{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Realization of Non-Recursive Filters\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Segmented Convolution\n",
    "\n",
    "In many applications one of the signals of a convolution is much longer than the other. For instance when filtering a speech signal $x_L[k]$ of length $L$ with a room impulse response $h_N[k]$ of length $N \\ll L$. In such cases the [fast convolution](fast_convolution.ipynb), as introduced before, does not bring a benefit since both signals have to be zero-padded to a total length of at least $N+L-1$. Applying the fast convolution may then even be impossible in terms of memory requirements or overall delay. The filtering of a signal which is captured in real-time is also not possible by the fast convolution. \n",
    "\n",
    "In order to overcome these limitations, various techniques have been developed that perform the filtering on limited portions of the signals. These portions are known as partitions, segments or blocks. The respective algorithms are termed as *segmented* or *block-based* algorithms. The following section introduces two techniques for the segmented convolution of signals. The basic concept of these is to divide the convolution $y[k] = x_L[k] * h_N[k]$ into multiple convolutions operating on (overlapping) segments of the signal $x_L[k]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overlap-Add Algorithm\n",
    "\n",
    "The [overlap-add algorithm](https://en.wikipedia.org/wiki/Overlap%E2%80%93add_method) is based on splitting the signal $x_L[k]$ into non-overlapping segments $x_p[k]$ of length $P$\n",
    "\n",
    "\\begin{equation}\n",
    "x_L[k] = \\sum_{p = 0}^{L/P - 1} x_p[k - p \\cdot P]\n",
    "\\end{equation}\n",
    "\n",
    "where the segments $x_p[k]$ are defined as\n",
    "\n",
    "\\begin{equation}\n",
    "x_p[k] = \\begin{cases} x_L[k + p \\cdot P] & \\text{ for } k=0,1,\\dots,P-1 \\\\ 0 & \\text{ otherwise} \\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "Note that $x_L[k]$ might have to be zero-padded so that its total length is a multiple of the segment length $P$. Introducing the segmentation of $x_L[k]$ into the convolution yields\n",
    "\n",
    "\\begin{align}\n",
    "y[k] &= x_L[k] * h_N[k] \\\\\n",
    "&= \\sum_{p = 0}^{L/P - 1} x_p[k - p \\cdot P] * h_N[k] \\\\\n",
    "&= \\sum_{p = 0}^{L/P - 1} y_p[k - p \\cdot P]\n",
    "\\end{align}\n",
    "\n",
    "where $y_p[k] = x_p[k] * h_N[k]$. This result states that the convolution of $x_L[k] * h_N[k]$ can be split into a series of convolutions $y_p[k]$ operating on the samples of one segment only. The length of $y_p[k]$ is $N+P-1$. The result of the overall convolution is given by summing up the results from the segments shifted by multiples of the segment length $P$. This can be interpreted as an overlapped superposition of the results from the segments, as illustrated in the following diagram\n",
    "\n",
    "![Signal flow of overlap-add algorithm](overlap_add.png)\n",
    "\n",
    "The overall procedure is denoted by the name *overlap-add* technique. The convolutions $y_p[k] = x_p[k] * h_N[k]$ can be realized efficiently by the [fast convolution](fast_convolution.ipynb) using zero-padding and fast Fourier transformations (FFTs) of length $M \\geq P+N-1$. \n",
    "\n",
    "A drawback of the overlap-add technique is that the next input segment is required to compute the result for the actual segment of the output. For real-time applications this introduces an algorithmic delay of one segment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example\n",
    "\n",
