{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.style.use('seaborn-white')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fourier Pairs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\cos(2\\pi f_0 t)\n",
    "\\Longleftrightarrow\n",
    "\\frac{1}{2}\\left[\\delta(f - f_0) + \\delta(f + f_0)\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sin(2\\pi f_0 t)\n",
    "\\Longleftrightarrow\n",
    "\\frac{1}{2i}\\left[\\delta(f - f_0) - \\delta(f + f_0)\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{1}{\\sqrt{2\\pi\\sigma_t^2}}e^{-t^2 / (2\\sigma_t^2)}\n",
    "\\Longleftrightarrow\n",
    "e^{-f^2 / (2\\sigma_f^2)};~~~~ \\sigma_f = \\frac{1}{2\\pi\\sigma_t}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\Pi_T(t)\n",
    "\\Longleftrightarrow\n",
    "{\\rm sinc}(fT)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{n=-\\infty}^\\infty \\delta(t - nT)\n",
    "\\Longleftrightarrow\n",
    "\\frac{1}{T} \\sum_{n=-\\infty}^\\infty \\delta(f - n/T)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vX76cli1bqhhR6rl58yY6nY4bN25w48YNPD09MTMzIygoCHh/Qn3q1ClOnTrF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\nah5rWiH4/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cc04da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.font_manager import FontProperties\n",
    "\n",
    "fig, ax = plt.subplots(4, 2, figsize=(10, 6))\n",
    "fig.subplots_adjust(left=0.04, right=0.98, bottom=0.02, top=0.95,\n",
    "                    hspace=0.3, wspace=0.2)\n",
    "\n",
    "x = np.linspace(-5, 5, 1000)\n",
    "\n",
    "for axi in ax.flat:\n",
    "    axi.xaxis.set_major_formatter(plt.NullFormatter())\n",
    "    axi.yaxis.set_major_formatter(plt.NullFormatter())\n",
    "    \n",
    "    # draw center line\n",
    "    axi.axvline(0, linestyle='dotted', color='gray')\n",
    "    axi.axhline(0, linestyle='dotted', color='gray')\n",
    "    \n",
    "style_re = dict(linestyle='solid', color='k', linewidth=2)\n",
    "style_im = dict(linestyle='solid', color='gray', linewidth=2)\n",
    "text_style = dict(size=14, color='gray')\n",
    "\n",
    "    \n",
    "# sine -> delta\n",
    "ax[0, 0].plot(x, np.cos(x),**style_re)\n",
    "ax[0, 0].set(xlim=(-5, 5), ylim=(-1.2, 1.2))\n",
    "ax[0, 0].annotate('', (-np.pi, 0), (np.pi, 0),\n",
    "                  arrowprops=dict(arrowstyle='|-|', color='gray'))\n",
    "ax[0, 0].text(0, 0, '$1/f_0$', ha='center', va='bottom', **text_style)\n",
    "ax[0, 0].set_title('Sinusoid')\n",
    "\n",
    "ax[0, 1].plot([-5, 2, 2, 2, 5], [0, 0, 1, 0, 0], **style_re)\n",
    "ax[0, 1].plot([-5, -2, -2, -2, 5], [0, 0, 1, 0, 0], **style_re)\n",
    "ax[0, 1].set(xlim=(-5, 5), ylim=(-0.2, 1.2))\n",
    "ax[0, 1].annotate('', (0, 0.4), (2, 0.4), arrowprops=dict(arrowstyle='<-', color='gray'))\n",
    "ax[0, 1].annotate('', (0, 0.4), (-2, 0.4), arrowprops=dict(arrowstyle='<-', color='gray'))\n",
    "ax[0, 1].text(1, 0.45, '$+f_0$', ha='center', va='bottom', **text_style)\n",
    "ax[0, 1].text(-1, 0.45, '$-f_0$', ha='center', va='bottom', **text_style)\n",
    "ax[0, 1].set_title('Delta Functions')\n",
    "\n",
    "# gaussian -> gaussian\n",
