{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f4344b65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import signal\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy\n",
    "from scipy import signal\n",
    "\n",
    "\n",
    "Ap= 1 \n",
    "As = 40  \n",
    "Wp = 4000  \n",
    "Ws = 8000 \n",
    "omega_p = 2*np.pi*(Wp)\n",
    "omega_s = 2*np.pi*(Ws)\n",
    "\n",
    "N, Wn = signal.buttord(omega_p, omega_s, Ap, As, analog=True)\n",
    "b, a = signal.butter(N, Wn, 'low', True)\n",
    "w, h = signal.freqs(b,a) \n",
    "\n",
    "plt.plot(w/(2*np.pi), 20*np.log10(abs(h)))\n",
    "plt.grid()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ce023de-0001-4e83-bbd4-ef51d826762f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_z_plane(zeros, poles, show_roc=1):\n",
    "    fig, ax = plt.subplots(figsize=(7, 7), facecolor='white')\n",
    "    # Maximum pole for ROC calculation and axis limits\n",
    "    max_p = np.max(np.abs(poles)) if len(poles) > 0 else 0\n",
    "    # ROC Plotting (Only if show_roc == 1)\n",
    "    if show_roc == 1:\n",
    "        roc_limit = max(2.5, max_p + 1.0)\n",
    "        # Green area\n",
    "        roc_area = plt.Circle((0, 0), roc_limit, color='lightgreen', alpha=0.2, label=f'ROC: $|z| > {max_p:.2f}$', zorder=1)\n",
    "        ax.add_artist(roc_area)\n",
    "    # White \"hole\" (on top of ROC, below the X markers)\n",
    "    white_center = plt.Circle((0, 0), max_p, color='white', zorder=2)\n",
    "    ax.add_artist(white_center)\n",
    "    # Unit Circle\n",
    "    theta = np.linspace(0, 2*np.pi, 200)\n",
    "    ax.plot(np.cos(theta), np.sin(theta), color='black', linestyle='--',\n",
    "    linewidth=1, label='Unit Circle', zorder=3)\n",
    "    # Poles and Zeros\n",
    "    ax.scatter(np.real(zeros), np.imag(zeros), s=150, marker='o',\n",
    "    facecolors='none', edgecolors='blue', linewidth=2,\n",
    "    label='Zeros', zorder=4)\n",
    "    ax.scatter(np.real(poles), np.imag(poles), s=150, marker='x',\n",
    "    color='red', linewidth=2, label='Poles', zorder=4)\n",
    "    # Automatic axis adjustment\n",
    "    all_coords = np.concatenate(([1.2], np.abs(poles), np.abs(zeros)))\n",
    "    limit = np.max(all_coords) + 0.3\n",
    "    ax.set_xlim([-limit, limit])\n",
    "    ax.set_ylim([-limit, limit])\n",
    "    ax.axhline(0, color='black', lw=1, zorder=3)\n",
    "    ax.axvline(0, color='black', lw=1, zorder=3)\n",
    "    ax.set_aspect('equal')\n",
    "    ax.legend(loc='upper right', frameon=True).set_zorder(5)\n",
    "    ax.grid(True, linestyle=':', alpha=0.5, zorder=0)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "357bfaec",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotzp(zeros, poles):\n",
    "    ax = plt.subplot(1, 1, 1)\n",
    "    circle = plt.Circle((0, 0), 1, color='black', fill=False)\n",
    "    ax.add_artist(circle)\n",
    "\n",
    "    plt.plot(np.real(zeros), np.imag(zeros), 'ob')\n",
    "    plt.plot(np.real(poles), np.imag(poles), 'xr')\n",
    "\n",
    "    plt.legend(['Zeros', 'Poles'], loc=2)\n",
    "    plt.title('Pole / Zero Plot')\n",
    "    plt.xlabel('Real')\n",
    "    plt.ylabel('Imaginary')\n",
    "\n",
    "    plt.xlim([-50000, 20000])\n",
    "    plt.ylim([-30000, 30000])\n",
    "    ax.set_aspect(1.0) # Make aspect ratio square\n",
    "    plt.grid()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f458bc60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z, p, c = scipy.signal.tf2zpk(b,a)\n",
    "plotzp(z,p)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2cbce5f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Ap= 3\n",
    "As = 60  \n",
    "\n",
    "Wp = 200000\n",
    "Ws = 400000\n",
    "omega_p = 2*np.pi*(Wp)\n",
    "omega_s = 2*np.pi*(Ws)\n",
    "\n",
    "N, Wn = signal.buttord(omega_p, omega_s, Ap, As, analog=True)\n",
    "\n",
    "b, a = signal.butter(N, Wn, 'low', True) \n",
    "w, h = signal.freqs(b,a)\n",
    "\n",
    "plt.plot(w/(2*np.pi), 20*np.log10(abs(h)))\n",
    "plt.grid()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baae68d3",