    "The following example illustrates the overlap-add algorithm by showing the (convolved) segments and the overall result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 80.0, 0.0, 4.0)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uuyzldbt27aply5Zp//79+stf/qKRI0e6jW3iSXp6ujp16qTXXntNXbp00aBBg/TVV18pPDzcdjukkn88lsb5o7Ik06dP1+uvv64ZM2boscce09SpU/X6669bWq+vP5Md6enpJY6btG3bNl122WVuTzg9raO82r979263/9H/6aefVFRUVOw43HnnnRo3bpzeeecdnT59WjVq1HB1mytNTEyMatWqpR9++KHYvF27dqlatWpuXRbvuOMO/fOf/9SqVau0c+dOGWPctmH3vLRj0aJFSk5Odisqkp+fX+r4P972m7Nb6vmcgbOVbcXExKhmzZravXt3sW2fvz+tLueJ3c/u1LBhQ4WHh+unn34qNu/8aXa/B3ZQfhwIfOQ0AUGkZ8+e6tatm1588UXl5+crJCREt956qz744AO3UsdOR48elXTuSdGF3VcaNmyoJk2aqKCgwDUtPj5eOTk5rtwUSTp06FCJZZwv5MzZsTN4Y5cuXVRUVKS7775bxhj9+c9/tvS+wsJC7dy5U1dccYViYmL04Ycfavv27Ro5cqTlbV/IFzlNS5Ys0ZNPPqkpU6YoJSVFDzzwgN58803t3bvXL5/JKue2ExISis377rvvLA1CW97tnzlzptvfr7zyiiS55aRIUoMGDVwDQS9YsEA33nhjsW5LFwoJCdENN9ygpUuXunX3O3LkiN5++211797drXtU7969Va9ePb377rt699131a1bN7fAxOp5WRYhISHFnh688sorpT4N9rbfnN1Sz385g1wr2woJCVGfPn20ZMkS7d+/3zV9586d+uyzz2wv58vPfv77evfurSVLlrjldP7000/65JNP3Jaz8z2woyzXRwAViydNQJB57LHHdNttt2nevHl68MEHNW3aNK1evVpXXXWV7r//frVr107Hjx/Xli1btHLlSh0/flwnTpxQ06ZNNXjwYCUkJCgiIkIrV67Upk2b3P7X9s4779QTTzyhQYMG6eGHH9apU6c0a9YsXXbZZR4TrSUpMTFRkvTnP/9Zd955p2rUqKH+/ft7LIDg7Hr473//W5MmTfJYovx8u3fvVn5+vqsEdmJiombNmqURI0YoMTFRo0ePtrSe811sTtPmzZs1ZMgQDRkyxBX8Pf7445o9e7alp03l8Zmscm77wuDo9OnT+umnn0rtYlbSOsqr/Xv37tUf//hH3XjjjVq/fr3mz5+vu+++u8RAb9iwYRo8eLAkacqUKZbW/8wzz2jFihXq3r27Ro0aperVq2vOnDkqKCjQ888/77ZsjRo1dMstt2jhwoXKy8vTX/7yl2Lrs3JelsXNN9+st956S1FRUWrXrp3Wr1+vlStXqn79+iUub2e/lXVbkydP1qeffqprrrlGo0aN0tmzZ/XKK6+offv2bv8BY3U5X332802aNEmff/65rr76ao0cOVKFhYWaMWOGOnTooLS0NNdydr4HdpTl+giggvmhYh+Ai+QsWbtp06Zi8woLC018fLyJj493lT0+cuSISUlJMc2aNTM1atQwsbGxplevXubVV181xhhTUFBgHnvsMZOQkGDq1KljateubRISEszf//73Yuv//PPPTYcOHUxoaKhp06aNmT9/vqWS48YYM2XKFBMXF2eqVatmufx4y5YtTUxMjDlx4kSJ80sqb/3ee+8ZSeb77793mz5q1ChTo0YNs3bt2mLrsVLeuqwOHDhgGjdubK6++mqTn5/vNm/kyJGmRo0a5ueff3ZNC7TP5Nz29u3b3aZv3LjRSDIff/yx2/SKbL9zmR07dpjBgwebOnXqmOjoaDN69Ghz+vTpEt9TUFBgoqOjTVRUVKnLlGTLli2mT58+JiIiwtSqVctce+215uuvvy5x2RUrVhhJxuFwuA0BcD5v56W3fVDSeZaVlWVGjBhhGjRoYCIiIkyfPn3Mrl27TIsWLdzKS5dlv13I6raMMWbt2rUmMTHRhIaGmtatW5vZs2cXu27YWe5i2lPa9WnVqlXmyiuvNKGhoSY+Pt68/vrr5n//939NeHi423JWvwelHTu710er6yltueTkZFO7du1i7evRo4dp3759sekASuYwhixAAIHp559/1mWXXaYXXnhBDz/8cInLDB8+XF988YW2bNmi6tWr2y4skJ+fr5MnT+r555/X9OnTdfToUa/dtcpbZf9Mgd7+s2fPqkmTJurfv7/+8Y9/+Gy9lcmkSZM0efLkgPi+B7KBAwfq+++/LzHXCkDVQk4TgIA1fvx4tWzZ0us4JwcOHFBMTIy6d+9uexuzZ89WTEyMpk+fXtZmlovK/pkCuf1LlizR0aNHNWzYsHJZPyqn06dPu/29e/du/etf//LJOGIAKj9ymgAElOzsbH3yySdas2aN3n//fX3yySceB059/PHHXQOTOgdqtePWW291G/cpKirKfqN9rLJ/pkBt/zfffKNt27ZpypQpuvLKK9WjRw+frBfBoXXr1ho+fLhat26tffv2adasWQoNDdXjjz/u76YBCAB0zwMQUD744AMNHjxYTZs21VNPPaX777/f301CkBg+fLjmz5+vTp06ad68eZYGSQ5WdM8rbsSIEVq9erUOHz6ssLAwJSUl6dlnn1Xnzp393TQAASBgg6Zp06Zp/PjxGjNmjF588UV/NwcAAABAFRWQOU2bNm3SnDlzLI39AQAAAADlKeCCppMnT2rIkCF67bXXFB0d7e/mAAAAAKjiAq4QREpKivr166fevXvrmWee8bhsQUGBCgoKXH8XFRXp+PHjql+/vhwOR3k3FQAAAECAMsboxIkTatKkiapVu7hnRQEVNC1cuFBbtmzRpk2bLC2fmpqqyZMnl3OrAAAAAFRWBw4cUNOmTS9qHQETNB04cEBjxozRihUrFB4ebuk948eP17hx41x/5+TkqHnz5jpw4IAiIyPLq6kAELQKi4w2/5KloyfzFRMRrsSW0QqpxpN7AEDlk5ubq2bNmqlOnToXva6AqZ63ZMkSDRo0SCEhIa5phYWFcjgcqlatmgoKCtzmlSQ3N1dRUVHKyckhaAKACxQWGW3ce1wZJ/LVsE64urWq5xYQfbr9kCZ/tEOHcvJd0xpHhWti/3a6sUNjW+sCAMDffBkbBEzQdOLECe3bt89t2ogRI9S2bVs98cQTlsbTIGgCgJJ5C4g+3X5II+dv0YU3BGcYNGtoZ1fgZCe4AgDAX3wZGwRM97w6deoUC4xq166t+vXrV+kBCAHgYpUWEB3OydfI+Vs08+4rNWX5zmLzJcnoXOA0+aMdur5drFbsOOxxXecHVwAABIuACZoAAGXjqatcYZHR5I92eAyI/r+l23U877dS128kHcrJ14Y9mV7X5Qyuzt8+3fgAAJVdQAdNa9as8XcTACCgeesqt3Hvcbd5FzKSx4DpfOt/PuZ1XYdy8rVx73ElxdenGx8AIGgE3OC2AABrnN3uLgxknF3lPt1+SBknSg9y7LP2hCjjRL6ltgEAUFkQNAFAJeSt2510rqtcg4gwS+urVzu01JDIoXNPiJLi61taV4PaYZbaVlgUEHWIAADwiqAJAAJUYZHR+j2ZWpp2UOv3ZLoFGVa63R3KyZfMuYDHW0D0zIAOrr8vnC9JE/u30+9a17e0LjlkuRuft88JAEAgCOicJgCoqrzlA1ntdncsr0AT+7fTyPlb5JDcnv6cHxDd2KGxZlXrrInLvteR3ALXMrEX5CBZWdexkwWywtmNj7wnAECg40kTAAQYK/lADeuEW1pXwzrh5wKioZ3VMNK9q15sVLhbifAbOzTWynE9XPPnjeiqdU9c5xa8WFmX1bb9cuwUeU8AgEqBoAkAAojVXKXEFtGWusp1a1VPkrWASJJbOfDSyoN7W1e3VvW8ti02MkzvbNxP3hMAoFIgaAKAAGI1V2nzvixN7N9Okuc8pPODHisBkVWe1hVSzeG1bXd1a67DudbzngAA8CeCJgCoYJ4KH1jNVco4kW+5250/eGtbywa1La3n/P1BwQgAgL9QCAIAKpC3wgd2cpWkc8HJ1Zc00BWTPpd0rqvcNZfGXNRTJF/x1Lb1ezItrcP5OSkYAQDwJ540AUAFsVLgwUo+0Pm5SpJvu935Wmlts/M5GSgXAOBvBE0AUAGsFniQZDtXqTKykvfknM9AuQAAfyNoAoAKYLXAw8a9xwM6V8mXrHxOO/sNAIDyQk4TAPhQYZHRxr3HlXEiXw3rhLu6pNkp8CAFdq6SL3n7nHb3m1T6MQAAoKwImgDARzwVK7Bb4EEK7FwlX/L0Oe3uNwpGAADKA93zAMAHvBUryMorsF3gARSMAAAEBoImALhIVoo8TFm+UxP6BX+BB1+jYAQAIBAQNAHARbJarCC6dmiVKPDgaxSMAAD4GzlNAGCBp+ICdooVDOgUVyUKPPiarwtGUCwCAGAHQRMAeOGtuIDdYgVVpcCDr/mqYATFIgAAdtE9DwA8sFJcwE6xApQPq8cgK+8MxSIAALYRNAFAKawUeJj80Q5JslSsgCdK5cdKwYgJ/S7XlOUUiwAA2EfQBKBKKywyWr8nU0vTDmr9nky3H8x2igtYKVaA8uXtGETXDrNdLMLT9wMAUHWQ0wSgyvKW22K3uIC3YgUof56OwdK0g5bW4Tye5D4BAJx40gSgSrKSq2S3wINEkYdAUNoxsFssgtwnAIATQROAKsdqrlJii2gKPAQRq8UiEltEM1AuAMANQROAKsdqrtLmfVkUeAgiVopFTOzfTpv3ZTFQLgDADUETgKBVWhK/nVwlCjwEFyvH024um0TBCAAIdgFVCGLWrFmaNWuWfvnlF0lS+/bt9dRTT6lv377+bRiASsdTEr/dXCUKPAQXb8fT7veDghEAEPwC6klT06ZNNW3aNG3evFnffvutrrvuOg0YMEDff/+9v5sGoBLxlsSflVdgO1eJAg/BxdPxtDNYMQUjAKBqCKigqX///rrpppt06aWX6rLLLtPUqVMVERGhDRs2+LtpACoJK0UepizfqQn9yFVCyazmPkmiYAQAVBEBFTSdr7CwUAsXLlReXp6SkpJKXKagoEC5ubluLwBVm9UiD9G1Q8lVQqms5D7ZGfwYAFC5BVROkySlp6crKSlJ+fn5ioiI0OLFi9WuXbsSl01NTdXkyZMruIUA/K2wyGjj3uPKOJGvhnXC3bpX2UniH9ApjlwllMpb7pPdghGevrcAgMAWcEFTmzZtlJaWppycHC1atEjJyclau3ZtiYHT+PHjNW7cONffubm5atasWUU2F0AF85Z0bzeJn1wleOLp+2F3sFyKRQBA5RVw3fNCQ0N1ySWXKDExUampqUpISNBLL71U4rJhYWGKjIx0ewEIXlaS7u0k8QMXw+p3LSvvDMUiAKCSC7ig6UJFRUUqKCjwdzMA+JmVAg+TP9ohSQxIiwphpWDEhH6Xa8pyikUAQGUXUEHT+PHj9eWXX+qXX35Renq6xo8frzVr1mjIkCH+bhoAP7OTdM+AtKgo3r5r0bXDKBYBAEEgoHKaMjIyNGzYMB06dEhRUVHq2LGjPvvsM11//fX+bhqACuCrAg8SA9Ki4nj6ri1NO2hpHed/vykYAQCBJ6CCpn/84x/+bgIAP/F1gQeJIg+oOKV91+x+bykYAQCBKaC65wGomijwgGBl53tr5TwAAPgHQRMAv6LAA4KZlWIRzvlWzgMKRgCAfxA0AfArCjwg2Fn53to5DwAAFS+gcpoABK/Sktsp8ICqwNv31u55IFEwAgAqEkETgHLnKbmdAg+oKjx9bykYAQCBje55AMqVt+T2rLwCCjygyqNgBAAENoImAOXGSpGHKct3akI/CjygaqNgBAAENoImABelsMho/Z5MLU07qPV7Mt1+rFlNbo+uHUqBB1R55VEwwtP5CQCwjpwmAGXmLa/CTnL7gE5xFHhAlefLghHkPQGA7/CkCUCZWMmrsJvcToEHwDcFI345doq8JwDwIYImALZZHZA2sUU0RR4AH7JSMCI2MkzvbNxP3hMA+BBBEwDbrOZVbN6XZSm5nSdKgDVWCkbc1a25DucyUC4A+BJBE4ASeUogt5NXYSW5HYB13s6plg1qW1rPhQPlUjACAEpHIQgAxXhLILebq+QtuR2APZ7OqfV7Mi2tg4FyAcA6njQBcGOlwIOdgTidKPIA+FZp5xQD5QKA7xE0AXCxWuBBErlKQIBioFwA8D2CJgAudgbOJFcJCFzlMVAuAFRl5DQBVVBhkdHGvceVcSJfDeuEu7r22CnwIJGrBAQyXw6U61TatQMAgh1BE1DFeEr6tlvgQSJXCQhkvhgol4IRAGAzaFq2bJntDVx//fWqWbOm7fcB8D1n0veFGQrOpO+Zd1+pxlHhOpyTX2Keg0PnuvcwGC1Q+TkLRlg5371dO+iSCyDY2QqaBg4caGvlDodDu3fvVuvWrW29D4DveSvy4JA0ZflOTejXTilvb5FDcluWAg9AcHEWjBg53/P5LnkuGOH4f/OvbxfLtQFA0LJdCOLw4cMqKiqy9KpVq1Z5tBlAGVhN+o6uHUqBB6CKoGAEAFhj60lTcnKyra52Q4cOVWRkpO1GASgbT0nadpK+B3SKo8ADUEVQMAIAvLMVNM2dO9fWymfNmmVreQBl5y1J227SNwUegKqDghEA4FmZx2nKyMjwZTsAXARnkvaFXWicSdqfbj/kSvouLfRx6NwPG4o8ADifnWuHlWsRAFRGZQ6aBg8erMLCwhLnnT17tswNAmCPtwIP0rkkbem/Sd0X/vihyAOA0jgLRkierx2S54IRzvmFRSUtAQCBrcxBU926dfXwww8Xm56ZmanevXtfVKMAWGcnSdtK0jcAXIiCEQCqujIPbvvmm2+qW7dueuONN3TPPfdIknbu3Kmbb75Zbdu29VkDAfiuwIPkPekbAEri64IRFIsAUJmUOWiqW7euPvjgA/Xs2VMdOnRQVlaW7rjjDt17772aPn16mdaZmpqqDz/8ULt27VLNmjX1+9//Xs8995zatGlT1mYClZ6vCzxIFHkAUDa+KhhBsQgAlY2t7nm33HKLnn76aS1btkz79+/XFVdcoRkzZuimm27Srbfeqr/97W/661//qmrVytbrb+3atUpJSdGGDRu0YsUK/fbbb7rhhhuUl5dXpvUBlR0FHgBUFlavRVl5ZygWAaDSsRXdxMfH66uvvtJ9992nli1bqn79+nrttddkjNHdd9+tzp0767fffitzYz799FMNHz5c7du3V0JCgubNm6f9+/dr8+bNZV4nUFlR4AFAZWKlYMSEfpdrynKKRQCofGwFTdOnT9eKFSuUkZGhAwcO6M0331SvXr103XXXafXq1ercubMiIiKUkJDgk8bl5ORIkurVK/l/yAsKCpSbm+v2AoIFBR4AVDberkXRtcMoFgGgUipzTlNcXJzi4uLUr18/17STJ08qLS1N33333UU3rKioSGPHjtXVV1+tDh06lLhMamqqJk+efNHbAvyptGRoCjwAqIw8XYuWph20tI7zr38UjAAQCGwFTdu2bVOHDh1KzVmKiIhQ9+7d1b17d0nS999/rzZt2qh6dfuxWUpKirZv365169aVusz48eM1btw419+5ublq1qyZ7W0B/uIpGZoCDwAqq9KuRXavaxSMABAobHXPu/LKK5WZmWl5+aSkJO3fv992o0aPHq2PP/5Yq1evVtOmTUtdLiwsTJGRkW4voLLwVuQhK6+AAg8AgoqdwjVWCuEAQEWx9QjIGKMJEyaoVq1alpY/c+aMrcYYY/TQQw9p8eLFWrNmjVq1amXr/UBl4a3Ig0PSlOU7NaFfO6W8vUUOyW1ZCjwAqIycxSJGzvd8XZPk9Ro5+aMdur5dLNdAABXCVtD0hz/8QT/88IPl5ZOSklSzZk3Ly6ekpOjtt9/W0qVLVadOHR0+fFiSFBUVZWs9QCDw1A/fapGH6NqhmjW0syYu+15Hcgtc82PpngKgknIWi/B0XVu/J9NywYik+PqSyH0CUL5sBU1r1qxx/fvAgQM+zx+aNWuWJKlnz55u0+fOnavhw4f7dFtAefLWD99OkYcBneIo8AAgqHgrXGO3EA65TwDKW9lGoZXUtm1bPfXUUzp9+rTPGmOMKfFFwITKxEo/fLvJ0BR4ABBsPF3X7FwjyX0CUBHKHDStWLFCn332mS655BLNmzfPh00CKi+rA9ImtoimyAMAlMJqwYjEFtGWrrkMlgvgYpU5aPr973+vb775RqmpqZowYYISExP11Vdf+bJtQKVjNVdp874sV7LzhT8KKPIAoKpzFoyQPF8jN+/LYrBcABWizEGT07Bhw/TDDz+oX79+6tu3rwYPHqy9e/f6om1AQCosMlq/J1NL0w5q/Z5Mt//BtNMP35kM3TAyzG1ebFS4Zg3tTD98AFWalWuk3dwnT9dvAPDE/qizpbjhhhuUm5urV155RcuXL9dDDz2kp556ShEREb7aBOB33pKN7eYqeUuGBoCqzNs10m7uE8UiAJRVmZ80zZ49W/fee686duyoqKgo9erVS1999ZUefPBBvfTSS/r222/Vrl07ffvtt75sL+A3VpKN7Qzc6ESRBwAonadrpNVrblbeGYpFALgoZQ6apk6dqpycHA0bNkyrV69Wdna2Nm/erJkzZ+qBBx7QF198oQcffJDKdwgKVgs8SCJXCQAqiJXcpwn9LteU5RSLAHBxyhw0HThwQIsWLdKjjz6q7t27lzj47L333qudO3deVAOBQGC1wMPGvcfJVQKACuTtmhtdO4xiEQAums9ymkrSsGFDffHFF+W5CcBnPI0mbzfZmFwlAKg4nq65S9MOWlrH+dd5T/cDAFVTuQZNDodDPXr0KM9NAD7h6wIPErlKAFCRSrvm2r1+UzACQEkuuuQ4UNmVV4EHAID/2bl+W7kfAKiaCJpQpVHgAQCCm9WBciVZuh9QMAKomgiaUKVR4AEAgp+V67ed+wGAqqdcc5qAQFFaUi8FHgCgavB2/bZ7P5AoGAFUJQRNCHqeknop8AAAVYen6zcFIwB4Qvc8BDVvSb1ZeQUUeAAAUDACgEcETQhaVoo8TFm+UxP6UeABAKo6CkYA8ISgCUHLalJvdO1QCjwAACgYAaBU5DShUvOUhGsnqXdApzgKPAAAfF4wgmIRQHAgaEKl5S0J125SLwUeAACS7wpGUCwCCB50z0OlZCUJ105SLwAAVli9t2TlnaFYBBBECJpQ6Vgp8DD5ox2SZCmplydKAACrrBSMmNDvck1ZTrEIIJgQNCEgFRYZrd+TqaVpB7V+T6bbjcVOEq6VpF4AAOzwdm+Jrh1mu1iEp/seAP8jpwkBx1sfcLtJuN6SegEAsMvTvWVp2kFL63Dep8h9AgIfT5oQUKzkKtkt8CBR5AEA4Hul3VvsFosg9wkIfARNCBhWc5USW0RT4AEAELCsFotIbBHNQLlAJUHQhIBhNVdp874sCjwAAAKWlWIRE/u30+Z9WQyUC1QSBE2ocKUlu9rJVaLAAwAgkFm5T9nN0ZUoGAH4S0AVgvjyyy81ffp0bd68WYcOHdLixYs1cOBAfzcLPuQp2dVurhIFHgAAgczbfcrufY+CEYD/BNSTpry8PCUkJGjmzJn+bgrKgbdk16y8Atu5ShR4AAAEMk/3KTuDsFMwAvCvgAqa+vbtq2eeeUaDBg3yd1PgY1aKPExZvlMT+pGrBACoGqzmPkmiYATgZwEVNNlVUFCg3NxctxcCk9UiD9G1Q8lVAgBUGVZyn+wM6g6gfARUTpNdqampmjx5sr+bgf+nsMho497jyjiRr4Z1wt26IdhJdh3QKY5cJQBAleEt98luwQhP92MAZVOpg6bx48dr3Lhxrr9zc3PVrFkzP7ao6vKWnGo32ZVcJQBAVeLpvmd3sFyKRQC+V6m754WFhSkyMtLthYpnJTnVTrIrAAD4L6v30Ky8MxSLAMpJpQ6a4H9WCjxM/miHJDEgLQAAZWClYMSEfpdrynKKRQDlJaCCppMnTyotLU1paWmSpL179yotLU379+/3b8NQKjvJqQxICwBA2Xi7h0bXDqNYBFCOAiqn6dtvv9W1117r+tuZr5ScnKx58+b5qVXwVYEHiQFpAQAoK0/30KVpBy2t4/z7NgUjAOsCKmjq2bOnjOGxcSDxdYEHiSIPAACUVWn3ULv3YwpGAPYEVPc8BBYKPAAAUDnYuR9bub8DcEfQhBJR4AEAgMrDSrEI53wr93cKRgDuCJpQIgo8AABQuVi5H9u5vwP4r4DKaULFKy0JlAIPAABUPt7ux3bv7xIFIwCJoKlK85QESoEHAAAqJ0/3YwpGAGVD97wqylsSaFZeAQUeAAAIMhSMAMqGoKkKslLkYcrynZrQjwIPAAAEEwpGAGVD0BSkCouM1u/J1NK0g1q/J9PtomY1CTS6digFHgAACDLlUTDC0+8OIBiQ0xSEvPU/tpMEOqBTHAUeAAAIMr4sGEHeE6oCnjQFGSv9j+0mgVLgAQCA4OOLghG/HDtF3hOqBIKmIGJ1QNrEFtEUeQAAAKWyUjAiNjJM72zcT94TqgSCpiBitf/x5n1ZlpJAeaIEAEDVZKVgxF3dmutwLgPlomogaKpkPCVa2ul/bCUJFAAAVF3efiu0bFDb0nouHCiXghGojCgEUYl4S7S0m6vkLQkUAABUbZ5+K6zfk2lpHQyUi2DAk6ZKwkqBBzsD1jlR5AEAAHhS2m8FBspFVULQVAlYLfAgiVwlAABQIRgoF1UJQVMlYGeAOXKVAABARSmPgXKBQEROUwApLDLauPe4Mk7kq2GdcNcjcDsFHiRylQAAQMXx5UC5TqX9JgL8haApQHhKjrRb4EEiVwkAAFQcXwyUS8EIBDK65wUAb8mRWXkFDEYLAAAqJQpGIBgQNFUAT2MSWCnyMGX5Tk3oR4EHAABQ+ZRnwQjGfUJFoXteOfP2iNlqcmR07VDNGtpZE5d9ryO5Ba75sTyuBgAAAc5ZMMLT75j1ezItF4xIiq9PNz5UKIKmcuR8xHzh/3k4HzHPGtpZBWeLLK0r40S+BnSKo8ADAAColHxZMMLKbywCJ/gS3fMuwsV2u5v80Q41iAgrYYninMmRFHgAAACVlS8KRjSoHWarGx9d+OALPGkqI191u5M5977DOfklnvwOnXt0TZEHAAAQzJwFI7z9JpJDlrvx5Zw+Qxc++ARPmkrh6X8lrFR2sfqI+VhegaXkSJ4oAQCAYGa1YMSxkwWyYsWOw7Yq8fFECp5UuSdNVgZL8/QU6fp2sR4fCTt07pHwX25LsNSehnXClRRfnyIPAACgyrNaMMKKJWm/ev29dn27WIVUc9gqKsHAu1VTUAZNG38+rms71rEVDDlPCG+JhWN7X1ou3e68JUcCAABUBd5+E1npxhddu4aO550pdRsXduGzWlTCanBlNbAiAKs8ArJ73syZM9WyZUuFh4frqquu0saNG229/55/blL3575we+xqpUudleINc//9i6U2lKXbHUUeAAAAPP8mstKNb1CnOEvbOZxz2nJRCasD7366/ZC6P/eF7nptg8YsTNNdr20o9rvUznIIDAEXNL377rsaN26cJk6cqC1btighIUF9+vRRRkaGrfXYDYYmf7RDG372Pj5A9unfLG2/YZ1w1yPmhpHuFfJio8IphQkAAFBG3n5j9W4Xa2k9x/POWOpBtGFPpqXfkv/aZj2wspNvBf8LuO55L7zwgu6//36NGDFCkjR79mwtX75cb7zxhp588klL6wg9W6CQkBA5JKV+uFV1dIWOZ+bIU3Hv45kF2rjjoMLOek8urFuzhnJO/1bqI+FGkeHq0ihcRadO6YbWUUoa2VXdpq6SJM35U6Kujm+gkGoOFZ065fbeojNnXdsvOnVKRWeLHx4ry/h6Obbp/+XYJtsM5raxzeDaZiC3jW0G1zY9/cYqLDJqUcuhI7mld+FrFBmu+tWLLP3227jzP5Z+S075YLNCz5bcLdD5u7Rn8zpK/XCrQi/YbkFIqIzDUSzfCoHBYYwJmNIgZ86cUa1atbRo0SINHDjQNT05OVnZ2dlaunSp2/IFBQUqKPjvFy4nJ0fNmzfXF61bK6JaSEU1GwAAALgod934lM5U/29Y9kZyV3VrzZAzFyM3N1fNmjVTdna2oqKiLmpdAfWk6dixYyosLFSjRo3cpjdq1Ei7du0qtnxqaqomT55cbPp1P/9cbm0EAAAAfG7Gn9z+vP5F/zQjGGVmZgZX0GTX+PHjNW7cONff2dnZatGihfbv33/ROwZl44zoDxw4oMjISH83