path: root/notebooks/FIR_mehrere.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d828ae1c",
   "metadata": {},
   "source": [
    "# FIR Filter Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9aed9f51",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "from numpy.fft import fft,ifft,fftshift\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9a16a6d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Anfangs werte noch variabel machen \n",
    "delays = [3,5,2]\n",
    "ampl = [0.2,0.5,0.8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "04de21c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#if len(delays)!= len(ampl):\n",
    "# Exeption ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "01fe08fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 0, 0, 0, 0.2]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1]+[0 for n in range (0,delays[0])]+[ampl[0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9ab70ca5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f55da062",
   "metadata": {},
   "outputs": [],
   "source": [
    "i = len(ampl)\n",
    "x = [([1]+[0 for n in range (0,delays[i])]+[ampl[i]]) for i in range(0,i)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ad0edf9",
   "metadata": {},
   "source": [
    "# Dealy Window\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bf92d73a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = 3.3\n",
    "k = np.linspace(-5,10,1000)\n",
    "h_ideal = np.sinc(k-d)\n",
    "plt.plot(k,h_ideal)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dd93e444",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 4.5\n",
    "window_sample= np.arange(np.round(d-(n-1)/2),np.round(d+(n+1)/2))\n",
    "window = []\n",
    "for ws in window_sample:  \n",
    "    idx = (np.abs(k-ws)).argmin()\n",
    "    window.append(idx)\n",
    "    \n",
    "plt.plot(k,h_ideal)\n",
    "plt.plot(window_sample,h_ideal[window],\"-*\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12b0c2d2",
   "metadata": {},
   "source": [
    "# FIR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "efc93b69",
   "metadata": {},
   "outputs": [],
   "source": [
    "delay = 3\n",
    "amplitude = 1\n",
    "\n",
    "d_int = int(np.floor(delay))\n",
    "d_frac = delay - d_int\n",
    "\n",
    "h_int = np.concatenate([np.zeros(d_int-1), [amplitude], np.zeros(3)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "43372541",
   "metadata": {},
   "outputs": [],
   "source": [
    "H_int = fft(h_int)\n",
    "h = ifft(H_int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a32cb580",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = np.random.randint(0, 10, size = 20)\n",
    "y = np.convolve(test.real, h_int)\n",
    "\n",
    "plt.stem(test, linefmt=\"C0-\")\n",
    "plt.stem(y, linefmt='C1-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "39fb3489",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 6, 5, 2, 9, 9, 5, 9, 2, 1, 5, 8, 0, 5, 1, 6, 9, 9, 9, 8])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7fd06347",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1., 0., 0., 0.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a9612999",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 3., 6., 5., 2., 9., 9., 5., 9., 2., 1., 5., 8., 0., 5., 1.,\n",
