DTSP/Experiments/Exp - 02/2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "506cd7b9",
   "metadata": {},
   "source": [
    "#### Problem Statement: Write a code to implement linear convolution x(n) & h(n)"
   ]
  },
  {
   "cell_type": "code",
   "id": "3295391a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-28T22:19:12.783130Z",
     "start_time": "2024-04-28T22:19:12.780882Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "execution_count": 3
  },
  {
   "cell_type": "code",
   "id": "00c67071",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-28T22:19:23.612884Z",
     "start_time": "2024-04-28T22:19:12.786420Z"
    }
   },
   "source": [
    "x = eval(input(\"Enter first sequence x(n) = \"))\n",
    "h = eval(input(\"Enter second sequence h(n) = \"))\n",
    "print(\"x(n) = \",x)\n",
    "print(\"h(n) = \",h)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x(n) =  (1, 2, 3, 4)\n",
      "h(n) =  (1, 2, -1)\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "code",
   "id": "cd7c3d50",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-28T22:19:23.633578Z",
     "start_time": "2024-04-28T22:19:23.619859Z"
    }
   },
   "source": [
    "L = len(x)\n",
    "M = len(h)\n",
    "N = L + M - 1\n",
    "print(\"Length is: \",N)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length is:  6\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "code",
   "id": "b170569d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-28T22:19:23.648115Z",
     "start_time": "2024-04-28T22:19:23.636428Z"
    }
   },
   "source": [
    "#Zero Padding sequence of x(n) & h(n)\n",
    "xp = np.append(x,np.zeros(N-L))\n",
    "hp = np.append(h,np.zeros(N-M))\n",
    "print(xp)\n",
    "print(hp)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 2. 3. 4. 0. 0.]\n",
      "[ 1.  2. -1.  0.  0.  0.]\n"
     ]
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "code",
   "id": "27acfa78",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-28T22:19:23.658205Z",
     "start_time": "2024-04-28T22:19:23.651438Z"
    }
   },
   "source": [
    "#Implementation of Convolution sum\n",
    "Y = np.zeros(N)\n",
    "y = np.zeros(N)\n",
    "for n in range(N):\n",
    "    for k in range(N):\n",
    "        if n >= k:\n",
    "            y[n]+= hp[k] * xp[n-k]\n",
    "            Y = y\n",
    "\n",
    "print(Y)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  4.  6.  8.  5. -4.]\n"
     ]
    }
   ],
   "execution_count": 7
  },
  {
   "cell_type": "code",
   "id": "2a5f2956",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-28T22:19:23.843950Z",
     "start_time": "2024-04-28T22:19:23.659416Z"
    }
   },
   "source": [
    "plt.stem(Y,linefmt = 'red')\n",
    "plt.xlabel('Discrete Time Variable n',fontsize = 15)\n",
    "plt.ylabel('Convolution Sum',fontsize = 15)\n",
    "plt.title('Your Name', fontsize = 12)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Your Name')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 8
  },
  {
   "cell_type": "code",
   "id": "9276cb71",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-28T22:19:23.850489Z",
     "start_time": "2024-04-28T22:19:23.845261Z"
    }
   },
   "source": [
    "#Verification through inbuilt syntax\n",
    "P = np.convolve(x,h)\n",
    "P"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  4,  6,  8,  5, -4])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 9
  },
  {
   "cell_type": "code",
   "id": "1fb581c8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-04-28T22:19:23.866427Z",
     "start_time": "2024-04-28T22:19:23.851813Z"
    }
   },
   "source": [
    "#Summation of sequences\n",
    "X = np.sum(x)\n",
    "H = np.sum(h)\n",
    "W = np.sum(y)\n",
    "print(X)\n",
    "print(H)\n",
    "\n",
    "#Verification\n",
    "W = X * H\n",
    "print(W)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "2\n",
      "20\n"
     ]
    }
   ],
   "execution_count": 10
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}