DTSP/Experiments/Exp - 06/6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c0825187123fd814",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#### Problem Statement: Determine Spectrum of a known siganl using DFT and comment on the result obtain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b727f6b7d9a64158",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-11-07T15:07:01.257100617Z",
     "start_time": "2023-11-07T15:07:00.989178374Z"
    }
   },
   "outputs": [],
   "source": [
    "# Importing inbuilt python libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d7d291d2a8eca706",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-11-07T15:07:01.262365684Z",
     "start_time": "2023-11-07T15:07:01.259505275Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n",
      "0.3\n"
     ]
    }
   ],
   "source": [
    "# Sketching gtime domain representation of input signals x1(n),x2(n),x3(n) and joint\n",
    "F1=10\n",
    "F2=30\n",
    "Ft=100\n",
    "f1=np.divide(F1,Ft)\n",
    "f2=np.divide(F2,Ft)\n",
    "print(f1)\n",
    "print(f2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "772de042d4772e51",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-11-07T15:07:01.696594322Z",
     "start_time": "2023-11-07T15:07:01.265912981Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0.5, 0, 'Discrete Time Variable n')"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x400 with 1 Axes>",
      "image/png": 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NsGDBAlRWVqJPnz4YMmQIhgwZggceeABCiBr/GK1vQ4cORVRUFH777TeT61966SUAd++K1q9fP4wfPx4PPvggFixYgHnz5tmkxn79+uGtt95CXl4e+vbti65du2LMmDEYNmwYunTpgtatW2Px4sU2qUVm4sSJ6NGjBwYPHownnngC7du3x+HDh/Hggw8iKSnJYNtx48ahY8eOSE9PR+fOnTFmzBj06NEDsbGxmDlzpsnxY2Ji4O7ujjfffBNDhgzB5MmTMWXKlBobIyEEDh06hJiYGPj6+iI2NhYTJkxAbGwsgoODsXHjRnh4eOBf//qXwTyV2bBhA7y9vfHWW28hNDQU48ePR69evTBp0iR97VVnr+rKxcUFL7zwAiorKxEdHY2YmBg8+eSTaN++PTZu3IhZs2bd1/hERLXFRoiIyISBAwciIyMD48aNw9WrV7Fr1y4UFBTob51d/bK4KkuXLsXrr7+OoKAgHDlyBNnZ2Zg8eTKSk5Pv+4/Iuqg6K2TKhAkT8Pnnn+Mvf/kLsrKy8MUXXyAwMBApKSkYMWKEzWqcPXs2Tp06hQkTJqC4uBh79+7FiRMn4OTkhOnTp+Ozzz6zWS2mrF27FitWrMDly5fx2WefQaVSYdasWTh+/LjRZYUeHh44cuQIxo0bh7KyMhw4cAA6nQ47d+6U/pEfGBiIzz77DH/5y1+QlpaGDz74AO+//770dt5VwsLCcOTIETz//PPo0KEDLly4gI8//hjp6ekIDAzE3LlzceHCBZO3OjelY8eOOHXqFMaMGYOCggJ97vv379dfOteyZUuLxjJn0aJF+PDDD/HQQw/h66+/xuHDh9G1a1ecPHmyXm4hT0RUGyrB27MQEREZaNu2LS5fvsw7mAGYMWMGNm7ciB07duCJJ56wdzlERPWGZ4SIiIgcXHl5OS5evGi0/JNPPsF7770HjUaDoUOH2qEyIiLr4e2ziYiIHNzNmzcRGhqKTp06oUOHDnB1dcXFixdx8eJFODk5Yf369Wa/lJWIqCHiGSEiIiIHp9Fo8Nxzz8HNzQ1paWnYu3cvfvnlF8TFxSE1NRXjx4+3d4lERPWOnxEiIiIiIiKHY9UzQseOHcPw4cMRGBgIlUqFTz/91GC9EAJLly5FYGAgPDw80L9/f1y4cMGaJREREREREVm3Ebp16xa6du2KdevWmVy/cuVKrFq1CuvWrUNGRgb8/f0xaNAglJWVWbMsIiIiIiJycDa7NE6lUmHPnj0YOXIkgLtngwIDA5GQkICFCxcCACoqKuDn54fXXnsN06ZNs2hcnU6H69evw9PTEyqVylrlExERERGRwgkhUFZWhsDAQDg5mT/nY7e7xuXm5qKgoAAxMTH6ZWq1GtHR0UhPT7e4Ebp+/TqCg4OtVSYRERERETUweXl5CAoKMruN3RqhgoICAICfn5/Bcj8/P1y+fFn6vIqKClRUVOgfV53QysvLg5eXlxUqtQ6tTiDmzVT8t7Si5o3voQLg66XGoXnRcHZqfGfBmI0cs5FjNnLMRs6SbJxUgE5y7QTzkWM2csxGjtnINfZs6ktpaSmCg4Ph6elZ47Z2/x6hey9nE0KYvcRtxYoVSEpKMlru5eXVoBqhE//7C36ucIaTukmdnv9zBfCfXyrR888t67ky+2M2csxGjtnIMRs5S7Mxd3EF85FjNnLMRo7ZyDXmbOqbJR+Zsdv3CPn7+wP448xQlcLCQqOzRNW99NJLKCkp0f/Ly8uzap3WUlhWrogxlIjZyDEbOWYjx2zk6mu/mI91x1AiZiPHbOSYjbLYrREKCQmBv78/kpOT9cvu3LmD1NRU9OrVS/o8tVqtP/vT0M4CVefr6a6IMZSI2cgxGzlmI8ds5Oprv5iPdcdQImYjx2zkmI2yWLUR+vXXX5GVlYWsrCwAd2+QkJWVhStXrkClUiEhIQGvvPIK9uzZg+zsbDz99NNo0qSJQ3yDdVSINwI07qjLFZ4qAAEad0SFeNd3WYrAbOSYjRyzkWM2cpZk46SCdD3zkWM2csxGjtnINfZs7MGqjdA333yD8PBwhIeHAwDmz5+P8PBwLFmyBADwwgsvICEhATNnzkRkZCSuXbuGQ4cOWfThpobO2UmFxOGhAIzfYFWS/67+OHF4aKP9oByzkWM2csxGjtnI1ZSNCsDUviHS9YBj52Pqv6s/ZjbMhtkYYjbKYrPvEbKW0tJSaDQalJSUNMjL5A5m5yNx7wWDu4cEaNz1B4ls3eCwAJvXamvMRo7ZyDEbOWYjZy6bwWEBNa5v7Dh35JiNHLORYzbWU5vegI2QApSV/44uSw8BALY88zD6dviTvts3t84RMBs5ZiPHbOSYjVxN+898OHdkmI0cs5FjNtZRm97AbjdLoD9Un9hRId4Gj82tcwTMRo7ZyDEbOWYjV9P+Mx/OHRlmI8ds5JiN/dn9e4QcgVYncDq3CIVl5fD1dK+3CW2tcW3NGvvBbGw7pj0wGzlmI8fXYzlmYx6PKzlmI8dslI2NkJUdzM5H0r4c5Jf8cc/3+rjO01rj2po19oPZ2HZMe2A2csxGjq/HcszGPB5XcsxGjtkoHy+Ns6KD2fmYsfWMwWQFgIKScszYegYHs/MVNa6tWWM/mI1tx7QHZiPHbOT4eizHbMzjcSXHbOSYTcPARshKtDqBpH05MHUniqplSftyoNXV7l4V1hrX1qyxH8zGtmPaA7ORYzZyfD2WYzbm8biSYzZyzKbhYCNkJadzi4w69uoEgPyScpzOLVLEuLZm6X5kXi6u9zGZjXxMZiMfk9nIx3TEbGozrpLz4XuVeTyu5JiNHLNpONgIWUlhmXyy1mU7a49ra5bW93NZRc0b1XJMZnP/29kLs5FjNnLWyKY24yo5H75XmcfjSo7ZyDGbhoONkJX4errX63bWHtfWLK3vT57qeh+T2dz/dvbCbOSYjZw1sqnNuErOh+9V5vG4kmM2csym4WAjZCVRId4I0LhDdjNDFe7e5SMqxFsR49qapfsR0aZFvY/JbORjMhv5mMxGPqYjZlObcZWcD9+rzONxJcds5JhNw8FGyEqcnVRIHB4KAEaTtupx4vDQWt/33Vrj2po19oPZ2HZMe2A2csxGjq/HcszGPB5XcsxGjtk0HGyErGhwWAA2TOwOXy/DU5/+GndsmNi9zvd7t9a4tmaN/WA2th3THpiNHLOR4+uxHLMxj8eVHLORYzYNA79Q1coGhwWgd3sfdFl6CACw5ZmH0bfDn+67Y7fWuLZmjf1gNrYd0x6YjRyzkePrsRyzMY/HlRyzkWM2ysczQjZQfXJGhXjX22S11ri2Zo39YDa2HdMemI0cs5Hj67EcszGPx5Ucs5FjNsrGRoiIiIiIiBwOGyEiIiIiInI4bISIiIiIiMjhsBEiIiIiIiKHw0aIiIiIiIgcDhshIiIiIiJyOGyEiIiIiIjI4SjiC1XXr1+P119/Hfn5+XjwwQexevVq9O3b195l1YpWJ3A6twiFZeXw9XS3+33dlVSPkmphPQ2nFqXVo6RaWE/DqUVp9SipFqXVo6RaWE/DqUVp9SiplobA7o3Qzp07kZCQgPXr16N379545513MGTIEOTk5KB169b2Ls8iB7PzkbQvB/kl5fplARp3JA4PxeCwAIeuR0m1sJ6GU4vS6lFSLayn4dSitHqUVIvS6lFSLayn4dSitHqUVEtDYfdL41atWoXJkydjypQp6Ny5M1avXo3g4GBs2LDB3qVZ5GB2PmZsPWMw6QCgoKQcM7aewcHsfIetR0m1sJ6GU4vS6lFSLayn4dSitHqUVIvS6lFSLayn4dSitHqUVEtDYtczQnfu3EFmZiZefPFFg+UxMTFIT0+3U1WW0+oEkvblQACAEFBr7xisVwFYsfsses7pDXVlBQBAd/s2dJWGsevuVErX12bd73ecsWL3Wbj9/2X3qqpnYFsvq58m1eqExbXoKrX1sv8NJRvA8nzMzR1mw2xk9dgiG12lS62Oc6W85tQ1m5rWK3nu1Ec2QOM8rvheZZ6SXnOYTcPIRuXhAZWq4VyKpxJCCHv98OvXr6NVq1b4+uuv0atXL/3yV155BR9++CG+++47o+dUVFSgouKPX3RpaSmCg4NRUlICLy8vm9Rd5cT//oJx754EAKgrK/Dp/sU2/flERERERErR8UwmnJo0sWsNpaWl0Gg0FvUGdr80DoBR5yiEkHaTK1asgEaj0f8LDg62RYkmFZaV17wREREREZEDuH2n0t4l1IpdL43z8fGBs7MzCgoKDJYXFhbCz8/P5HNeeuklzJ8/X/+46oyQPfh6uuv/u8LZDSOHLTe53ZZnotAjxNvq9ZzKLcLTm0/XuN07kyIw7d+ZAIDMlx9BE7c/psHtO5WI+H+H73vd+WulFtXiCNmYWq+kfKydTU3rG0M2W56JQpdWXvVy7DSUbAC+5pjDbOSYjRzfq+T4XiWnpPeqMx4e979DNmTXRsjNzQ0RERFITk7GqFGj9MuTk5MRFxdn8jlqtRpqtdpWJZoVFeKNAI07CkrKIVQqVLgY1qUC4K9xR1TnVnCywfWqUZ094N1Sc7ceE+ur6onoGIgKl2wAgFOTJnCqNpmdXCr1+3E/66I6e1pUiyNkY2q9kvKxdjY1rW8M2UR1boWKSm29HDsNJRuArznmMBs5ZiPH9yo5vlfJKem9qiF9PghQwKVx8+fPx3vvvYcPPvgAFy9exLx583DlyhVMnz7d3qXVyNlJhcThoQDuTrLqqh4nDg+12f3blVSPkmphPQ2nFqXVo6RaWE/DqUVp9SipFqXVo6RaWE/DqUVp9SiplobG7o3QE088gdWrV2PZsmXo1q0bjh07hgMHDqBNmzb2Ls0ig8MCsGFid/hr3A2W+2vcsWFid5vft11J9SipFtbTcGpRWj1KqoX1NJxalFaPkmpRWj1KqoX1NJxalFaPkmppSOz+haoAMHPmTMycOdPeZdTZ4LAADAr1V8w3+SqpHiXVwnoaTi1Kq0dJtbCehlOL0upRUi1Kq0dJtbCehlOL0upRUi0NhSIaocbA2UmFnn9uae8y9JRUj5JqAViPOUqqBVBWPUqqBWA95iipFkBZ9SipFkBZ9SipFoD1mKOkWgBl1aOkWhoCu18aR0REREREZGtshIiIiIiIyOGwESIiIiIiIofDRoiIiIiIiBwOGyEiIiIiInI4bISIiIiIiMjhsBEiIiIiIiKHw0bIAWl1Qv/fp3OLDB4raUx7sNZ+NIZ8mI15PK7kmI0cs5FjNnJ8PZZjNubxuDLERsjBHMzOxyOrUvWPn96cgT6vpeBgdr6ixrQHa+1HY8iH2ZjH40qO2cgxGzlmI8fXYzlmYx6PK2NshBzIwex8zNh6Bv8trTBYXlBSjhlbz9Rp0lpjTHuw1n40hnyYjXk8ruSYjRyzkWM2cnw9lmM25vG4Mo2NkIPQ6gSS9uXA1MnKqmVJ+3JqdTrTGmPag7X2ozHkw2zM43Elx2zkmI0cs5Hj67EcszGPx5UcGyEHcTq3CPkl5dL1AkB+STkyLxfX+5inc4tqUantWSOb2oyr5HyYjXk8ruSYjRyzkWM2cnw9lmM25vG4kmMj5CAKy+STtbqfyypq3qiWY1q6nb1YI5vajKvkfJiNeTyu5JiNHLORYzZyfD2WYzbm8biSYyPkIHw93S3a7k+e6nof09Lt7MUa2dRmXCXnw2zM43Elx2zkmI0cs5Hj67EcszGPx5UcGyEHERXijQCNO1SS9SoAARp3RLRpUe9jRoV417Ja27JGNrUZV8n5MBvzeFzJMRs5ZiPHbOT4eizHbMzjcSXHRshBODupkDg8FACMJm3V48ThoXB2kk1p24xpD9baj8aQD7Mxj8eVHLORYzZyzEaOr8dyzMY8HldybIQcyOCwAGyY2B3+GsPTlP4ad2yY2B2DwwIUMaY9WGs/GkM+zMY8HldyzEaO2cgxGzm+HssxG/N4XJnmYu8CyLYGhwVgUKg/TucWobCsHL6ed09b3k/Hbo0x7cFa+9EY8mE25vG4kmM2csxGjtnI8fVYjtmYx+PKGBshB+TspELPP7c0ua76/d5P5xahb4c/6SezuXXmxmxIrJFNTeM2FHXNpqb1jSEbgMeVOcxGjtnIMRs5vlfJ8b3KPB5XhlRCCGV/01ENSktLodFoUFJSAi8vL3uX06AdzM5H4t4LBt8QHKBx118DKlvXEE593i9mI2cum8FhATWub+w4d+SYjRyzkWM2csxGju9V5jWmuVOb3sCqjdDy5cvx+eefIysrC25ubrh586bRNleuXMGsWbOQkpICDw8PjB8/Hv/85z/h5uZm0c9gI1Q/DmbnY8bWM0bfEKwCTH5rcNU6AA3mOtC6YjZy5rIBgL/3C8GmY7nS9Y6cD+cOs5FhNnLMRo7ZyPG9yrzGNndq0xtY9WYJd+7cweOPP44ZM2aYXK/VajF06FDcunULaWlp2LFjBz755BM899xz1iyL7qHVCSTtyzE52c11yVXrkvblGJwybUyYjVxN2QgA7x43fmOpWg84dj4yzEaO2cgxGzlmI8ds+F7l6HPHqo1QUlIS5s2bhy5duphcf+jQIeTk5GDr1q0IDw/HI488gjfeeAPvvvsuSktLrVkaVXM6twj5JXX75l8BIL+kHKdzi+q3KIVgNnKWZGPutZH5yDEbOWYjx2zkmI0cs+F7lSPPHbvePvvEiRMICwtDYGCgfllsbCwqKiqQmZlpx8ocS2FZ3Q6A+h5DiZiNXH3tF/Ox7hhKxGzkmI0cs5FjNnJ8rzLP0eeOXe8aV1BQAD8/P4NlLVq0gJubGwoKCkw+p6KiAhUVf3xYi2eO7p+vp3vNG9lgDCViNnL1tV/Mx7pjKBGzkWM2csxGjtnI8b3KPEefO7VuhJYuXYqkpCSz22RkZCAyMtKi8VQq4/uMCyFMLgeAFStWmPz5bIjqrlNLF/xJrUVhaYXZ60FNUQHw9VKjU0uXRvk7YDZylmTjpAKEMH2dMfORYzZyzEaO2cgxGzlmw/eqxjZ3qmqx5H5wtb5r3I0bN3Djxg2z27Rt2xbu7n90h1u2bEFCQoLRXeOWLFmCzz77DOfOndMvKy4uhre3N1JSUvDXv/7VaOx7zwhdu3YNoaGhtdkFIiIiIiJqxPLy8hAUFGR2m1qfEfLx8YGPj0+di6quZ8+eWL58OfLz8xEQcPfWe4cOHYJarUZERITJ56jVaqjVav3jZs2aIS8vD56entKzSLZSWlqK4OBg5OXl8VbeVCucO1QXnDdUF5w3VFecO1QXtp43QgiUlZUZ3INAxqqfEbpy5QqKiopw5