diff options
Diffstat (limited to '')
40 files changed, 758 insertions, 29 deletions
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/teil0.tex b/buch/papers/fm/01_AM-FM.tex index 55697df..55697df 100644 --- a/buch/papers/fm/teil0.tex +++ b/buch/papers/fm/01_AM-FM.tex diff --git a/buch/papers/fm/teil1.tex b/buch/papers/fm/02_frequenzyspectrum.tex index 6f9edf1..6f9edf1 100644 --- a/buch/papers/fm/teil1.tex +++ b/buch/papers/fm/02_frequenzyspectrum.tex diff --git a/buch/papers/fm/teil2.tex b/buch/papers/fm/03_bessel.tex index 6ab6fa0..6ab6fa0 100644 --- a/buch/papers/fm/teil2.tex +++ b/buch/papers/fm/03_bessel.tex diff --git a/buch/papers/fm/teil3.tex b/buch/papers/fm/04_fazit.tex index 3bcfc4d..3bcfc4d 100644 --- a/buch/papers/fm/teil3.tex +++ b/buch/papers/fm/04_fazit.tex diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index 0f144b6..e5cd9f6 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,9 +6,9 @@ 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/01_AM-FM.tex \ + papers/fm/02_frequenzyspectrum.tex \ + papers/fm/03_bessel.tex \ + papers/fm/04_fazit.tex \ + papers/fm/references.bib 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..bfbb83d --- /dev/null +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -0,0 +1,233 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 117, + "metadata": {}, + "outputs": [], + "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", + "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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yUkkiCnSpvVLFlOLSy0D8oGgAid48KferVxih69R/SYECXWqu+PK5pYwYoVe6QVWQH6EPJKkfhdBhqQoFulSdFS17iYXikfqIaYsBBFxTU1RyGRi7hp6neeiSlAJdqs5sZKSPvB566fAaOUIf3mfrG8c4fbY/3QZWwC9eO1II7zjNQ5c0KdCl6kbdiafEmaLDIZZ7MmJ6X7Tt1Nl+PvC1p/nMt5+rUEvTsePAKT7yvzbxJz/YUVhX/JeHrrooaVCgS82NmIdevC1aEa8155929w4CucDMsvxfEDsODrczf1Gu/sJB0bFphC5JKdCl5kpNWyy+CmH/wOiSS09/LtAnN2X7x3hyc659I0ouhRH62CWXwhROjdEloWz/JkiYoppLuZFn78DIkWt/iRF6V3TG5NTmbP8YN0XHDHoH4idHRZc0KJRcxg/toRDOqJKKyvZvgjSEUvPQe6PRd+9A7nEgNpI9G23r7ss9Tsl4oOcPfBbKK+6cHcivy/W4t8QB0/zB41JlJ5FSsv2bIEEbnpo4ekri2SjIu6I6ebw00dOX35YboWc90Pui69D0RX3oGxwqXDY336/uvuHrsxSP1vNLgwp0GUe2fxMkSBbVXPIlhFK3oDvbPzLo4vPQu6J1+ces19DzoZ2voecP5sLw6L0rtm7UaD1fnkkwxVEaW7Z/EyRoA4WbO8RWRs97JzJCz3ig54O4EOj9w+GdH73HR+jFgV7q8gcipWT7N0GCNjg0+jom+WfFI/T4JWO7+0aGfb2UXPJ/ZfTEwvtMb25KY1dfbIQeC3xQDV2Sy/ZvggQpf6JooYxS4sSi/IHPfNAdPdMHQNMkKwR6d72WXKL2N08yjnflAr079oGV/zDLy9fUVUOX8TTXugHSuAbL1tBzodc3MET/4BDHu/uYO2My7sMj3DPRCN2KLw6TMYWSy+DIQF80bzpHu3IfVPERev6A8PA89Jxyc9ZFQCN0qYF8/pYqIXihhj4cXt29gxzt6mP+jCnMmNI0aoSe9aAbebel4WMAbfOmc7y7D3cfWUPvL90fjdBlPAp0qZlSd+uJ19BnTc39AXno9FmOnull/swptExr5mRPrkyRr6tnPdD7itqXb/+S+TMZHHJOdPfz5smztET9zY/Q84Zr6Nnup9SeAl2qrjBro1ByGX3zip6+Aa5c2ALA7iNddBw+w7IFM1k4ZzoHTvYAw9P/ktxouZbiJ0UNDjn7T+Taf9PlFwDw8pun2XushysXzgaGZ+/kFb9fImNRoEvV5eefD5aYtuieu5hVV98g71w6H4CfvdrJkTN9XLlwNovmTefAibPA8Dz0rI/Q4x84Pf2DHDjRw7wZk7n2knkAPLHtAH2DQ7xzWW758KmRt5jzossEiIxFgS5Vlx9p9hemLY508GQusN96cQtXtc3hm5v2AHDzFa20zZvOsa4+Tvb0F0ayWQ/0eMmlq3eAN4520zZvBhfPnsZbL2op9O+D1y4GKPwFUkwjdBmPAl2qLj8yH+vCVPmSxFvmTudzv3kFLdOaufvGS7j8wln8m7a5QO7GFnuO9Yx4nayKt29XZxfP7TnOVYvnYGZ84ba30jK1mY//2lKWLZhJa8tUDkT9H3Utl4x/cEntadqiVNwvdx9j4ZxpLJ4/Axg+uHc8mrIXz/OTPf1s23sSM7jiwhbmzJjMi19+b2H71Uvm0TK1mT/5wU6OnMmVJrr7Rh5EzJru/uGa+Jf+8UW6+ga5eXkrALe+7SJe/K/D/XvrRS1s23cSGL6Oev4Yw7Ho/YJc2WrSJGNgcIgNL73J+9+xkEmTMj5/UypOI3SpuA//1dP8xsNPFZbzI9b8SDxu58FTPLnzTVYsnM2cGZNHbZ8+pYnVN1/Ka51dzJjSxO9cs4gDJ3oKZZdXD53m4Bgli2rpGxjiFx1HCst7j3Vz6YKZ/PrlC9jV2cXb3zKbW992Ycl/e+NlF/Dym6d5af9JjpwZ+YGXL0XBcBnnr//fbv79t5/j/247UKHeSD1JFOhmttLMXjGzDjO7r8T2qWb2nWj7JjNbmnpLpS7l51zHy7+vH+0CSgf6/d/fzkv7T3H3jUvHfM17br2cx37/Otbf8+v82mULGBhy9h7rBuC3vvIzbvzTf67pnO17H3+Bj3x9Ey/tz420d3V2sWzBTL720Wt49KPX8K1P3kDzGGe3fujaNqZPbuJDjz49atuB2Pu1J+pv/jEf/tLYxg10M2sCHgFuA1YAd5nZiqLdPgEcd/fLga8AD6bdUKlPxQf4jnX1setIF9MmT2Lf8R46Dp/h8Olc6eQj1y/hyoUtfPbdy/lQe9uYr2lm3HxFa66mvngOABu3H+JU7GbR+Q+NWvjR9jeB3K3xdh/p4pVDp7lq8Vxapk1m5a8sZM700X955F04exprPnYtb3/LbFbffClTmifRebqXoSHnX/71SOFmHlvfOA4MH4+IXx9GGleSGvp1QIe77wIws7XAKmBHbJ9VwJej598Fvmpm5kluwyJ1zd3pHRiiu2+Qnv5BDp06y67OLtovmceBkz08se1gYd/vP7+f72zeC8DXP/ZOPvXNrXz8b37JZa2zAPjMrZezcM70CX3/yy9s4eYrWnlo48s8vnVvYf1TLx+mbd50DOPnrx3hxksvYNrkphR6PJK7s/WN47TNm0Fry1T2HOsunOX64A9fZsidWVOay35AFXvX8lbeFdXYN+0+xhPbDrL3eDc7Dp7ioQ/8Kt/4+W4e+uHLTG6axHN7TgCw4cU3uXLhbJbMn8G+Ez0MDDpXLZ7DrKnNNE0ymidNYpINH2iVMNl4mWtmHwRWuvsfRMu/C1zv7vfE9nkp2mdftPxatM+RUq8J0N7e7lu2bJlwg5/fe4LffuTnE/53ki2XXDCDN452j1i3ZP6Mc7ouy+mzAyMOGGbRJRfMOKd/V+o9ypdZpH798HPv4m0Xzz6nf2tmW929vdS2qs5yMbPVwGqAJUuWnNNrzJ8xJc0mScom2XC9vLVlKpe1zuTi2dPYfuAUB070cONlFxRO6b968Vz6B52ndx3l6sVzaZmWzo/jmd4BfrzzcCqvdS7esWgOl7XOTOW1rmqby6bdR7n8wlm0zpoKwDVL5jLk8Oye4xzv6uPWKy+ip2+QVw+dZt/xbjRdPfvKld3OR5LfoP3A4thyW7Su1D77zKwZmAMcLX4hd18DrIHcCP1cGrzkghm8/mfvO5d/KiIStCSzXDYDy81smZlNAe4E1hftsx64O3r+QeCfVT8XEamucUfo7j5gZvcAG4Em4Bvuvt3MHgC2uPt64K+BvzezDuAYudAXEZEqSlS0dPcNwIaidffHnp8FPpRu00REZCJ0pqiISCAU6CIigVCgi4gEQoEuIhIIBbqISCDGPfW/Yt/YrBN4oybf/PwsAMa8pEGg1OfGoD7Xh0vcvbXUhpoFer0ysy1jXUchVOpzY1Cf659KLiIigVCgi4gEQoE+cWtq3YAaUJ8bg/pc51RDFxEJhEboIiKBUKCPw8zuNTM3swXRspnZX0Q3xN5mZtfE9r3bzP41+rp77FfNJjN72Mxejvr1f8xsbmzbF6M+v2Jm742tL3sD8XoTWn/yzGyxmT1lZjvMbLuZfTZaP9/Mnox+Zp80s3nR+jF/zuuNmTWZ2XNm9kS0vCy6mX1HdHP7KdH6+r/Zvbvra4wvcjft2EhuvvyCaN3