{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aliasing and the Nyquist Theorem\n",
    "\n",
    "Aliasing can be seen when signals are at the $nf_s \\pm f_0$ where $f_s$ is the sampling frequency, and $f_0$ is the frequency in the baseband range, $-f_s/2 < f_0 < f_s/2$ and $n$ is any integer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "The sampling frequency, $f_s$ in Hz is:"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Nyquist frequency is  5.0 Hz.\n",
      "The actual signal frequency is  3.2 Hz.\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"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from IPython.display import Latex\n",
    "\n",
    "N = 10\n",
    "T = 0.1\n",
    "f_s = 1/T\n",
    "T_0 = N*T\n",
    "f_0 = 3.2  # Harmonic number.\n",
    "display(Latex('The sampling frequency, $f_s$ in Hz is:'), f_s,)\n",
    "print('The Nyquist frequency is ', 1/2/T, 'Hz.')\n",
    "print('The actual signal frequency is ', f_0, 'Hz.')\n",
    "k = np.arange(0,N)\n",
    "t = np.arange(0, T_0, 0.01*T)\n",
    "kt = k*T\n",
    "plt.plot(t, np.cos(2*np.pi*f_0*t), t, np.cos(2*np.pi*(-f_0 + 1/T)*t),\n",
    "         t, np.cos(2*np.pi*(f_0 + 1/T)*t), kt, np.cos(2*np.pi*f_0*kt),'*')\n",
    "plt.xlabel('t')\n",
    "plt.title('Aliasing Example')\n",
    "plt.legend(['Actual Signal', 'First Alias', 'Second Alias', 'Sample Points'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