   "metadata": {},
   "source": [
    "### Chebyshev filter (Type 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c31aba3",
   "metadata": {},
   "source": [
    "### Example 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e024379e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Filter order: 8\n",
      "Critical frequency: 4500.0 Hz\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.signal import cheb1ord, cheby1, freqs\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "rp = 10  # maximum ripple in the passband (dB)\n",
    "rs = 100  # minimum attenuation in the stopband (dB)\n",
    "wp = 4500  # passband edge frequency (Hz)\n",
    "ws = 10000  # stopband edge frequency (Hz)\n",
    "\n",
    "# Since it's an analog filter, we directly use the angular frequencies (rad/s).\n",
    "wp = 2 * np.pi * wp\n",
    "ws = 2 * np.pi * ws\n",
    "\n",
    "# Calculate the minimum order of the filter and the critical frequency\n",
    "N, Wn = cheb1ord(wp, ws, rp, rs, analog=True)\n",
    "\n",
    "# Design the Chebyshev Type I filter\n",
    "b, a = cheby1(N, rp, Wn, btype='low', analog=True)\n",
    "\n",
    "# Print filter parameters\n",
    "print(f\"Filter order: {N}\")\n",
    "print(f\"Critical frequency: {Wn / (2 * np.pi)} Hz\")\n",
    "\n",
    "# Frequency response\n",
    "w, h = freqs(b, a, worN=np.logspace(1, 5, 1000))\n",
    "\n",
    "# Plot the magnitude response\n",
    "plt.figure()\n",
    "plt.semilogx(w / (2 * np.pi), 20 * np.log10(abs(h)))\n",
    "plt.title('Chebyshev Type I frequency response')\n",
    "plt.xlabel('Frequency [Hz]')\n",
    "plt.ylabel('Amplitude [dB]')\n",
    "plt.grid(which='both', axis='both')\n",
    "plt.axvline(4500, color='green')  # passband edge\n",
    "plt.axvline(10000, color='red')  # stopband edge\n",
    "plt.axhline(-100, color='red')  # stopband attenuation\n",
    "plt.axhline(-10, color='green')  # passband ripple\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d06e713f",
   "metadata": {},
   "source": [
    "### Elliptic filter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eadb413e",
   "metadata": {},
   "source": [
    "### Example 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "542a8123",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Filter order: 3\n",
      "Critical frequency: 3999.9999999999995 Hz\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.signal import ellipord, ellip, freqs\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the filter specifications\n",
    "fp = 4000  # Passband frequency in Hz\n",
    "fs = 8000  # Stopband frequency in Hz\n",
    "Rp = 1     # Passband ripple in dB\n",
    "Rs = 30    # Stopband attenuation in dB\n",
    "\n",
    "# Normalize frequencies for an analog filter (frequencies are in radians per second)\n",
    "Wp = 2 * np.pi * fp\n",
    "Ws = 2 * np.pi * fs\n",
    "\n",
    "# Calculate the minimum filter order and the critical frequencies\n",
    "N, Wn = ellipord(Wp, Ws, Rp, Rs, analog=True)\n",
    "\n",
    "# Design the elliptic filter\n",
    "b, a = ellip(N, Rp, Rs, Wn, btype='low', analog=True)\n",
    "\n",
    "# Frequency response\n",
    "w, h = freqs(b, a, worN=20000)\n",
    "\n",
    "# Plot the frequency response\n",
    "plt.figure()\n",
    "plt.semilogx(w / (2 * np.pi), 20 * np.log10(abs(h)))\n",
    "plt.title('Elliptic Lowpass Filter Frequency Response')\n",
    "plt.xlabel('Frequency [Hz]')\n",
    "plt.ylabel('Amplitude [dB]')\n",
    "plt.grid(which='both', axis='both')\n",
    "plt.axvline(fp, color='green')  # Passband edge\n",
    "plt.axvline(fs, color='red')    # Stopband edge\n",
    "plt.axhline(-Rs, color='red')   # Stopband attenuation\n",
    "plt.axhline(-Rp, color='green') # Passband ripple\n",
    "plt.show()\n",
    "\n",
    "# Print filter order and critical frequency\n",
    "print(f\"Filter order: {N}\")\n",
    "print(f\"Critical frequency: {Wn / (2 * np.pi)} Hz\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0fa83d6a-163c-4de6-abcb-c70b8cb3d006",
   "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": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