p0riGPgfx8D/OAb+xzHwL/a//3EM/M/ZC61evYt/YhdQQVODBg0UEhKiI0eOuE0/cuSIYmOLJ/SFhYUpLKx479KoqCi+nH4WGRnJMfAzjoH/cQz8j2PgfxwD/2L/+x/HwP+qVbv42ncBVT0vNDRUiYmJWrVqlWtaUVGRVq1apaSkJD+2DAAAAEBVFVBPmiRp3LhxSk5OVpcuXdStWze9+OKLysvLc1XTAwAAAICKFHBB0x133KGjR4/qqaee0uHDh9WpUyd9+umnxYpDlCQsLEwTJ04sscseKgbHwP84Bv7HMfA/joH/cQz8i/3vfxwD//PlMQiokuMAAAAAEGgCKqcJAAAAAAINQRMAAAAAeEDQBAAAAAAeEDQBAAAAgAdBFTTNnDlTLVu2VHh4uK666ipt3LjR300KWl9++aX69++vJk2ayOFwaMmSJW7zjTF66qmn1LhxY9WsWVO9e/fW7t27/dPYIJSamqquXbuqTp06atiwoQYOHKgffvjBbZn8/HylpKSofv36ioiI0K233lps4GiU3axZs9SxY0fXoIVJSUn65JNPXPPZ/xVv2rRpcjgcGjt2rGsax6F8TZo0SQ6Hw+3Vtm1b13z2f8U4ePCghg4dqvr166tmzZq64oor9O2337rmc08uXy1btix2HjgcDqWkpEjiPChvhYWFmjBhglq1aqWaNWsqPj5eU6ZM0fm17nxxDgRN0PTuu+9q3LhxmjhxorZs2aKEhAT16dNHGRkZ/m5aUMrLy1NCQoJmzpxZ4vznn39eL7/8smbPnq1vvvlGtWvXVp8+fZSfn1/BLQ1Oa9euVUpKijZs2KAVK1bot99+0w033KC8vDzXMo888og++ugjvf/++1q7dq1+/fVX3XLLLX5sdXBp2rSppk2bps2bN+vbb7/VddddpwEDBuj777+XxP6vaJs2bdKcOXPUsWNHt+kch/LXvn17HTp0yPVat26dax77v/xlZWXp6quvVo0aNfTJJ59ox44d+utf/6ro6GjXMtyTy9emTZvczoEVK1ZIkm677TZJnAfl7bnnntOsWbM0Y8YM7dy5U88995yef/55vfLKK65lfHIOmCDRrVs3k5KS4vq7sLDQNGnSxKSmpvqxVVWDJLN48WLX30VFRSY2NtZMnz7dNS07O9uEhYWZd955xw8tDH4ZGRlGklm7dq0x5tz+rlGjhnn//fddy+zcudNIMuvXr/dXM4NedHS0ef3119n/FezEiRPm0ksvNStWrDA9evQwY8aMMcZwHlSEiRMnmoSEhBLnsf8rxhNPPGG6d+9e6nzuyRVvzJgxJj4+3hQVFXEeVIB+/fqZe+65x23aLbfcYoYMGWKM8d05EBRPms6cOaPNmzerd+/ermnVqlVT7969tX79ej+2rGrau3evDh8+7HY8oqKidNVVV3E8yklOTo4kqV69epKkzZs367fffnM7Bm3btlXz5s05BuWgsLBQCxcuVF5enpKSktj/FSwlJUX9+vVz298S50FF2b17t5o0aaLWrVtryJAh2r9/vyT2f0VZtmyZunTpottuu00NGzbUlVdeqddee801n3tyxTpz5ozmz5+ve+65Rw6Hg/OgAvz+97/XqlWr9OOPP0qSvvvuO61bt059+/aV5LtzoLpvm+0fx44dU2FhoRo1auQ2vVGjRtq1a5efWlV1HT58WJJKPB7OefCdoqIijR07VldffbU6dOgg6dwxCA0NVd26dd2W5Rj4Vnp6upKSkpSfn6+IiAgtXrxY7dq1U1paGvu/gixcuFBbtmzRpk2bis3jPCh/V111lebNm6c2bdro0KFDmjx5sq655hpt376d/V9Bfv75Z82aNUvjxo3T//3f/2nTpk16+OGHFRoaquTkZO7JFWzJkiXKzs7W8OHDJXEdqghPPvmkcnNz1bZtW4WEhKiwsFBTp07VkCFDJPnud2lQBE1AVZaSkqLt27e75RGgYrRp00ZpaWnKycnRokWLlJycrLVr1/q7WVXGgQMHNGbMGK1YsULh4eH+bk6V5PyfXEnq2LGjrrrqKrVo0ULvvfeeatas6ceWVR1FRUXq0qWLnn32WUnSlVdeqe3bt2v27NlKTk72c+uqnn/84x/q27evmjRp4u+mVBnvvfeeFixYoLffflvt27dXWlqaxo4dqyZNmvj0HAiK7nkNGjRQSEhIsUokR44cUWxsrJ9aVXU59znHo/yNHj1aH3/8sVavXq2mTZu6psfGxurMmTPKzs52W55j4FuhoaG65JJLlJiYqNTUVCUkJOill15i/1eQzZs3KyMjQ507d1b16tVVvXp1rV27Vi+//LKqV6+uRo0acRwqWN26dXXZZZfpp59+4jyoII0bN1a7du3cpl1++eWubpLckyvOvn37tHLlSt13332uaZwH5e+xxx7Tk08+qTvvvFNXXHGF/vSnP+mRRx5RamqqJN+dA0ERNIWGhioxMVGrVq1yTSsqKtKqVauUlJTkx5ZVTa1atVJsbKzb8cjNzdU333zD8fARY4xGjx6txYsX64svvlCrVq3c5icmJqpGjRpux+CHH37Q/v37OQblqKioSAUFBez/CtKrVy+lp6crLS3N9erSpYuGDBni+jfHoWKdPHlSe/bsUePGjTkPKsjVV19dbMiJH3/8US1atJDEPbkizZ07Vw0bNlS/fv1c0zgPyt+pU6dUrZp7SBMSEqKioiJJPjwHfFK2IgAsXLjQhIWFmXnz5pkdO3aYBx54wNStW9ccPnzY300LSidOnDBbt241W7duNZLMCy+8YLZu3Wr27dtnjDFm2rRppm7dumbp0qVm27ZtZsCAAaZVq1bm9OnTfm55cBg5cqSJiooya9asMYcOHXK9Tp065VrmwQcfNM2bNzdffPGF+fbbb01SUpJJSkryY6uDy5NPPmnWrl1r9u7da7Zt22aefPJJ43A4zOeff26MYf/7y/nV84zhOJS3//3f/zVr1qwxe/fuNf/+979N7969TYMGDUxGRoYxhv1fETZu3GiqV69upk6danbv3m0WLFhgatWqZebPn+9ahnty+SssLDTNmzc3TzzxRLF5nAflKzk52cTFxZmPP/7Y7N2713z44YemQYMG5vHHH3ct44tzIGiCJmOMeeWVV0zz5s1NaGio6datm9mwYYO/mxS0Vq9ebSQVeyUnJxtjzpV3nDBhgmnUqJEJCwszvXr1Mj/88IN/Gx1EStr3kszcuXNdy5w+fdqMGjXKREdHm1q1aplBgwaZQ4cO+a/RQeaee+4xLVq0MKGhoSYmJsb06tXLFTAZw/73lwuDJo5D+brjjjtM48aNTWhoqImLizN33HGH+emnn1zz2f8V46OPPjIdOnQwYWFhpm3btubVV191m889ufx99tlnRlKJ+5XzoHzl5uaaMWPGmObNm5vw8HDTunVr8+c//9kUFBS4lvHFOeAw5rzhcgEAAAAAboIipwkAAAAAygtBEwAAAAB4QNAEAAAAAB4QNAEAAACABwRNAAAAAOABQRMAAAAAeEDQBAAAAAAeEDQBAAAAgAcETQAAAADgAUETACBoPProoxo4cKC/mwEACDIETQCAoJGWlqZOnTr5uxkAgCBD0AQACBrfffcdQRMAwOcImgAAQeE///mPjh075gqasrOz1b9/f3Xv3l2HDx/2b+MAAJUaQRMAICikpaWpbt26atmypdLT09W1a1fFxcVp9erVio2N9XfzAACVGEETACAopKWlKSEhQW+//bZ69Oihxx9/XLNnz1aNGjX83TQAQCXnMMYYfzcCAICLNXjwYH3xxReSpOXLlyspKcnPLQIABAueNAEAgkJaWppuueUW5efnKzs729/NAQAEEZ40AQAqvRMnTigqKkqbN2/W1q1b9cgjj+jrr79W+/bt/d00AEAQqO7vBgAAcLG+++47hYSEqF27drryyiu1fft29e/fXxs3blSDBg383TwAQCVH9zwAQKWXlpamtm3bKiwsTJI0ffp0tWnTRrfccovOnDnj59YBACo7uucBAAAAgAc8aQIAAAAADwiaAAAAAMADgiYAAAAA8ICgCQAAAAA8IGgCAAAAAA8ImgAAAADAA4ImAAAAAPCAoAkAAAAAPCBoAgAAAAAPCJoAAAAAwAOCJgAAAADw4P8HUkDVxIuvSeYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.signal as sig\n",