       "       6., 9., 9., 9., 8., 0., 0., 0.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "706a51b1",
   "metadata": {},
   "source": [
    "# FIR mit Delay \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d51e107c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "System frequencies fs=10, T=0.1\n",
      "Tap with amplitude=4, delay=0.7250000000000001\n",
      "Creating filter of order N=15.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Wc6bTIuL1iHiu+vEvVCmgwl0p3/ZWSTdL+mreWVaz/V5Jvy/pPkmKiFMRMZdrqLVdIKlk+wJJF0mayTmPIuIHkt5ctfk2SV+rfvw1SQObmWm5tfJFxHcj4t3qzR9K2rrpwVbmWetnKEn/IGmPpMKuDEmpyLslHV92+4QKWJSSZHu7pF5Jz+QcZS1fUuVJuZhzjrX8pqRZSf9Wnfr5qu2L8w61XERMS/p7VfbOXpf084j4br6pzurXI+J1qbKjIen9Oec5lz+V9J28Q6xm+1ZJ0xHxQt5ZziWlIl/r3SsK9z+k7UskfVPSZyPirbzzLGf7FkknI+Jw3lnO4gJJH5T0LxHRK+mXync64AzVeebbJF0pqUvSxbY/kW+qtNm+R5WpyQfzzrKc7Ysk3SPpr/POcj4pFfkJSduW3d6qArykXc52uyol/mBEjOSdZw07Jd1q+6eqTE3dYPvr+UZa4YSkExGx9ErmoCrFXiQ3Sno1ImYjYl7SiKTfyznT2fyv7cslqfr3yZzznMH2nZJukfTHUbyTWn5Llf+wX6j+zmyV9Jzttd6fIVcpFfmzkq6yfaXtC1U5wPRIzplOc+X97u6TdDQivph3nrVExFBEbI2I7ar8/J6IiMLsTUbEzyQdt730duofkfRyjpHWckzSh21fVH3MP6KCHZBd5hFJd1Y/vlNSzW8Esxls75L0V5JujYj/yzvPahExGRHvj4jt1d+ZE5I+WH2eFkoyRV49KPJpSWOq/OJ8IyJeyjfVCjslfVKVvdznq38+lneoBP25pAdtH5H0AUl/l2+claqvFg5Kek7SpCq/Q7mfxm37gKSnJfXYPmH7U5L2SbrJ9o9VWXWxr2D5/lnSpZIer/6+/Gte+c6RMQmcog8AiUtmjxwAsDaKHAASR5EDQOIocgBIHEUOAImjyAEgcRQ5ACTu/wFMUCb5B1ImMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "samp_rate = 10\n",
    "period = 1 / samp_rate\n",
    "print(f\"System frequencies fs={samp_rate}, T={period}\")\n",
    "\n",
    "delay = 7.25 * period\n",
    "ampl = 4\n",
    "print(f\"Tap with amplitude={ampl}, delay={delay}\")\n",
    "\n",
    "order = 2 * np.floor(delay / period) + 1 #N\n",
    "print(f\"Creating filter of order N={order}\")\n",
    "\n",
    "skip = np.floor(delay / period) - (order - 1) / 2 #M\n",
    "assert skip >= 0\n",
    "\n",
    "samples = np.arange(0, order + 1) * period - delay\n",
    "h = ampl*(np.sin(samp_rate * samples) / (samp_rate * samples)) #sinc\n",
    "\n",
    "plt.stem(h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c89c83ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, delay + period, samp_rate)\n",
    "f = np.sin(2 * np.pi * samp_rate * t)\n",
    "\n",
    "f_shift = np.convolve(h, f)[:len(f)]\n",
    "\n",
    "plt.stem(t, f, linefmt=\"C0-\")\n",
    "plt.stem(t, f_shift, linefmt='C1-')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15f663c6",
   "metadata": {},
   "source": [
    "#  Test Delay  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "afb9e748",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "System frequencies fs=10, T=0.1\n",
      "Tap with amplitude=4, delay_freq=0.7250000000000001, delay_int=7\n",
      "Creating filter of order N=15.0\n",
      "samples_freq[-0.725 -0.625 -0.525 -0.425 -0.325 -0.225 -0.125 -0.025  0.075  0.175\n",