twD8BBtwAbIrWzwd2RY/zoufzat2HCfb3t4Dm6PmDwIPR8xXAC8BUYBnwGrlLKTdFzy8FpkT7rKh1P86j/0H1p6hvC4FrouctwKvR/+tDwH3R+vti/+clf87r8Qv4PPAt4IloeR1wZ/T8UeDfRc8/BTwaPb8T+E6t2z7RL43Qy/sK8J+A+IGGVcBjnvMMMNfMFgLvBZ5092Pufhx4ElhZ9RafB3f/kbvnbx//DLm7U0Guz2vdvdfddwMd5G4eXriBuLv3AfkbiNer0PpT4O4H3f3Z6PlpYCewiFz//i7a7e+A346ej/VzXlfMrA14H/D1aNmAW8ndzB5G9zn/XnwXeLfV2V21FehjMLNVwH53f6Fo0yJgb2x5X7RurPX16vfJjdCgcfocWn9KikoJVwObgIvc/WC06U3gouh5KO/Fn5MblA1FyxcAJ2IDl3i/Cn2Otp+M9q8bVb1JdNaY2Y+Bi0ts+hLwh+RKEEEp12d3/360z5eAAeCb1WybVJ6ZzQK+B3zO3U/FB6Du7mYWzLQ3M3s/cNjdt5rZLTVuTlU0dKC7+3tKrTezd5CrFb8Q/cC3Ac+a2XWMfdPs/cAtRet/mnqjz9NYfc4zs48D7wfe7VExkfI3Ch/vBuL1JMkN0euWmU0mF+bfdPf/Ha0+ZGYL3f1gVFI5HK0P4b24CbjDzG4HpgGzgf9JrnzUHI3C4/1KdLP7TKt1Eb8evoDXGT4o+j5GHiz6ZbR+PrCb3AHRedHz+bVu+wT7uRLYAbQWrX87Iw+K7iJ3ALE5er6M4YOIb691P86j/0H1p6hvBjwG/HnR+ocZeVD0oeh5yZ/zev0iN9jKHxR9nJEHRT8VPf80Iw+Krqt1uyf61dAj9HO0gdwMgA6gG/g9AHc/ZmZ/BGyO9nvA3Y/Vponn7KvkQvvJ6C+TZ9z933rupuDryIX9APBpdx8EKHUD8do0/fz5GDdEr3Gz0nIT8LvAi2b2fLTuD4E/A9aZ2SfIzeb6cLSt5M95IL4ArDWzPwaeI3eTewjgZvc6U1REJBCa5SIiEggFuohIIBToIiKBUKCLiARCgS4iEggFuohIIBToIiKBUKCLiATi/wO3Cq7Lzsky6gAAAABJRU5ErkJggg==", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Number of samplepoints\n", + "N = 800\n", + "# sample spacing\n", + "T = 1.0 / 1000.0\n", + "x = np.linspace(0.01, N*T, N)\n", + "\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.xlim(-150, 150)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fm(1)" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.7651976865579666\n" + ] + } + ], + "source": [ + "\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.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": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "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()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "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": { + "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/FM_presentation.pdf b/buch/papers/fm/RS presentation/FM_presentation.pdf Binary files differnew file mode 100644 index 0000000..496e35e --- /dev/null +++ b/buch/papers/fm/RS presentation/FM_presentation.pdf 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 Binary files differnew file mode 100644 index 0000000..a6e701c --- /dev/null +++ b/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf 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 new file mode 100644 index 0000000..8a67619 --- /dev/null +++ b/buch/papers/fm/RS presentation/RS.tex @@ -0,0 +1,123 @@ +%% !