{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frequency Translation\n",
    "\n",
    "A bandpass signal is a narrow band signal centered at a frequency, $f_c$.  Bandpass signals occur often in communications systems, especially wireless communications.  This is because we have only a limited amount of baseband spectrum that we must all share.  The most common way of getting around this problem is to move the baseband signal up so it is centered on the carrier frequency, $f_c$.  Moving it up and down involves frequency shifting.  That is the topic of this notebook.  \n",
    "\n",
    "Often we wish to move a bandpass  into the computer.  Getting an A/D converter with a sufficient sampling rate for that signal is expensive.  The solution is to move the frequency down to baseband.  How can we do frequency translation?  In the frequency domain, frequency translation is rather obvious.  Shifting a specturm, $X(f)$ up $f_c$ Hz would just be $X(f-f_c)$.  What is it in time?  $$ \\mathscr {F^{-1}} [X(f-f_c)] = \\int_{-\\infty}^{\\infty} X(f-f_c) e^{j2\\pi ft} df$$  Let's make a substitition, $u = f-f_c$.  This gives us $$\\mathscr {F^{-1}} [X(f-f_c)] = \\int_{-\\infty}^{\\infty} X(u) e^{j2\\pi (u+f_c) t} du = e^{j2\\pi f_ct} \\int_{-\\infty}^{\\infty} X(u) e^{j2\\pi (u) t} du = e^{j2\\pi f_ct} [\\mathscr {F^{-1}} [X(f)]] = e^{j2\\pi f_ct} x(t)$$  From this we see that frequency shifts can be achieved by multiplying by $e^{j2\\pi f_ct}$.  This looks rather easy, but how do we multiply a real signal, $x(t)$ by a complex function of frequency and time?  How about if we multiply by $cos(2\\pi f_c t + \\theta) = 1/2[e^{j2\\pi f_ct+\\theta} + e^{-j2\\pi f_ct+\\theta}]$?  This makes two \"half  copies\" of $X(f)$ and moves one up $f_c$ and the other down $f_c$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the discrete domain, you can do this too, but the frequency shift must be a sample frequency.  $$X(n-m) = \\sum_{k=0}^{N-1} x(k) e^{-j2\\pi (n-m)k/N} = \\sum_{k=0}^{N-1} [x(k)e^{j2\\pi mk/N}]$$  The last sum is recognized as the $DFT[x(k)e^{j2\\pi mk/N}]$.  This means that shifting a signal $m$ points up in frequency is done by multiplying by $e^{j2\\pi mk/N}$.  A demo of this is seen below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "N = 105  # Needs to be odd, to make x(t) a real number\n",
    "T = 1/8000\n",
    "\n",
    "m = np.arange(-N/2, N/2)\n",
    "n = np.arange(0, N)\n",
    "f = 1/N/T*m\n",
    "t = n*T\n",
    "X = np.concatenate((np.zeros(np.int(N/2)-3),[1, 2, 3, 4, 4, 3, 2, 1], np.zeros(np.int(N/2)-4)),0)\n",
    "x = np.fft.ifft(X)\n",
    "plt.plot(t,np.real(x), t, np.imag(x))\n",
    "plt.title('IDFT of X');\n",
    "plt.xlabel('t (s)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the signal $x(t)$ is large at the beginning and end of the period.  This can lead to unexpected results if somehow your signal has frequencies that are not exactly on the sample frequencies, as would happen when you shift to a frequency not equal to a sample point.  If you must have frequencies that are not sample frequencies, then it would give better results if you use fftshift to delay the signal so the signal is small at the beginning and end of the sampling interval.  In general it is best to have sample points at all the frequencies you have.  This happens naturally if you have a periodic signal.  There are comments in the code below showing how you can investigate this if you like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "#x = np.fft.fftshift(x)\n",
    "plt.plot(f, X)\n",
    "plt.title('Original Frequency Spectra (all Real in this case)')\n",
    "plt.xlabel('f (Hz)')\n",
    "plt.show()\n",
    "plt.plot(t, np.real(x),t,np.imag(x))\n",
    "plt.title('Time for Original Signal')\n",
    "plt.xlabel('t (s)')\n",
    "plt.show()\n",
    "f_c = np.int(N/2)/4/T/N  # Note: This must be one of the frequencies sampled for no distortion.\n",
    "# It is interesting to change this to be a non sampled frequency and see what happens.  The \n",
    "# results are disturbing.  They can be made better by uncommenting x = np.fft.fftshift(x)\n",
    "# at the beginning of this cell.\n",
    "#xs = x*np.exp(np.complex(0,1)*2*np.pi*f_c*t)  # To test shifting only one way.\n",
    "x = np.real(x)  # It is real, but now make it real we get no warning from the plot.\n",
    "xs = x*np.cos(2*np.pi*f_c*t)\n",
    "Xs = np.fft.fftshift(np.fft.fft(xs))\n",
    "plt.plot(f, np.abs(Xs), f, np.real(Xs), '.', f, np.imag(Xs), '.')\n",
    "plt.title('Cosine Shifted Frequency Spectra')\n",
    "plt.xlabel('f (Hz)')\n",
    "plt.legend(['Magnitude','Real Part','Imaginary Part']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how using the fftshift is so important.  The two spectra that come from each frequency of $cos(2\\pi f_c t)$. If you don't want distortion from  leakage, you need to make sure th frequency shift. $f_c$ is one of the sample frequencies.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.  It isn't easy to do a multiplication of $x(t)$ by $cos(2\\pi f_c t)$ in analog electronics, so the most common way of shifting frequency is to multiply $x(t)$ by $sgn(cos(2\\pi f_c t))$, a square wave with fundamental frequency $f_c$.  The $sgn(t)$ function is one for $t>0$, negative one for $t<0$, and zero for $t=0$. The circuit that does this is called a doubly balanced mixer, and is often implimented with voltage controlled switches.  What is the frequency spectra (up to $10 f_c$) of this mixed signal, $x(t) sgn(cos(2\\pi f_c t))$?  We used this concept in the WWU Vector Network Analyzer.  You could easily make code to do this problem."
   ]
  },
  {
   "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"
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 "nbformat": 4,
 "nbformat_minor": 4
}