      "  0.275  0.375  0.475  0.575  0.675  0.775]\n",
      "samples_int[0 1 2 3 4 5 6]\n",
      "h_freq[ 0.45411359 -0.0212347  -0.65442628 -0.84234293 -0.13316324  1.38324124\n",
      "  3.03675078  3.95846335  3.63540672  2.24911074  0.55514326 -0.60966541\n",
      " -0.84150972 -0.35358545  0.26669278  0.51334131]\n",
      "h_ideal[ 3.10262780e-02  2.99830750e-02  2.88692595e-02  2.76870500e-02\n",
      "  2.64388245e-02  2.51271158e-02  2.37546068e-02  2.23241246e-02\n",
      "  2.08386353e-02  1.93012375e-02  1.77151562e-02  1.60837364e-02\n",
      "  1.44104353e-02  1.26988161e-02  1.09525398e-02  9.17535764e-03\n",
      "  7.37110346e-03  5.54368515e-03  3.69707648e-03  1.83530854e-03\n",
      " -3.75389411e-05 -1.91734645e-03 -3.79996360e-03 -5.68121819e-03\n",
      " -7.55692534e-03 -9.42289669e-03 -1.12749496e-02 -1.31089164e-02\n",
      " -1.49206538e-02 -1.67060518e-02 -1.84610433e-02 -2.01816127e-02\n",
      " -2.18638056e-02 -2.35037373e-02 -2.50976019e-02 -2.66416805e-02\n",
      " -2.81323506e-02 -2.95660937e-02 -3.09395037e-02 -3.22492951e-02\n",
      " -3.34923102e-02 -3.46655271e-02 -3.57660666e-02 -3.67911991e-02\n",
      " -3.77383512e-02 -3.86051122e-02 -3.93892397e-02 -4.00886655e-02\n",
      " -4.07015008e-02 -4.12260407e-02 -4.16607694e-02 -4.20043635e-02\n",
      " -4.22556964e-02 -4.24138408e-02 -4.24780722e-02 -4.24478711e-02\n",
      " -4.23229246e-02 -4.21031285e-02 -4.17885880e-02 -4.13796183e-02\n",
      " -4.08767448e-02 -4.02807029e-02 -3.95924372e-02 -3.88131000e-02\n",
      " -3.79440498e-02 -3.69868493e-02 -3.59432624e-02 -3.48152516e-02\n",
      " -3.36049739e-02 -3.23147774e-02 -3.09471966e-02 -2.95049475e-02\n",
      " -2.79909227e-02 -2.64081855e-02 -2.47599639e-02 -2.30496441e-02\n",
      " -2.12807638e-02 -1.94570050e-02 -1.75821866e-02 -1.56602563e-02\n",
      " -1.36952827e-02 -1.16914466e-02 -9.65303250e-03 -7.58441946e-03\n",
      " -5.49007187e-03 -3.37453002e-03 -1.24240037e-03  9.01654268e-04\n",
      "  3.05292479e-03  5.20666595e-03  7.35810667e-03  9.50246043e-03\n",
      "  1.16349357e-02  1.37507466e-02  1.58451231e-02  1.79133223e-02\n",
      "  1.99506380e-02  2.19524121e-02  2.39140447e-02  2.58310043e-02\n",
      "  2.76988383e-02  2.95131833e-02  3.12697744e-02  3.29644561e-02\n",
      "  3.45931908e-02  3.61520691e-02  3.76373182e-02  3.90453114e-02\n",
      "  4.03725766e-02  4.16158043e-02  4.27718560e-02  4.38377715e-02\n",
      "  4.48107764e-02  4.56882893e-02  4.64679278e-02  4.71475148e-02\n",
      "  4.77250846e-02  4.81988877e-02  4.85673958e-02  4.88293061e-02\n",
      "  4.89835454e-02  4.90292733e-02  4.89658850e-02  4.87930140e-02\n",
      "  4.85105339e-02  4.81185596e-02  4.76174484e-02  4.70078001e-02\n",
      "  4.62904572e-02  4.54665036e-02  4.45372638e-02  4.35043009e-02\n",
      "  4.23694144e-02  4.11346372e-02  3.98022324e-02  3.83746893e-02\n",
      "  3.68547189e-02  3.52452494e-02  3.35494203e-02  3.17705767e-02\n",
      "  2.99122632e-02  2.79782166e-02  2.59723589e-02  2.38987898e-02\n",