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 Binary files differnew file mode 100644 index 0000000..371b9bf --- /dev/null +++ b/buch/papers/fm/RS presentation/images/100HZ.png diff --git a/buch/papers/fm/RS presentation/images/200HZ.png b/buch/papers/fm/RS presentation/images/200HZ.png Binary files differnew file mode 100644 index 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+\documentclass[aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{epic} +\usepackage{color} +\usepackage{array} +\usepackage{ifthen} +\usepackage{lmodern} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{nccmath} +\usepackage{mathtools} +\usepackage{adjustbox} +\usepackage{multimedia} +\usepackage{verbatim} +\usepackage{wasysym} +\usepackage{stmaryrd} +\usepackage{tikz} +\usetikzlibrary{shapes.geometric} +\usetikzlibrary{decorations.pathreplacing} +\usetikzlibrary{calc} +\usetikzlibrary{arrows} +\usetikzlibrary{3d} +\usetikzlibrary{arrows,shapes,math,decorations.text,automata} +\usepackage{pifont} +\usepackage[all]{xy} +\usepackage[many]{tcolorbox} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\begin{document} + +\def\spektrum#1#2{ +\only<#1>{ + \begin{scope} + \color{red} + \input{#2} + \end{scope} +} +} + +\begin{frame} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\def\df{0.37} +\def\da{1} + +\draw[->,color=gray] (0,-0.1) -- (0,6.3) [right] coordinate[label={right:$a$}]; + +\foreach \a in {1,...,5}{ + \draw[color=gray!50] (-6,{(6-\a)*\da}) -- (6,{(6-\a)*\da}); +} +\draw[color=gray!50] (-6,{6*\da}) -- (6,{6*\da}); +\foreach \f in {-15,-10,-5,5,10,15}{ + \draw[color=gray!50] ({\f*\df},0) -- ({\f*\df},{6*\da}); +} + +\input{parts.tex} + +\draw[->] (-6.1,0) -- (6.9,0) coordinate[label={$f$}]; +\foreach \f in {-16,...,16}{ + \draw ({\f*\df},-0.05) -- ({\f*\df},0.05); +} +\foreach \f in {-15,-10,-5,5,10,15}{ + \node at ({\f*\df},-0.1) [below] {$\f f_m$}; + \draw ({\f*\df},-0.1) -- ({\f*\df},0.1); +} +\node at (0,-0.1) [below] {$0$}; + +\foreach \a in {1,...,5}{ + \node at (6,{(6-\a)*\da}) [right] {$-\a$}; +} +\node at (6,{6*\da}) [right] {$\phantom{-}0$}; + +\end{tikzpicture} +\end{center} +\end{frame} + +\end{document} diff --git a/buch/papers/fm/anim/fm.m b/buch/papers/fm/anim/fm.m new file mode 100644 index 0000000..9062818 --- /dev/null +++ b/buch/papers/fm/anim/fm.m @@ -0,0 +1,98 @@ +# +# fm.m -- animation frequenzspektrum +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global fc; +fc = 1e6; +global width; +width = 16; +global fm; +fm = 1000; +global gamma; +gamma = 2; +global resolution; +resolution = 300; + +function retval = spektrum(beta, fm) + global width; + global fc; + retval = zeros(2 * width + 1, 2); + center = width + 