coVaLVaZGVlAQDat2+PZs2aISYmBqGhoZg0aRJef/11FBUVYcGCBZg6darFQTk5OdXY7dmal5cXXyCoTjh3qC44b6guOG+orjh3qC5sOW80Go1F21m1EVqyZAk+/PBD/ePw8HAAwNGjR9G/f384Ozvj888/x8yZM9G7d2+DL1QlIiIiIiKyFqs2Qlu2bMGWLVvMbtO6dWvs37/fmmUQEREREREZsOv3CDU2arUaiYmJBp9hIrIE5w7VBecN1QXnDdUV5w7VhZLnTa3vGkdERERERNTQ8YwQERERERE5HDZCRERERETkcNgIERERERGRw2EjREREREREDoeNUD1av349QkJC4O7ujoiICBw/ftzeJZGCrFixAg8//DA8PT3h6+uLkSNH4rvvvjPYRgiBpUuXIjAwEB4eHujfvz8uXLhgp4pJiVasWAGVSoWEhAT9Ms4bMuXatWuYOHEiWrZsiSZNmqBbt27IzMzUr+e8IVMqKyvx8ssvIyQkBB4eHmjXrh2WLVsGnU6n34Zzh44dO4bhw4cjMDAQKpUKn376qcF6S+ZIRUUF5syZAx8fHzRt2hQjRozA1atXbbgXbITqzc6dO5GQkIDFixfj7Nmz6Nu3L4YMGYIrV67YuzRSiNTUVMyaNQsnT55EcnIyKisrERMTg1u3bum3WblyJVatWoV169YhIyMD/v7+GDRoEMrKyuxYOSlFRkYGNm3ahIceeshgOecN3au4uBi9e/eGq6srvvjiC+Tk5OCNN95A8+bN9dtw3pApr732GjZu3Ih169bh4sWLWLlyJV5//XWsXbtWvw3nDt26dQtdu3bFunXrTK63ZI4kJCRgz5492LFjB9LS0vDrr79i2LBh0Gq1ttoNQFC9iIqKEtOnTzdY1qlTJ/Hiiy/aqSJSusLCQgFApKamCiGE0Ol0wt/fX7z66qv6bcrLy4VGoxEbN260V5mkEGVlZaJDhw4iOTlZREdHi7lz5wohOG/ItIULF4o+ffpI13PekMzQoUPF3/72N4Nlo0ePFhMnThRCcO6QMQBiz549+seWzJGbN28KV1dXsWPHDv02165dE05OTuLgwYM2q51nhOrBnTt3kJmZiZiYGIPlMTExSE9Pt1NVpHQlJSUAAG9vbwBAbm4uCgoKDOaRWq1GdHQ05xFh1qxZGDp0KB555BGD5Zw3ZMrevXsRGRmJxx9/HL6+vggPD8e7776rX895QzJ9+vTBkSNH8P333wMAzp07h7S0NDz66KMAOHeoZpbMkczMTPz+++8G2wQGBiIsLMym88jFZj+pEbtx4wa0Wi38/PwMlvv5+aGgoMBOVZGSCSEwf/589OnTB2FhYQCgnyum5tHly5dtXiMpx44dO3DmzBlkZGQYreO8IVMuXbqEDRs2YP78+Vi0aBFOnz6NZ599Fmq1Gk899RTnDUktXLgQJSUl6NSpE5ydnaHVarF8+XKMGzcOAF9zqGaWzJGCggK4ubmhRYsWRtvY8m9nNkL1SKVSGTwWQhgtIwKA2bNn49tvv0VaWprROs4jqi4vLw9z587FoUOH4O7uLt2O84aq0+l0iIyMxCuvvAIACA8Px4ULF7BhwwY89dRT+u04b+heO3fuxNatW7F9+3Y8+OCDyMrKQkJCAgIDAxEfH6/fjnOHalKXOWLrecRL4+qBj48PnJ2djTrYwsJCo26YaM6cOdi7dy+OHj2KoKAg/XJ/f38A4DwiA5mZmSgsLERERARcXFzg4uKC1NRUrFmzBi4uLvq5wXlD1QUEBCA0NNRgWefOnfU38OHrDck8//zzePHFF/Hkk0+iS5cumDRpEubNm4cVK1YA4NyhmlkyR/z9/XHnzh0UFxdLt7EFNkL1wM3NDREREUhOTjZYnpycjF69etmpKlIaIQRmz56N3bt3IyUlBSEhIQbrQ0JC4O/vbzCP7ty5g9TUVM4jBzZw4ECcP38eWVlZ+n+RkZGYMGECsrKy0K5dO84bMtK7d2+j2/N///33aNOmDQC+3pDc7du34eRk+Oehs7Oz/vbZnDtUE0vmSEREBFxdXQ22yc/PR3Z2tm3nkc1uy9DI7dixQ7i6uor3339f5OTkiISEBNG0aVPx008/2bs0UogZM2YIjUYjvvrqK5Gfn6//d/v2bf02r776qtBoNGL37t3i/PnzYty4cSIgIECUlpbasXJSmup3jROC84aMnT59Wri4