      "  2.17617778e-02  1.95657526e-02  1.73152954e-02  1.50151300e-02\n",
      "  1.26701130e-02  1.02852236e-02  7.86555385e-03  5.41629729e-03\n",
      "  2.94273859e-03  4.50242226e-04 -2.05575891e-03 -4.56977505e-03\n",
      " -7.08627130e-03 -9.59967955e-03 -1.21044105e-02 -1.45948660e-02\n",
      " -1.70654508e-02 -1.95105853e-02 -2.19247178e-02 -2.43023365e-02\n",
      " -2.66379819e-02 -2.89262594e-02 -3.11618507e-02 -3.33395267e-02\n",
      " -3.54541587e-02 -3.75007304e-02 -3.94743496e-02 -4.13702594e-02\n",
      " -4.31838493e-02 -4.49106660e-02 -4.65464241e-02 -4.80870163e-02\n",
      " -4.95285232e-02 -5.08672230e-02 -5.20996007e-02 -5.32223566e-02\n",
      " -5.42324150e-02 -5.51269319e-02 -5.59033024e-02 -5.65591677e-02\n",
      " -5.70924219e-02 -5.75012172e-02 -5.77839701e-02 -5.79393658e-02\n",
      " -5.79663626e-02 -5.78641958e-02 -5.76323807e-02 -5.72707150e-02\n",
      " -5.67792814e-02 -5.61584481e-02 -5.54088703e-02 -5.45314899e-02\n",
      " -5.35275352e-02 -5.23985195e-02 -5.11462399e-02 -4.97727743e-02\n",
      " -4.82804791e-02 -4.66719848e-02 -4.49501926e-02 -4.31182690e-02\n",
      " -4.11796405e-02 -3.91379878e-02 -3.69972390e-02 -3.47615623e-02\n",
      " -3.24353588e-02 -3.00232534e-02 -2.75300867e-02 -2.49609055e-02\n",
      " -2.23209526e-02 -1.96156571e-02 -1.68506230e-02 -1.40316187e-02\n",
      " -1.11645646e-02 -8.25552183e-03 -5.31067933e-03 -2.33634137e-03\n",
      "  6.61085556e-04  3.67510610e-03  6.69914965e-03  9.72658419e-03\n",
      "  1.27507304e-02  1.57648758e-02  1.87622895e-02  2.17362360e-02\n",
      "  2.46799907e-02  2.75868541e-02  3.04501664e-02  3.32633224e-02\n",
      "  3.60197865e-02  3.87131066e-02  4.13369293e-02  4.38850140e-02\n",
      "  4.63512470e-02  4.87296560e-02  5.10144235e-02  5.31999005e-02\n",
      "  5.52806201e-02  5.72513099e-02  5.91069054e-02  6.08425615e-02\n",
      "  6.24536651e-02  6.39358460e-02  6.52849882e-02  6.64972404e-02\n",
      "  6.75690260e-02  6.84970525e-02  6.92783207e-02  6.99101326e-02\n",
      "  7.03900998e-02  7.07161501e-02  7.08865344e-02  7.08998325e-02\n",
      "  7.07549582e-02  7.04511638e-02  6.99880440e-02  6.93655393e-02\n",
      "  6.85839378e-02  6.76438776e-02  6.65463469e-02  6.52926850e-02\n",
      "  6.38845812e-02  6.23240737e-02  6.06135477e-02  5.87557322e-02\n",
      "  5.67536966e-02  5.46108466e-02  5.23309188e-02  4.99179751e-02\n",
      "  4.73763961e-02  4.47108739e-02  4.19264040e-02  3.90282768e-02\n",
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      "  4.61370892e-02  4.53141056e-02  4.43942707e-02  4.33800555e-02\n",
