4. convolution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6b967200",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f2f93678",
   "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": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD4CAYAAAD8Zh1EAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAQv0lEQVR4nO3df2zcd33H8ed7jlvMj9UTsUbjpKQTVaZCKV6t0q7SVMGQC6to1BU1RSsUMaVCMGCqMhH+KBPSFFAmRkURXdR2tKwqnUqUZSjMq1SkwgRtnR8QmhAp6qCNE1TT4hTGAUn23h93aW3Xzp3js7/nzz0fkpW7z/fj+770zd3L5+/3e/5GZiJJWv5+r+oAkqT2sNAlqRAWuiQVwkKXpEJY6JJUiBVVrXjlypW5du3aqlYvScvS7t27f56ZA7Mtq6zQ165dy9jYWFWrl6RlKSJ+Otcyd7lIUiEsdEkqhIUuSYWw0CWpEBa6JBWi6VkuEfEq4DHg3Mb8hzPzMzPmnAvcD1wGPA/cmJk/aXta6Qx27B1n6+ghjk7WWNXfx6aRdawfGqw6lrRkWnmH/lvgHZl5KfA24JqIuGLGnA8Dv8jMNwH/BHy+rSmlJnbsHWfz9v2MT9ZIYHyyxubt+9mxd7zqaNKSaVroWferxt3extfMv7l7HXBf4/bDwDsjItqWUmpi6+ghaidOTRurnTjF1tFDFSWSll5L+9Ajoici9gHPAY9k5uMzpgwCzwJk5kngOPD6WR5nY0SMRcTYxMTEgoJLUx2drM1rXCpRS4Wemacy823AauDyiHjL2awsM7dl5nBmDg8MzPrJVemsrOrvm9e4VKJ5neWSmZPAt4FrZiwaB9YARMQK4DzqB0elJbFpZB19vT3Txvp6e9g0sq6iRNLSa1roETEQEf2N233Au4Afz5i2E/hg4/YNwKPpte20hNYPDbLl+ks4p6f+lB7s72PL9Zd4lou6Sit/nOt84L6I6KH+A+DfMvObEfFZYCwzdwL3AF+LiMPAC8CGRUsszWH90CAPPvEMAA/demXFaaSl17TQM/OHwNAs47dPuf0b4H3tjSZJmg8/KSpJhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCmGhS1IhLHRJKoSFLkmFsNAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSpE00KPiDUR8e2IOBART0XEJ2aZc3VEHI+IfY2v2xcnriRpLitamHMSuC0z90TE64DdEfFIZh6YMe87mXlt+yNKklrR9B16Zh7LzD2N278EDgKDix1MkjQ/89qHHhFrgSHg8VkWXxkRP4iIb0XEm+f4/o0RMRYRYxMTE/NPK0maU8uFHhGvBb4BfDIzX5yxeA/wxsy8FPgSsGO2x8jMbZk5nJnDAwMDZxlZkjSblgo9Inqpl/kDmbl95vLMfDEzf9W4vQvojYiVbU0qSTqjVs5yCeAe4GBmfmGOOW9ozCMiLm887vPtDCpJOrNWznK5CrgZ2B8R+xpjnwYuAMjMu4AbgI9ExEmgBmzIzGx/XEnSXJoWemZ+F4gmc+4E7mxXKEnS/PlJUUkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCmGhS1IhLHRJKoSFLkmFsNAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiFWNJsQEWuA+4E/BBLYlpl3zJgTwB3Ae4BfA7dk5p72x1Un2rF3nK2jhzg6WWNVfx+bRtaxfmiw6liVcXuoKk0LHTgJ3JaZeyLidcDuiHgkMw9MmfNu4KLG19uBrzT+VeF27B1n8/b91E6cAmB8ssbm7fsBurLE3B6qUtNdLpl57PS77cz8JXAQmPnMvA64P+u+D/RHxPltT6uOs3X00EvldVrtxCm2jh6qKFG13B6q0rz2oUfEWmAIeHzGokHg2Sn3j/DK0iciNkbEWESMTUxMzDOqOtHRydq8xkvn9lCVWi70iHgt8A3gk5n54tmsLDO3ZeZwZg4PDAyczUOow6zq75vXeOncHqpSS4UeEb3Uy/yBzNw+y5RxYM2U+6sbYyrcppF19PX2TBvr6+1h08i6ihJVy+2hKjUt9MYZLPcABzPzC3NM2wl8IOquAI5n5rE25lSHWj80yJbrL+GcnvpTabC/jy3XX9K1BwDdHqpSK2e5XAXcDOyPiH2NsU8DFwBk5l3ALuqnLB6mftrih9qeVB1r/dAgDz7xDAAP3XplxWmq5/ZQVZoWemZ+F4gmcxL4aLtCSZLmz0+KSlIhLHRJKoSFLkmFsNAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCtG00CPi3oh4LiJ+NMfyqyPieETsa3zd3v6YkqRmVrQw56vAncD9Z5jzncy8ti2JJElnpek79Mx8DHhhCbJIkhagXfvQr4yIH0TEtyLizXNNioiNETEWEWMTExNtWrUkCdpT6HuAN2bmpcCXgB1zTczMbZk5nJnDAwMDbVi1JOm0BRd6Zr6Ymb9q3N4F9EbEygUnkyTNy4ILPSLeEBHRuH154zGfX+jjSpLmp+lZLhHxIHA1sDIijgCfAXoBMvMu4AbgIxFxEqgBGzIzFy2xJGlWTQs9M29qsvxO6qc1SpIq5CdFJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCmGhS1IhLHRJKoSFLkmFsNAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhVjRbEJE3AtcCzyXmW+ZZXkAdwDvAX4N3JKZe9odVK+0Y+84W0cPcXSyxqr+PjaNrGP90GDVsdQBfG50p1beoX8VuOYMy98NXNT42gh8ZeGx1MyOveNs3r6f8ckaCYxP1ti8fT879o5XHU0V87nRvZoWemY+BrxwhinXAfdn3feB/og4v10BNbuto4eonTg1bax24hRbRw9VlEidwudG92rHPvRB4Nkp9480xl4hIjZGxFhEjE1MTLRh1d3r6GRtXuPqHj43uteSHhTNzG2ZOZyZwwMDA0u56uKs6u+b17i6h8+N7tWOQh8H1ky5v7oxpkW0aWQdfb0908b6envYNLKuokTqFD43ulc7Cn0n8IGouwI4npnH2vC4OoP1Q4Nsuf4Szump/xcO9vex5fpLPJNBPje6WCunLT4IXA2sjIgjwGeAXoDMvAvYRf2UxcPUT1v80GKF1XTrhwZ58IlnAHjo1isrTqNO4nOjOzUt9My8qcnyBD7atkSSpLPiJ0UlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCmGhS1IhLHRJKoSFLkmFaKnQI+KaiDgUEYcj4lOzLL8lIiYiYl/j66/bH1WSdCYrmk2IiB7gy8C7gCPAkxGxMzMPzJj6UGZ+bBEySpJa0Mo79MuBw5n5dGb+Dvg6cN3ixpIkzVcrhT4IPDvl/pHG2Ex/GRE/jIiHI2LNbA8UERsjYiwixiYmJs4iriRpLu06KPofwNrMfCvwCHDfbJMyc1tmDmfm8MDAQJtWLUmC1gp9HJj6jnt1Y+wlmfl8Zv62cfdu4LL2xJMktaqVQn8SuCgiLoyIc4ANwM6pEyLi/Cl33wscbF9ESVIrmp7lkpknI+JjwCjQA9ybmU9FxGeBsczcCXw8It4LnAReAG5ZxMySpFk0LXSAzNwF7JoxdvuU25uBze2NJkmaDz8pKkmFsNAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCmGhS1IhLHRJKsSKViZFxDXAHUAPcHdmfm7G8nOB+4HLgOeBGzPzJ+2NCjv2jrN19BBHJ2us6u9j08g61g8Ntns1yyaH1Ok65bXSLTmaFnpE9ABfBt4FHAGejIidmXlgyrQPA7/IzDdFxAbg88CNbUtJfUNs3r6f2olTAIxP1ti8fT/Akv7HdEoOqdN1ymulm3JEZp55QsSVwN9n5kjj/maAzNwyZc5oY873ImIF8DNgIM/w4MPDwzk2NtZy0Ks+9yjjkzVu/eG/80fHx18aP3dFD0MX9Lf8OAu195lJfnvy1CvGlzrHaQeOvQjAxef//pKv2xydnaPqDJ3yWunEHE+fN8g/v/U6AAb7+/jvT72j5ceJiN2ZOTzbslZ2uQwCz065fwR4+1xzMvNkRBwHXg/8fEaQjcBGgAsuuKCl8KcdnazNOj7bf9Rimmt9S53jtKqL6zRzTNcJOarO0CmvlU7PMVe3nY2W9qG3S2ZuA7ZB/R36fL53VX8f45O1l36qnTbY38eN8/jptlDvb/ymMNNS55A6Xae8Vjo9x6r+vrato5WzXMaBNVPur26MzTqnscvlPOoHR9tm08g