    "\n",
    "\n",
    "L = 64  # length of input signal\n",
    "N = 8  # length of impulse response\n",
    "P = 16  # length of segments\n",
    "\n",
    "\n",
    "# generate input signal\n",
    "x = sig.windows.triang(L)\n",
    "# generate impulse response\n",
    "h = sig.windows.triang(N)\n",
    "\n",
    "# overlap-add convolution\n",
    "xp = np.zeros((L // P, P))\n",
    "yp = np.zeros((L // P, N + P - 1))\n",
    "y = np.zeros(L + P - 1)\n",
    "for p in range(L // P):\n",
    "    xp[p, :] = x[p * P : (p + 1) * P]\n",
    "    yp[p, :] = np.convolve(xp[p, :], h, mode=\"full\")\n",
    "    y[p * P : (p + 1) * P + N - 1] += yp[p, :]\n",
    "y = y[0 : N + L]\n",
    "\n",
    "\n",
    "# plot signals\n",
    "plt.figure(figsize=(10, 2))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.stem(x)\n",
    "for n in np.arange(L // P)[::2]:\n",
    "    plt.axvspan(n * P, (n + 1) * P - 1, facecolor=\"g\", alpha=0.5)\n",
    "plt.title(r\"Signal $x[k]$ and segments\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$x[k]$\")\n",
    "plt.axis([0, L, 0, 1])\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.stem(h)\n",
    "plt.title(r\"Impulse response $h[k]$\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$h[k]$\")\n",
    "plt.axis([0, L, 0, 1])\n",
    "\n",
    "for p in np.arange(L // P):\n",
    "    plt.figure(figsize=(10, 2))\n",
    "\n",
    "    plt.stem(np.concatenate((np.zeros(p * P), yp[p, :])))\n",
    "    plt.title(r\"Result of segment $p=%d$\" % (p))\n",
    "    plt.xlabel(r\"$k$\")\n",
    "    plt.ylabel(r\"$y_%d[k - %d P]$\" % (p, p))\n",
    "    plt.axis([0, L + P, 0, 4])\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10, 2))\n",
    "plt.stem(y)\n",
    "plt.title(r\"Result $y[k] = x[k] * h[k]$ by overlap-add algorithm\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$y[k]$\")\n",
    "plt.axis([0, L + P, 0, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercises**\n",
    "\n",
    "* Change the length `N` of the impulse response and the length `P` of the segments. What changes?\n",
    "* What influence have these two lengths on the numerical complexity of the overlap-add algorithm?\n",
    "\n",
    "Solution: The parameters `N` and `P` influence the overlap in the output and the total number of segments. The number of overlapping samples of two consecutive output segments $y_p[k]$ and $y_{p+1}[k]$ is given as $N-1$, and the total number of segments as $\\frac{L}{P}$. The segmented convolution requires $\\frac{L}{P}$ linear convolutions of length $P+N-1$ each. The numerical complexity is mainly determined by the overall number of multiplications which is given as $\\frac{L}{P} (P+N-1)^2$. For fixed $L$ and $N$, the optimum segment length is computed by finding the minimum in terms of multiplications. It is given as $P=N-1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overlap-Save Algorithm\n",
    "\n",
    "The [overlap-save](https://en.wikipedia.org/wiki/Overlap%E2%80%93save_method) algorithm, also known as *overlap-discard algorithm*, follows a different strategy as the overlap-add technique introduced above. It is based on an overlapping segmentation of the input $x_L[k]$ and application of the periodic convolution for the individual segments.\n",
    "\n",
    "Lets take a closer look at the result of the periodic convolution $x_p[k] \\circledast_P h_N[k]$, where $x_p[k]$ denotes a segment of length $P$ of the input signal and $h_N[k]$ the impulse response of length $N$. The result of a linear convolution $x_p[k]* h_N[k]$ would be of length $P + N -1$. The result of the periodic convolution of period $P$ for $P > N$ would suffer from a circular shift (time aliasing) and superposition of the last $N-1$ samples to the beginning. Hence, the first $N-1$ samples are not equal to the result of the linear convolution. However, the remaining $P- N + 1$ do so.\n",