      "  4.22741272e-02  4.10793427e-02  3.97987415e-02  3.84355384e-02]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iYc7QCgDU2N7+IY1N5Iu2jU3ktbd/KJHjE+QAUGMjubGytpeLIAeAGlvb3lrW9nIR5ABQY7u2bVRrS1PRttaWJu3atjGR4zPZCQA1VpjQ3Ns/pJHcmNa2t7JqBQBi09PVmVhwn4+hFQCIHEEOAJEjyAEgcgQ5AESOIAeAyJm7L/2Lmp2S9FaFu6+W9F6C5cSOfsyiF8XoR7F66Mdl7n7p+RuDBHk1zGzA3TOh60gL+jGLXhSjH8XquR8MrQBA5AhyAIhcjEG+P3QBKUM/ZtGLYvSjWN32I7oxcgBAsRjPyAEAcxDkABC5qILczLab2ZCZvW5m94SuJxQzW29m3zOzV83sZTPbGbqmNDCzJjMbNLMnQ9cSmpm1m9mjZvbazO/JL4euKRQz+4OZ98kPzOybZvZToWtKWjRBbmZNkr4m6WZJV0m6w8yuCltVMJOS/tDdPyRps6TfbeBezLVT0quhi0iJfZIOu/uVkj6sBu2LmXVK+j1JGXe/WlKTpNvDVpW8aIJc0nWSXnf3N9z9rKSDkm4NXFMQ7v5Dd39p5t//p+k3aW1udBwJM1sn6dckPRC6ltDM7BJJvyLpbyTJ3c+6ey5oUWE1S2o1s2ZJKyWNBK4ncTEFeaekd+Y8PqEGDy9JMrMNkrokvRC4lND+XNIXJE0FriMNrpB0StJDM0NND5hZW+iiQnD3YUl/KultST+U9GN3/07YqpIXU5DbPNsaeu2kma2S9G1Jv+/u/xu6nlDM7BZJP3L3o6FrSYlmSb8o6S/dvUvSaUkNOadkZu/T9Cf3yyWtldRmZneGrSp5MQX5CUnr5zxepzr8iFQqM2vRdIg/7O6HQtcT2BZJnzSzNzU95HaDmX0jbElBnZB0wt0Ln9Ie1XSwN6KbJP2nu59y9wlJhyR9NHBNiYspyF+U9EEzu9zMlmt6wuKJwDUFYWam6fHPV939q6HrCc3dd7v7OnffoOnfiyPuXndnXaVy95OS3jGzwle03yjplYAlhfS2pM1mtnLmfXOj6nDiN5ovX3b3STO7W1K/pmeeH3T3lwOXFcoWSXdJOm5mx2a2fcndnwpXElLmc5IenjnpeUPSjsD1BOHuL5jZo5Je0vRqr0HV4aX6XKIPAJGLaWgFADAPghwAIkeQA0DkCHIAiBxBDgCRI8gBIHIEOQBE7v8B0HnepyNCSJIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "samp_rate = 10\n",
    "period = 1 / samp_rate\n",
    "print(f\"System frequencies fs={samp_rate}, T={period}\")\n",
    "\n",
    "delay_freq = 7.25 * period\n",
    "delay_int = int(np.floor(delay_freq/period))\n",
    "ampl = 4\n",
    "print(f\"Tap with amplitude={ampl}, delay_freq={delay_freq}, delay_int={delay_int}\")\n",
    "\n",
    "order = 2 * np.floor(delay / period) + 1 #N\n",
    "print(f\"Creating filter of order N={order}\")\n",
    "\n",
    "skip = np.floor(delay / period) - (order - 1) / 2 #M\n",
    "assert skip >= 0\n",
    "\n",
    "samples_freq = np.arange(0, order + 1) * period - delay_freq\n",
    "print(f\"samples_freq{samples_freq}\")\n",
    "\n",
    "samples_int = np.arange(0,delay_int,1)\n",
    "print(f\"samples_int{samples_int}\")\n",
    "\n",
    "h_freq = ampl*(np.sin(samp_rate * samples_freq) / (samp_rate * samples_freq)) #sinc\n",
    "\n",
    "#h_ideal = np.exp(-1j*delay_int*2*np.pi*samp_rate)\n",
    "print(f\"h_freq{h_freq}\")\n",
    "print(f\"h_ideal{h_ideal}\")\n",
    "\n",
    "t_freq = np.linspace(0, delay_freq + period, samp_rate)\n",
    "t_int = np.linspace(0, delay_int + period, samp_rate)\n",
    "\n",
    "f_freq = np.sin(2 * np.pi * samp_rate * t_freq)#test Signal\n",
    "f_int = np.sin(2 * np.pi * samp_rate * t_int)#test Signal\n",
    "\n",
    "f_shift_freq = np.convolve(h_freq , f_freq)[:len(f_freq)]#Faltung freq \n",
    "f_shift_int = np.convolve(h_int , f_int)[:len(f_int)]#Faltung int \n",
    "\n",
    "\n",
    "\n",
    "#h_int = np.concatenate([np.zeros(delay_int-1), [ampl], np.zeros(3)])\n",
    "#y1 = np.convolve(test.real, h_int)\n",
    "plt.grid(True)\n",
    "plt.stem(t_freq, f_shift_freq, linefmt=\"C0-\")\n",
    "plt.stem(t_int, f_shift_int, linefmt='C1-')\n",
    "plt.show()\n",
    "plt.grid(True)\n",
    "plt.stem(f_shift_freq, linefmt=\"C2-\", label='freq')\n",
    "plt.stem(f_shift_int, linefmt='C3-', label = 'int')\n",
    "#plt.legend(loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e5f23991",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f224987a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}