    "ax[1, 0].plot(x, np.exp(-(2 * x) ** 2), **style_re)\n",
    "ax[1, 0].set(xlim=(-5, 5), ylim=(-0.2, 1.2))\n",
    "ax[1, 0].annotate('', (0, 0.35), (0.6, 0.35), arrowprops=dict(arrowstyle='<-', color='gray'))\n",
    "ax[1, 0].text(0, 0.4, '$\\sigma$', ha='center', va='bottom', **text_style)\n",
    "ax[1, 0].set_title('Gaussian')\n",
    "\n",
    "ax[1, 1].plot(x, np.exp(-(x / 2) ** 2), **style_re)\n",
    "ax[1, 1].set(xlim=(-5, 5), ylim=(-0.2, 1.2))\n",
    "ax[1, 1].annotate('', (0, 0.35), (2, 0.35), arrowprops=dict(arrowstyle='<-', color='gray'))\n",
    "ax[1, 1].text(0, 0.4, '$(2\\pi\\sigma)^{-1}$', ha='center', va='bottom', **text_style)\n",
    "ax[1, 1].set_title('Gaussian')\n",
    "\n",
    "# top hat -> sinc\n",
    "ax[2, 0].plot([-2, -1, -1, 1, 1, 2], [0, 0, 1, 1, 0, 0], **style_re)\n",
    "ax[2, 0].set(xlim=(-2, 2), ylim=(-0.3, 1.2))\n",
    "ax[2, 0].annotate('', (-1, 0.5), (1, 0.5), arrowprops=dict(arrowstyle='<->', color='gray'))\n",
    "ax[2, 0].text(0.0, 0.5, '$T$', ha='center', va='bottom', **text_style)\n",
    "ax[2, 0].set_title('Top Hat')\n",
    "\n",
    "ax[2, 1].plot(x, np.sinc(x), **style_re)\n",
    "ax[2, 1].set(xlim=(-5, 5), ylim=(-0.3, 1.2))\n",
    "ax[2, 1].annotate('', (-1, 0), (1, 0), arrowprops=dict(arrowstyle='<->', color='gray'))\n",
    "ax[2, 1].text(0.0, 0.0, '$2/T$', ha='center', va='bottom', **text_style)\n",
    "ax[2, 1].set_title('Sinc')\n",
    "\n",
    "# comb -> comb\n",
    "ax[3, 0].plot([-5.5] + sum((3 * [i] for i in range(-5, 6)), []) + [5.5],\n",
    "              [0] + 11 * [0, 1, 0] + [0], **style_re)\n",
    "ax[3, 0].set(xlim=(-5.5, 5.5), ylim=(-0.2, 1.2))\n",
    "ax[3, 0].annotate('', (0, 0.5), (1, 0.5), arrowprops=dict(arrowstyle='<->', color='gray'))\n",
    "ax[3, 0].text(0.5, 0.6, '$T$', ha='center', va='bottom', **text_style)\n",
    "ax[3, 0].set_title('Dirac Comb')\n",
    "\n",
    "ax[3, 1].plot([-5.5] + sum((3 * [i] for i in range(-5, 6)), []) + [5.5],\n",
    "              [0] + 11 * [0, 1, 0] + [0], **style_re)\n",
    "ax[3, 1].set(xlim=(-2.5, 2.5), ylim=(-0.2, 1.2));\n",
    "ax[3, 1].annotate('', (0, 0.5), (1, 0.5), arrowprops=dict(arrowstyle='<->', color='gray'))\n",
    "ax[3, 1].text(0.5, 0.6, '$1/T$', ha='center', va='bottom', **text_style)\n",
    "ax[3, 1].set_title('Dirac Comb')\n",
    "\n",
    "for i, letter in enumerate('abcd'):\n",
    "    ax[i, 0].set_ylabel('({0})'.format(letter), rotation=0,\n",
    "                        fontproperties=FontProperties(size=12, style='italic'))\n",
    "\n",
    "# Draw arrows between pairs of axes\n",
    "for i in range(4):\n",
    "    left = ax[i, 0].bbox.inverse_transformed(fig.transFigure).bounds\n",
    "    right = ax[i, 1].bbox.inverse_transformed(fig.transFigure).bounds\n",
    "    x = 0.5 * (left[0] + left[2] + right[0])\n",
    "    y = left[1] + 0.5 * left[3]\n",
    "    fig.text(x, y, r'$\\Longleftrightarrow$',\n",
    "             ha='center', va='center', size=30)\n",
    "\n",
    "fig.savefig('fig03_Fourier_pairs.pdf')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.5",
   "language": "python",
   "name": "python3.5"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}