    "\n",
    "This motivates to split the input signal $x_L[k]$ into overlapping segments of length $P$ where the $p$-th segment overlaps its preceding $(p-1)$-th segment by $N-1$ samples\n",
    "\n",
    "\\begin{equation}\n",
    "x_p[k] = \\begin{cases}\n",
    "x_L[k + p \\cdot (P-N+1) - (N-1)] & \\text{ for } k=0,1, \\dots, P-1 \\\\\n",
    "0 & \\text{ otherwise}\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "The part of the circular convolution $x_p[k] \\circledast_P h_N[k]$ of one segment $x_p[k]$ with the impulse response $h_N[k]$ that is equal to the linear convolution of both is given as\n",
    "\n",
    "\\begin{equation}\n",
    "y_p[k] = \\begin{cases}\n",
    "x_p[k] \\circledast_P h_N[k] & \\text{ for } k=N-1, N, \\dots, P-1 \\\\\n",
    "0 & \\text{ otherwise}\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "The output $y[k]$ is simply the concatenation of the $y_p[k]$\n",
    "\n",
    "\\begin{equation}\n",
    "y[k] = \\sum_{p=0}^{\\frac{L}{P-N+1} - 1} y_p[k - p \\cdot (P-N+1) + (N-1)]\n",
    "\\end{equation}\n",
    "\n",
    "The overlap-save algorithm is illustrated in the following diagram\n",
    "\n",
    "![Signal flow of overlap-save algorithm](overlap_save.png)\n",
    "\n",
    "For the first segment $x_0[k]$, $N-1$ zeros have to be appended to the beginning of the input signal $x_L[k]$ for the overlapped segmentation. From the result of the periodic convolution $x_p[k] \\circledast_P h_N[k]$ the first $N-1$ samples are discarded, the remaining $P - N + 1$ are copied to the output $y[k]$. This is indicated by the alternative notation *overlap-discard* used for the technique. The periodic convolution can be realized efficiently by a FFT/IFFT of length $P$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example\n",
    "\n",
    "The following example illustrates the overlap-save algorithm by showing the results of the periodic convolutions of the segments. The discarded parts are indicated by the red background."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-7.0, 88.0, 0.0, 4.0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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33nhDBw4c8FjuxIkTWrBggWbNmuX1touLi7V3715de+21io6O1jvvvKOsrCyNHz++SrWWCA4OLtXDCxcurPInZtU516T/O85u3bqVmrd7926PMLN7925169ZNiYmJ+uCDDzymebufmh5PIJDxSQvgZ0888YRGjBihlStX6rHHHtOLL76oTZs2qU+fPnrkkUfUuXNnnTx5Ujt37tSGDRt08uRJ5efnq02bNho+fLi6deumJk2aaMOGDdq+fbvHXzRHjRqlp556SnfddZcef/xxFRQUaMmSJbrqqqvKvAn2Yj179pQkPf300xo1apTsdrsSExPLveH3hRdeUHp6uvr166cJEyaoQYMGWrZsmYqKijRv3rxqjdGBAwd055136rbbbtPWrVv15ptvavTo0R5vHrwZN1/5ckyzZs3SRx99pJtuukkTJkzQ+fPntXDhQnXp0sXjjXdZ5syZo/Xr16t///569NFHdc011+jw4cNavXq1Nm/eXO4lJd6sV1s/F7vdrmHDhumtt97SmTNn9Pvf/75a43cpb3vXlz6tzR6t7f3s2LFDY8aM0ZgxY/T0009Lkp588kktXbq01KctTz/9tFJSUny6FOnbb79VYWGh+1G/PXv21JIlSzRu3Dj17NlTEydOrFLdv/nNb/Sf//mfioiIUOfOnbV161Zt2LBBkZGRVdqeVL1zreQ4L/2k5ezZs/ruu+88Li/dvXu3Jk2apKioKN1555165ZVXvA4ttTWeQEDz01PLgIBS8ujVsh5NW1xcbDp27Gg6duzofoTs0aNHTXJysomLizN2u920aNHCDBw40CxfvtwYY0xRUZF54oknTLdu3UxYWJhp3Lix6datm/njH/9Yavvr1683Xbt2NSEhIebqq682b775plePPDbGmOeff960bt3aBAUFefX44507d5ohQ4aYJk2amNDQUHPzzTebLVu2eCxTlUce79mzxwwfPtyEhYWZZs2amYkTJ5qzZ8+WWr6ycbt4m2U9VrSscfDmmEpkZGSYnj17mpCQENOhQwezdOlSr8f6p59+Mvfff7/7MdgdOnQwycnJpqioqMIx8mY9b4+hvLEpr+b09HQjydhsNo/Hdl/Mm32Xt31veteY8vu0Oj9PX8eiKsdtjHfnw8GDB03Lli3NjTfeaAoLCz3mjR8/3tjtdvPDDz+499ujRw/375KxY8ea559/3r18eY/nffvtt40k8/XXX3tMnzBhgrHb7SYjI6PUOt48ovfUqVNm3LhxJioqyjRp0sQMGTLE7Nu3z7Rr186MHTu20m2VN97enGtlKTnOrKwsj+lffPGFkWTWrVtnjDEmPz/f2Gw2c+LECWOMMfHx8SYzM9MMGDDAvP766x7rljWmtTWeQCCzGePHuwkBoAIzZ87UrFmzdPz4cfcXBwIo34IFC/Tv//7vatKkiSQpNzdXDRo00PDhw/X666/rgQce0CeffKKdO3eqQYMGVboxvLCwUKdPn9a8efM0f/78y/L83LJli0aOHOl+0tvkyZMVGxur3//+99q4caOuv/5697LVHdNAGE+gJnB5GAAAl4lHH31Uo0aNcr+ePHmy4uPjNW3aNPe0gwcPKjo6Wl26dPH5ARCStHTpUk2ZMqVG6rWqS+9vSUxM1MMPP6z8/Hz308UuVp0xDYTxBGoCoQUAgMtEaGioQkND3a8bNWqkJk2auP/6/+STT+q+++6TJPenMb66++67Pb4fKCIiouoFW9SloaV///46deqUOnXq5PHdWlL1xzQQxhOoCVweBsCyuDwMAABI