6+np7po319fawaWRdO1ezbHJIna5TXivdlKOVd+hPAhdFxIXUi3sD8P4Zc3YCHwS+B9wAPHqm/edn4/RBg6qPVHdKDqnTdcprpZtyND0oChAR7wG+SP20xXsz8x8i4rPAWGbujIhXAV8DhoAXgA2Z+fSZHnO+B0UlSQs/KEpm7gJ2zRi7fcrt3wDvW0hISdLC+ElRSSqEhS5JhbDQJakQFrokFaKls1wWZcURE8BPz/LbVzLjU6hdzu0xndvjZW6L6UrYHm/MzIHZFlRW6AsREWNznbbTjdwe07k9Xua2mK707eEuF0kqhIUuSYVYroW+reoAHcbtMZ3b42Vui+mK3h7Lch+6JOmVlus7dEnSDBa6JBVi2RV6RFwTEYci4nBEfKrqPFWKiDUR8e2IOBART0XEJ6rOVLWI6ImIvRHxzaqzVC0i+iPi4Yj4cUQcbFxOsitFxN82XiM/iogHG38htjjLqtCnXLD63cDFwE0RcXG1qSp1ErgtMy8GrgA+2uXbA+ATwMGqQ3SIO4D/zMw/Bi6lS7dLRAwCHweGM/Mt1P8M+IZqUy2OZVXowOXA4cx8OjN/B3wduK7J9xQrM49l5p7G7V9Sf8F27ZU2ImI18BfA3VVnqVpEnAf8GXAPQGb+LjMnKw1VrRVAX+OKaq8GjlacZ1Est0Kf7YLVXVtgU0XEWuoXGHm84ihV+iLwd8D/VZyjE1wITAD/0tgFdXdEvKbqUFXIzHHgH4FngGPA8cz8r2pTLY7lVuiaRUS8FvgG8MnMfLHqPFWIiGuB5zJzd9VZOsQK4E+Ar2TmEPC/QFcec4qIP6D+m/yFwCrgNRHxV9WmWhzLrdBbuWB1V4mIXupl/kBmbq86T4WuAt4bET+hvivuHRHxr9VGqtQR4Ehmnv6N7WHqBd+N/hz4n8ycyMwTwHbgTyvOtCiWW6G/dMHqiDiH+oGNnRVnqkxEBPV9pAcz8wtV56lSZm7OzNWZuZb68+LRzCzyXVgrMvNnwLMRcfqS8u8EDlQYqUrPAFdExKsbr5l3UugB4pauKdopMvNkRHwMGOXlC1Y/VXGsKl0F3Azsj4h9jbFPN64BK/0N8EDjzc/TwIcqzlOJzHw8Ih4G9lA/M2wvhf4JAD/6L0mFWG67XCRJc7DQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiH+H/aQk0PPOtPiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(10)\n",
    "x = np.heaviside(n-3, 1) - np.heaviside(n-6, 1)\n",
    "Convolution = np.convolve(x, x, 'same')\n",
    "\n",
    "plt.stem(n, x)\n",
    "plt.show()\n",
    "plt.stem(n, Convolution)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8b4fa842",
   "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"
    }
   ],
   "source": [
    "dt = 0.1\n",
    "t = np.arange(0, 10, dt)\n",
    "x = np.heaviside(t-3, 1) - np.heaviside(t-6, 1)\n",
    "Convolution = np.convolve(x, x, 'same')\n",
    "\n",
    "plt.stem(t, x)\n",
    "plt.show()\n",
    "plt.stem(t, Convolution)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a0db792a",
   "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"
    }
   ],
   "source": [
    "dt = 0.1\n",
    "t = np.arange(0, 10, dt)\n",
    "x = np.heaviside(t-3, 1) - np.heaviside(t-6, 1)\n",
    "Convolution = np.convolve(x, x, 'same')*dt\n",
    "\n",
    "plt.plot(t, x)\n",
    "plt.show()\n",
    "plt.plot(t, Convolution)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}