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{
 "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": "markdown",
   "id": "5ad0edf9",
   "metadata": {},
   "source": [
    "# Dealy Window\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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 =0\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": 4,
   "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": 5,
   "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": 6,
   "id": "43372541",
   "metadata": {},
   "outputs": [],
   "source": [
    "#H_int = fft(h_int)\n",
    "#h = ifft(H_int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a32cb580",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 7,
     "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)# Signal\n",
    "\n",
    "y = np.convolve(test.real, h_int)#Faltung\n",
    "\n",
    "plt.stem(test, linefmt=\"C0-\")\n",
    "plt.stem(y, linefmt='C1-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "39fb3489",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 8, 9, 1, 3, 5, 7, 9, 8, 4, 8, 2, 6, 1, 5, 5, 3, 5, 0, 7])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7fd06347",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1., 0., 0., 0.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a9612999",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1., 8., 9., 1., 3., 5., 7., 9., 8., 4., 8., 2., 6., 1., 5.,\n",
       "       5., 3., 5., 0., 7., 0., 0., 0.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "706a51b1",
   "metadata": {},
   "source": [
    "# FIR mit Delay \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "79e18131",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tap with amplitude=1, delay=7.5\n",
      "Creating filter of order N=15.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 12,
     "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": [
    "\n",
    "delay = 7.5\n",
    "ampl = 1\n",
    "print(f\"Tap with amplitude={ampl}, delay={delay}\")\n",
    "\n",
    "order = 2 * np.floor(delay) + 1 #N\n",
    "print(f\"Creating filter of order N={order}\")\n",
    "\n",
    "skip = np.floor(delay) - (order - 1) / 2 #M\n",
    "assert skip >= 0\n",
    "\n",
    "samples = np.arange(0, order +1) - delay\n",
    "\n",
    "h = ampl*(np.sinc(samples)) #sinc\n",
    "\n",
    "plt.stem(samples, h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c89c83ae",
   "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"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0dfe9b7850>]"
      ]
     },
     "execution_count": 13,
     "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.arange(200)\n",
    "\n",
    "signal = np.sin(2 * np.pi * t * 0.05)\n",
    "\n",
    "signal_shifted = np.convolve(h, signal, mode='full')\n",
    "\n",
    "plt.plot(t, signal)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "plt.plot(signal_shifted)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d51d8a62",
   "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
}