{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd208a0ecc0>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KyD4R2dfb23upL62WoC7Gdd3Drq+7no7RDr2+ewL9/OzPAXhrfaxwbwdXAXjK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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd2340f0d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RnPNLfN3NRB69KOHN3JO/JrjlHQLHXTmkk8Z92nc+0QPPxffC/+EW/7L/0G+t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\ni4jkCQW+iEieUOCLiOQJBb6ISJ74/5kzHxCs7NwQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd2386f1438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def switch_on(x, x0, slope=20):\n",
    "    \"\"\" \n",
    "    switch from 0 to 1 at x0\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    \n",
    "    slope : float\n",
    "        defines how steep is the switching function\n",
    "    \"\"\"\n",
    "    return 1/( 1+ np.exp(slope*(x-x0)) )\n",
    "\n",
    "def switch_off(x, x0, slope=20):\n",
    "    \"\"\"\n",
    "    switch from 1 to 0 at x0\n",
    "    \"\"\"\n",
    "    \n",
    "    return 1 - switch_on(x, x0, slope)\n",
    "    \n",
    "\n",
    "N = 1000\n",
    "\n",
    "tt = np.linspace(-10, 10, N)\n",
    "tt = np.linspace(0, 3.5, N)\n",
    "\n",
    "# on_off_on\n",
    "\n",
    "yy1 = switch_on(tt, 0.9)\n",
    "\n",
    "yy2 = switch_off(tt, 2.1)\n",
    "\n",
    "yy3 = switch_on(tt, 0.9) + switch_off(tt, 2.1) \n",
    "\n",
    "\n",
    "plt.plot(tt, yy1)\n",
    "plt.plot(tt, yy2)\n",
    "offset = 0.3  # for better visability\n",
    "plt.plot(tt, yy3 + offset)\n",
    "\n",
    "\n",
    "signal = np.sinc(5*(tt - 1.6)) * 100\n",
    "signal_mod = signal * yy3\n",
    "\n",
    "plt.figure()\n",
    "\n",
    "plt.plot(tt, signal, lw=0.2)\n",
    "plt.plot(tt, signal_mod)"
   ]
  }
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