uIjly5eLH374QWzbtk00adJEbN26Vb8N5w2ZEh8fL1q1aiX2798vcnNzxe7du4WPj4944YUX9Ntw7lBZWZk4e/asOHv2rAAgVq1aJc6ePSsuX74shLBsjkyfPl0EBQWJw4cPizNnzogBAwaIrl27isrKSpvtBxuhevT222+LNm3aCDc3N9G9e3f9bZGJhLh7e0lT/zZv3qzfRqfTicTEROHv7y/UarXo16+fOH/+vP2KJkW6txHivCFT9u3bJ8LCwoRarRadOnUSmzZtMljPeUOmlJaWirlz54rWrVsLd3d30a5dO7F48WJRUVGh34Zzh44ePWryb5r4+HghhGVz5LfffhOzZ88W3t7ewsPDQwwbNkxcuXLFpvuhEkII251/IiIiIiIisj9+RoiIiIiIiBwOGyEiIiIiInI4bISIiIiIiMjhsBEiIiIiIiKHw0aIiIiIiIgcDhshIiIiIiJyOGyEiIiIiIjI4bARIiIiIiIih8NGiIiIiIiIHA4bISIiIiIicjhshIiIiIiIyOGwESIiIiIiIofzf+DgaG0QUo2mAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x400 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x400 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x400 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=np.arange(0,100)\n",
    "x1=10*np.sin(2*np.pi*f1*n)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(4,1,1)\n",
    "plt.stem(n,x1)\n",
    "plt.title(\"Your Name Input Signal\",fontsize=15)\n",
    "x2=5*np.sin(2*np.pi*f2*n)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(4,1,2)\n",
    "plt.stem(n,x2)\n",
    "x3=3*np.random.normal(0,1,100)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(4,1,3)\n",
    "plt.stem(n,x3)\n",
    "plt.ylabel('Amplitude',fontsize=12)\n",
    "x=np.add(x1,x2,x3)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(4,1,4)\n",
    "plt.stem(n,x)\n",
    "plt.xlabel('Discrete Time Variable n',fontsize=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "249e7fec23e13e5a",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-11-07T15:07:01.836017595Z",
     "start_time": "2023-11-07T15:07:01.696273261Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0.5, 1.0, 'Your Name Spectrum')"
     },
     "execution_count": 4,
     "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"
    }
   ],
   "source": [
    "# Spectrum visualization of joint sinusoidial\n",
    "X=np.fft.fft(x)\n",
    "X_mag = abs(X)\n",
    "plt.stem(X_mag)\n",
    "plt.xlabel('Discrete Frequence k',fontsize=12)\n",
    "plt.ylabel('Amplitude',fontsize=12)\n",
    "plt.title(\"Your Name Spectrum\",fontsize=15)"
   ]
  }
 ],
 "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}