1; + for k = (0:width) + retval(center - k, 1) = fc - k * fm; + retval(center + k, 1) = fc + k * fm; + a = besselj(k, beta); + retval(center - k, 2) = a; + retval(center + k, 2) = a; + endfor +endfunction + +function drawspectrum(fn, spectrum, foffset, fscale, beta) + n = size(spectrum)(1,1); + for i = (1:n) + f = (spectrum(i, 1) - foffset)/fscale; + a = log10(spectrum(i, 2)) + 6; + if (a < 0) + a = 0; + end + fprintf(fn, "\\draw[line width=3.5pt] "); + fprintf(fn, "({%.2f*\\df},0) -- ({%.2f*\\df},{%.5f*\\da});\n", + f, f, abs(a)); + fprintf(fn, "\\node at ({-15*\\df},5.5) [right] {$\\beta = %.3f$};", beta); + endfor +endfunction + +function drawhull(fn, beta) + global resolution; + fprintf(fn, "\\begin{scope}\n"); + fprintf(fn, "\\clip ({-16.5*\\df},0) rectangle ({16.5*\\df},{6*\\da});\n"); + p = zeros(resolution, 2); + for k = (1:resolution) + nu = 16.5 * (k - 1) / resolution; + p(k,1) = nu; + y = log10(abs(besselj(nu, beta))) + 6; + p(k,2) = y; + end + fprintf(fn, "\\draw[color=blue] ({%.4f*\\df},{%.5f*\\da})", + p(1,1), p(1,2)); + for k = (2:resolution) + fprintf(fn, "\n -- ({%.4f*\\df},{%.5f*\\da})", + p(k,1), p(k,2)); + endfor + fprintf(fn, ";\n\n"); + fprintf(fn, "\\draw[color=blue] ({%.4f*\\df},{%.5f*\\da})", + p(1,1), p(1,2)); + for k = (2:resolution) + fprintf(fn, "\n -- ({%.4f*\\df},{%.5f*\\da})", + -p(k,1), p(k,2)); + endfor + fprintf(fn, ";\n\n"); + fprintf(fn, "\\end{scope}\n"); +endfunction + +function animation(betamin, betamax, steps) + global fm; + global fc; + global gamma; + fa = fopen("parts.tex", "w"); + for k = (1:steps) + % add entry to parts.tex + fprintf(fa, "\\spektrum{%d}{texfiles/a%04d.tex}\n", k, k); + % compute beta + x = (k - 1) / (steps - 1); + beta = betamin + (betamax - betamin) * (x ^ gamma); + % create a new file + name = sprintf("texfiles/a%04d.tex", k); + fn = fopen(name, "w"); + % write the hull + drawhull(fn, beta); + % compute and write the spectrum + spectrum = spektrum(beta, fm); + drawspectrum(fn, spectrum, fc, fm, beta); + fclose(fn); + endfor + fclose(fa); +endfunction + +animation(0.001,10.1,200) diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 1e75235..1f8ebde 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -2,35 +2,42 @@ % main.tex -- Paper zum Thema <fm> % % (c) 2020 Hochschule Rapperswil -% +% +% !TeX root = buch.tex +%\begin {document} \chapter{Thema\label{chapter:fm}} \lhead{Thema} \begin{refsection} -\chapterauthor{Hans Muster} -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} +\chapterauthor{Joshua Bär} + +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} + +%\end {document} |
