%voluptatem sequi nesciunt +%\begin{equation} +%\int_a^b x^2\, dx +%= +%\left[ \frac13 x^3 \right]_a^b +%= +%\frac{b^3-a^3}3. +%\label{fm:equation1} +%\end{equation} +%Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, +%consectetur, adipisci velit, sed quia non numquam eius modi tempora +%incidunt ut labore et dolore magnam aliquam quaerat voluptatem. +% +%Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis +%suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? +%Quis autem vel eum iure reprehenderit qui in ea voluptate velit +%esse quam nihil molestiae consequatur, vel illum qui dolorem eum +%fugiat quo voluptas nulla pariatur? +% +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:finibus}} +%At vero eos et accusamus et iusto odio dignissimos ducimus qui +%blanditiis praesentium voluptatum deleniti atque corrupti quos +%dolores et quas molestias excepturi sint occaecati cupiditate non +%provident, similique sunt in culpa qui officia deserunt mollitia +%animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. +% +%Et harum quidem rerum facilis est et expedita distinctio +%\ref{fm:section:loesung}. +%Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil +%impedit quo minus id quod maxime placeat facere possimus, omnis +%voluptas assumenda est, omnis dolor repellendus +%\ref{fm:section:folgerung}. +%Temporibus autem quibusdam et aut officiis debitis aut rerum +%necessitatibus saepe eveniet ut et voluptates repudiandae sint et +%molestiae non recusandae. +%Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis +%voluptatibus maiores alias consequatur aut perferendis doloribus +%asperiores repellat. diff --git a/buch/papers/fm/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex deleted file mode 100644 index 80e1c65..0000000 --- a/buch/papers/fm/02_frequenzyspectrum.tex +++ /dev/null @@ -1,57 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{AM-FM im Frequenzspektrum -\label{fm:section:teil1}} -\rhead{Problemstellung} - -TODO -Hier Beschreiben ich das Frequenzspektrum und wie AM und FM aussehen und generiert werden. -Somit auch die Herleitung des Frequenzspektrum. -%Sed ut perspiciatis unde omnis iste natus error sit voluptatem -%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -%quae ab illo inventore veritatis et quasi architecto beatae vitae -%dicta sunt explicabo. -%Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -%aut fugit, sed quia consequuntur magni dolores eos qui ratione -%voluptatem sequi nesciunt -%\begin{equation} -%\int_a^b x^2\, dx -%= -%\left[ \frac13 x^3 \right]_a^b -%= -%\frac{b^3-a^3}3. -%\label{fm:equation1} -%\end{equation} -%Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -%consectetur, adipisci velit, sed quia non numquam eius modi tempora -%incidunt ut labore et dolore magnam aliquam quaerat voluptatem. -% -%Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -%suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -%Quis autem vel eum iure reprehenderit qui in ea voluptate velit -%esse quam nihil molestiae consequatur, vel illum qui dolorem eum -%fugiat quo voluptas nulla pariatur? -% -%\subsection{De finibus bonorum et malorum -%\label{fm:subsection:finibus}} -%At vero eos et accusamus et iusto odio dignissimos ducimus qui -%blanditiis praesentium voluptatum deleniti atque corrupti quos -%dolores et quas molestias excepturi sint occaecati cupiditate non -%provident, similique sunt in culpa qui officia deserunt mollitia -%animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. -% -%Et harum quidem rerum facilis est et expedita distinctio -%\ref{fm:section:loesung}. -%Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -%impedit quo minus id quod maxime placeat facere possimus, omnis -%voluptas assumenda est, omnis dolor repellendus -%\ref{fm:section:folgerung}. -%Temporibus autem quibusdam et aut officiis debitis aut rerum -%necessitatibus saepe eveniet ut et voluptates repudiandae sint et -%molestiae non recusandae. -%Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -%voluptatibus maiores alias consequatur aut perferendis doloribus -%asperiores repellat. diff --git a/buch/papers/fm/Makefile b/buch/papers/fm/Makefile index aee954f..f30c4a9 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -5,8 +5,9 @@ # SOURCES := \ - 01_AM-FM.tex \ - 02_frequenzyspectrum.tex \ + 00_modulation.tex \ + 01_AM.tex \ + 02_FM.tex \ 03_bessel.tex \ 04_fazit.tex \ main.tex diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index e5cd9f6..b686b98 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,8 +6,9 @@ dependencies-fm = \ papers/fm/packages.tex \ papers/fm/main.tex \ - papers/fm/01_AM-FM.tex \ - papers/fm/02_frequenzyspectrum.tex \ + papers/fm/01_modulation.tex \ + papers/fm/01_AM.tex \ + papers/fm/02_FM.tex \ papers/fm/03_bessel.tex \ papers/fm/04_fazit.tex \ papers/fm/references.bib diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 6af3386..731f56f 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -29,8 +29,10 @@ Zuerst wird erklärt was \textit{FM-AM} ist, danach wie sich diese im Frequenzsp Erst dann erklär ich dir wie die Besselfunktion mit der Frequenzmodulation( acro?) zusammenhängt. Nun zur Modulation im nächsten Abschnitt.\cite{fm:NAT} -\input{papers/fm/01_AM-FM.tex} -\input{papers/fm/02_frequenzyspectrum.tex} + +\input{papers/fm/00_modulation.tex} +\input{papers/fm/01_AM.tex} +\input{papers/fm/02_FM.tex} \input{papers/fm/03_bessel.tex} \input{papers/fm/04_fazit.tex} -- cgit v1.2.1 From 5ab407e87a3912b2a8e0b1698b9cf967c42c268d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 27 Jul 2022 22:00:28 +0200 Subject: comment out bessel.png --- buch/papers/fm/03_bessel.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index 7a0e20e..edb932b 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -117,7 +117,7 @@ Somit ist \ref{fm:eq:proof} bewiesen. Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. \begin{figure} \centering - \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} +% \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} \caption{Bessle Funktion \(J_{k}(\beta)\)} \label{fig:bessel} \end{figure} -- cgit v1.2.1 From b4c0297a9cf2e2bc38fcb9110f7b5c89ae0fe9fa Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Thu, 28 Jul 2022 17:49:24 +0200 Subject: Kapitel bessel unterteilt --- buch/papers/fm/03_bessel.tex | 87 ++++++++++++++++--------- buch/papers/fm/Python animation/Bessel-FM.ipynb | 26 ++++---- 2 files changed, 70 insertions(+), 43 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index edb932b..bf485b1 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -13,14 +13,18 @@ Somit haben wir unser \(x_c\) welches \cos(\omega_c t+\beta\sin(\omega_mt)) \] ist. + \subsection{Herleitung} -Das Ziel ist es Unser moduliertes Signal mit der Besselfunktion so auszudrücken: +Das Ziel ist es unser moduliertes Signal mit der Besselfunktion so auszudrücken: \begin{align} + x_c(t) + = \cos(\omega_ct+\beta\sin(\omega_mt)) &= \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) \label{fm:eq:proof} \end{align} +\subsubsection{Hilfsmittel} Doch dazu brauchen wir die Hilfe der Additionsthoerme \begin{align} \cos(A + B) @@ -54,70 +58,89 @@ und die drei Besselfunktions indentitäten, \label{fm:eq:besselid3} \end{align} welche man im Kapitel (ref), ref, ref findet. -\newline -Mit dem \refname{fm:eq:addth1} wird aus dem modulierten Signal -\[ -\cos(\omega_c t + \beta\sin(\omega_mt)) -\] -das Signal + +\subsubsection{Anwenden des Additionstheorem} +Mit dem \eqref{fm:eq:addth1} wird aus dem modulierten Signal \[ + x_c(t) + = + \cos(\omega_c t + \beta\sin(\omega_mt)) + = \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_c)\sin(\beta\sin(\omega_m t)). \label{fm:eq:start} \] -Zu beginn wird der erste Teil +\subsubsection{Cos-Teil} +Zu beginn wird der Cos-Teil \[ \cos(\omega_c)\cos(\beta\sin(\omega_mt)) \] -mit hilfe der Bessel indentität \ref{fm:eq:besselid1} zum -\[ - J_0(\beta)\cos(\omega_c) + \sum_{k=1}^\infty J_{2k}(\beta) 2\cos(\omega_c t)\cos(2k\omega_m t) -\] -\newline -TODO 2 und \(\cos( )\) in lime. -wobei mit dem \colorbox{lime}{Additionstheorem} \ref{fm:eq:addth2} zum +mit hilfe der Bessel indentität \eqref{fm:eq:besselid1} zum +\begin{align*} + \cos(\omega_c t) \cdot [\, J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\omega_m t)\, ] + &=\\ + J_0(\beta)\cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) + \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{Additionstheorem} +\end{align*} +wobei mit dem Additionstheorem \eqref{fm:eq:addth2} \(A = \omega_c t\) und \(B = 2k\omega_m t \) zum \[ - J_0(\beta)\dot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} + J_0(\beta)\cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} \] wird. Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term \[ - \sum_{n\, gerade} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) + \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t), \label{fm:eq:gerade} \] -\newline -nun zum zweiten Teil des Term \ref{fm:eq:start} +dabei gehen nun die Terme von \(-\infty \to \infty\), dabei bleibt n Ganzzahlig. + +\subsubsection{Sin-Teil} +Nun zum zweiten Teil des Term \eqref{fm:eq:start}, den Sin-Teil \[ \sin(\omega_c)\sin(\beta\sin(\omega_m t)). \] -Dieser wird mit der \ref{fm:eq:besselid2} Bessel indentität zu +Dieser wird mit der \eqref{fm:eq:besselid2} Bessel indentität zu +\begin{align*} + \sin(\omega_c t) \cdot [J_0(\beta) \sin(\omega_c t) + 2\sum_{k=1}^\infty J_{2k+1}(\beta) \cos((2k+1)\omega_m t)] + &=\\ + J_0(\beta) \cdot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{Additionstheorem}. +\end{align*} +Auch hier wird ein Additionstheorem \eqref{fm:eq:addth3} gebraucht, dabei ist \(A = \omega_c t\) und \(B = (2k+1)\omega_m t \), +somit wird daraus \[ - J_0(\beta) \dot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) 2\sin(\omega_c t)\cos((2k+1)\omega_m t). -\] -Auch hier wird ein Additionstheorem \ref{fm:eq:addth3} gebraucht um aus dem Sumanden diesen Term -\[ - J_0(\beta) \dot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{Teil1} - \cos((\omega_c+(2k+1)\omega_m) t) \} -\]zu gewinnen. + J_0(\beta) \cdot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{neg.Teil} - \cos((\omega_c+(2k+1)\omega_m) t) \} +\]dieser Term. Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. -Zusätzlich dabei noch die letzte Bessel indentität \ref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1 J_n(\beta)\). -Somit wird Teil1 zum negativen Term und die Summe vereinfacht sich zu +Zusätzlich dabei noch die letzte Bessel indentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). +Somit wird negTeil zum Term \(-\cos((\omega_c+(2k+1)\omega_m) t)\)und die Summe vereinfacht sich zu \[ - \sum_{n\, ungerade} -1 J_{n}(\beta) \cos((\omega_c + n\omega_m) t). + \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t). \label{fm:eq:ungerade} \] Substituiert man nun noch \(n \text{mit} -n \) so fällt das \(-1\) weg. -Beide Teile \ref{fm:eq:gerade} Gerade und \ref{fm:eq:ungerade} Ungerade ergeben zusammen + +\subsubsection{Summe Zusammenführen} +Beide Teile \eqref{fm:eq:gerade} Gerade +\[ + \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) +\]und \eqref{fm:eq:ungerade} Ungerade +\[ + \sum_{n\, \text{ungerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) +\] +ergeben zusammen \[ \cos(\omega_ct+\beta\sin(\omega_mt)) = \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t). \] -Somit ist \ref{fm:eq:proof} bewiesen. +Somit ist \eqref{fm:eq:proof} bewiesen. \newpage + +%---------------------------------------------------------------------------- \subsection{Bessel und Frequenzspektrum} Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. \begin{figure} \centering -% \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} +% \input{./PyPython animation/bessel.pgf} \caption{Bessle Funktion \(J_{k}(\beta)\)} \label{fig:bessel} \end{figure} diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb index bfbb83d..6f099a7 100644 --- a/buch/papers/fm/Python animation/Bessel-FM.ipynb +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 117, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -11,6 +11,9 @@ "from scipy.fft import fft, ifft, fftfreq\n", "import scipy.special as sc\n", "import scipy.fftpack\n", + "import matplotlib as mpl\n", + "# Use the pgf backend (must be set before pyplot imported)\n", + "#mpl.use('pgf')\n", "import matplotlib.pyplot as plt\n", "from matplotlib.widgets import Slider\n", "def fm(beta):\n", @@ -94,12 +97,12 @@ }, { "cell_type": "code", - "execution_count": 122, + "execution_count": 29, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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" ] @@ -119,18 +122,19 @@ ], "source": [ "\n", - "for n in range (-4,4):\n", - " x = np.linspace(0,11,1000)\n", + "for n in range (-2,4):\n", + " x = np.linspace(-11,11,1000)\n", " y = sc.jv(n,x)\n", - " plt.plot(x, y, '-')\n", - "plt.plot([1,1],[sc.jv(0,1),sc.jv(-1,1)],)\n", - "plt.xlim(0,10)\n", + " plt.plot(x, y, '-',label='n='+str(n))\n", + "#plt.plot([1,1],[sc.jv(0,1),sc.jv(-1,1)],)\n", + "plt.xlim(-10,10)\n", "plt.grid(True)\n", - "plt.ylabel('Bessel J_n(b)')\n", - "plt.xlabel('b')\n", + "plt.ylabel('Bessel $J_n(\\\\beta)$')\n", + "plt.xlabel(' $ \\\\beta $ ')\n", "plt.plot(x, y)\n", + "plt.legend()\n", "plt.show()\n", - "\n", + "#plt.savefig('bessel.pgf', format='pgf')\n", "print(sc.jv(0,1))" ] }, -- cgit v1.2.1 From e2b1ed24b607291b6af86ba43c8f6f656a92b476 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Thu, 28 Jul 2022 18:09:00 +0200 Subject: minor cosmetic changes --- buch/papers/fm/03_bessel.tex | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index bf485b1..760cdc4 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -74,16 +74,16 @@ Zu beginn wird der Cos-Teil \[ \cos(\omega_c)\cos(\beta\sin(\omega_mt)) \] -mit hilfe der Bessel indentität \eqref{fm:eq:besselid1} zum +mit hilfe der Besselindentität \eqref{fm:eq:besselid1} zum \begin{align*} - \cos(\omega_c t) \cdot [\, J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\omega_m t)\, ] + \cos(\omega_c t) \cdot \bigg[\, J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos( 2k \omega_m t)\, \bigg] &=\\ J_0(\beta)\cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) - \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{Additionstheorem} + \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{\text{Additionstheorem}} \end{align*} wobei mit dem Additionstheorem \eqref{fm:eq:addth2} \(A = \omega_c t\) und \(B = 2k\omega_m t \) zum \[ - J_0(\beta)\cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} + J_0(\beta)\cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k \omega_m) t)+\cos((\omega_c + 2k \omega_m) t) \} \] wird. Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term @@ -98,20 +98,20 @@ Nun zum zweiten Teil des Term \eqref{fm:eq:start}, den Sin-Teil \[ \sin(\omega_c)\sin(\beta\sin(\omega_m t)). \] -Dieser wird mit der \eqref{fm:eq:besselid2} Bessel indentität zu +Dieser wird mit der \eqref{fm:eq:besselid2} Besselindentität zu \begin{align*} - \sin(\omega_c t) \cdot [J_0(\beta) \sin(\omega_c t) + 2\sum_{k=1}^\infty J_{2k+1}(\beta) \cos((2k+1)\omega_m t)] + \sin(\omega_c t) \cdot \bigg[ J_0(\beta) + 2 \sum_{k=1}^\infty J_{ 2k + 1}(\beta) \cos(( 2k + 1) \omega_m t) \bigg] &=\\ - J_0(\beta) \cdot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{Additionstheorem}. + J_0(\beta) \cdot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{\text{Additionstheorem}}. \end{align*} Auch hier wird ein Additionstheorem \eqref{fm:eq:addth3} gebraucht, dabei ist \(A = \omega_c t\) und \(B = (2k+1)\omega_m t \), somit wird daraus \[ - J_0(\beta) \cdot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{neg.Teil} - \cos((\omega_c+(2k+1)\omega_m) t) \} + J_0(\beta) \cdot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{\text{neg.Teil}} - \cos((\omega_c+(2k+1)\omega_m) t) \} \]dieser Term. Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. -Zusätzlich dabei noch die letzte Bessel indentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). -Somit wird negTeil zum Term \(-\cos((\omega_c+(2k+1)\omega_m) t)\)und die Summe vereinfacht sich zu +Zusätzlich dabei noch die letzte Besselindentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). +Somit wird neg.Teil zum Term \(-\cos((\omega_c+(2k+1)\omega_m) t)\) und die Summe vereinfacht sich zu \[ \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t). \label{fm:eq:ungerade} -- cgit v1.2.1 From 54b20e3e34ccb7c11d2f78cbbdd0bbf951bb9cba Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 28 Jul 2022 21:01:15 +0200 Subject: typo korrigiert --- buch/papers/fm/Makefile.inc | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'buch/papers/fm') diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index b686b98..40f23b1 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,7 +6,7 @@ dependencies-fm = \ papers/fm/packages.tex \ papers/fm/main.tex \ - papers/fm/01_modulation.tex \ + papers/fm/00_modulation.tex \ papers/fm/01_AM.tex \ papers/fm/02_FM.tex \ papers/fm/03_bessel.tex \ -- cgit v1.2.1