1Xzk8YsvviibzaaUlJQaKgcA/s/MmTNljCGwAAAQ4KocWrZv365ly5aV+QVNAAAAAFBTqhRaTp8+rTFjxmjFihVq1qxZTdcEAAAAAG5VuhE/OTlZd9xxhwYNGqQXXnihwmWLioo8vqHb5XLp5MmTioyMlM1mq8ruAQAAAFwGjDHKz89Xq1atFBRU/ucpPoeWt956Szt37tT27du9Wj41NVWzZs3ydTcAAAAAAsTBgwfVpk2bcuf7FFoOHjyoyZMnKz09XQ0bNvRqnenTp2vq1Knu17m5uWrbtq0OHDigsLAwX3ZfbzidTm3atEk333yz7Ha7v8tBAKMXYRX0IqzCq1586aW6Lcof/t//83cFAY/fixfk5+crPj6+0lzgU2jZsWOHjh07ph49erinFRcX67PPPtOiRYtUVFSk4OBgj3UcDkepZ5pLUvPmzRUeHu7L7usNp9Op0NBQRUZGBnQTwv/oRVgFvQir8KoXQ0Lqtih/iIz0dwUBj9+LF5Qce2W3jfgUWgYOHKjMzEyPaePGjVOnTp301FNPlQosAAAAAFBdPoWWsLAwj29tlaTGjRsrMjKy1HQAAAAAqAnV+nJJAAAAAKhtVXrk8cU+/fTTGigDAAAAAMrGJy0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALM2n0LJkyRJdd911Cg8PV3h4uPr27asPP/ywtmoDAAAAAN9CS5s2bfTiiy9qx44d+vLLL3XLLbfoX/7lX/T111/XVn0AAAAAAlwDXxZOTEz0eD179mwtWbJE27ZtU5cuXWq0MAAAAACQfAwtFysuLtbq1at15swZ9e3bt9zlioqKVFRU5H6dl5cnSXI6nXI6nVXdvaWVHNflenyoP+hFWAW9CKvwqheDAuCWX85Fv+P34gXeHr/NGGN82XBmZqb69u2rwsJCNWnSRGlpabr99tvLXX7mzJmaNWtWqelpaWkKDQ31ZdcAAAAALiMFBQUaPXq0cnNzFR4eXu5yPoeWc+fO6eeff1Zubq7WrFmj1157TRkZGercuXOZy5f1SUtcXJyys7MrLKw+czqdSk9P1+DBg2W32/1dDgIYvQiroBdhFV71Ympq3RblD9On+7uCgMfvxQvy8vIUFRVVaWjx+fKwkJAQXXHFFZKknj17avv27XrllVe0bNmyMpd3OBxyOBylptvt9sv+BxQIx4j6gV6EVdCLsIoKe9Hlqtti/IHz0DIC/feit8de7Ys2XS6XxycpAAAAAFCTfPqkZfr06Ro6dKjatm2r/Px8paWl6dNPP9XHH39cW/UBAAAACHA+hZZjx47p/vvv1+HDhxUREaHrrrtOH3/8sQYPHlxb9QEAAAAIcD6Flv/4j/+orToAAAAAoEwB8CByAAAAAPUZoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApRFaAAAAAFgaoQUAAACApfkUWlJTU9W7d2+FhYUpJiZGSUlJ2r9/f23VBgAAAAC+hZaMjAwlJydr27ZtSk9Pl9Pp1K233qozZ87UVn0AAAAAAlwDXxb+6KOPPF6vXLlSMTEx2rFjh37961/XaGEAAAAAIPkYWi6Vm5srSWrevHm5yxQVFamoqMj9Oi8vT5LkdDrldDqrs3vLKjmuy/X4UH/Qi7AKehFW4VUvBgXALb+ci37H78ULvD1+mzHGVGUHLpdLd955p3JycrR58+Zyl5s5c6ZmzZpVanpaWppCQ0OrsmsAAAAAl4GCggKNHj1aubm5Cg8PL3e5KoeW8ePH68MPP9TmzZvVpk2bcpcr65OWuLg4ZWdnV1hYfeZ0OpWenq7BgwfLbrf7uxwEMHoRVkEvwiq86sXU1Lotyh+mT/d3BQGP34sX5OXlKSoqqtLQUqXLwyZOnKh169bps88+qzCwSJLD4ZDD4Sg13W63X/Y/oEA4RtQP9CKsgl6EVVTYiy5X3RbjD5yHlhHovxe9PXafQosxRpMmTdLatWv16aefKj4+vkrFAQAAAIC3fAotycnJSktL03vvvaewsDAdOXJEkhQREaFGjRrVSoEAAAAAAptPj8dYsmSJcnNzNWDAALVs2dL936pVq2qrPgAAAAABzufLwwAAAACgLgXAg8gBAAAA1GeEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGk+h5bPPvtMiYmJatWqlWw2m959991aKAsAAAAALvA5tJw5c0bdunXT4sWLa6MeAAAAAPDQwNcVhg4dqqFDh9ZGLQAAAABQis+hxVdFRUUqKipyv87Ly5MkOZ1OOZ3O2t69X5Qc1+V6fKg/6EVYBb0Iq/CqF4MC4JZfzkW/4/fiBd4ev80YY6q6E5vNprVr1yopKancZWbOnKlZs2aVmp6WlqbQ0NCq7hoAAABAPVdQUKDRo0crNzdX4eHh5S5X66GlrE9a4uLilJ2dXWFh9ZnT6VR6eroGDx4su93u73IQwOhFWAW9CKvwqhdTU+u2KH+YPt3fFQQ8fi9ekJeXp6ioqEpDS61fHuZwOORwOEpNt9vtl/0PKBCOEfUDvQiroBdhFRX2ostVt8X4A+ehZQT670Vvjz0ALtoEAAAAUJ/5/EnL6dOn9d1337lfHzhwQLt27VLz5s3Vtm3bGi0OAAAAAHwOLV9++aVuvvlm9+upU6dKksaOHauVK1fWWGEAAAAAIFUhtAwYMEDVuHcfAAAAAHzCPS0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSCC0AAAAALI3QAgAAAMDSGvi7AAAAAFxQbKQvXGE6Jrti5FRCUL6Cbf6uCvA/QgsAAEAdqSiUfFTcTLOccTosh3v5lirSDPtB3RZ8qtL1gcsZoQUAAKCGVDWUSNJ4Z0eZS7Z3RCEa7+yoJfpekgg1CFiEFgAAAC9UFgiqGkoec3ZUU53/5zzPhGFkk01G05ztlKsGNRdqdh1STFhDJcQ3V3AQqQbWR2gBAACQVOwy+uLASR0rbu7zpVsfFTerciiRjHJkL7cuI9s/55sy169SqHlr14VjiGioGYmddVvXlqXHIb+QYAPLILQAAICA91HWYc36YI8O5xZK6ijJ+0u3Fpvv9fz5uCqHkkvX8XW5aoWa3EKNf3OnltzXQ7d1bXnJOFxwabCpLNT4e74VavBm/ucHTmpHtk2RB06q7xUxljtGq6lSaFm8eLHmz5+vI0eOqFu3blq4cKESEhJqujYAAIBa91HWYY1/c2eVL9369/NtdVIhFeyhrt4IViXUXJgy64M9crmk5LQyxuGiYKN/LlteqKks9NT2fOnSAGq9Gj3nB+uNb7+03DFakc0Yc2lvVmjVqlW6//77tXTpUvXp00cLFizQ6tWrtX//fsXExFS6fl5eniIiIpSbm6vw8PAqF25lTqdTf/vb33T77bfLbq/oLytA7aIXYRX0Iqzi0l4sdhn1m/uJx5s3T6Xf6Nee8vZVNzU0bxyik2fOlTnPJiki1K7cAmepUFNS2aO/jtfyzw74bX5JqCorgFqlxvpwjCWfutUVb7OBz6GlT58+6t27txYtWiRJcrlciouL06RJkzRt2rQaK6w+4x9nWAW9CKugF2EVl/bi1u9P6N4V2y7MNEaO4rLftNcmm6QInVfuPy+AMZfMM5Ka/nO+T2/a6liQTXJVUGBtzrdJiglzSLLpaH55AdS/NVZ3fm0eY1FwiGSzySapRURDbX7qljq7VMzbbODT5WHnzp3Tjh07NH36dPe0oKAgDRo0SFu3bi1znaKiIhUVFblf5+bmSpJOnjwpp9Ppy+7rDafTqYKCAp04cYJ/nOFX9CKsgl6EVVzai9//44hcRQWSpJDzRXrzo+f8XCFQ9+697Vmda3DhIROHjhVow67v1atdszrZd35+viSpss9RfAot2dnZKi4uVmxsrMf02NhY7du3r8x1UlNTNWvWrFLT4+Pjfdk1AABAreMOXQSkRb/1eHnbgrovIT8/XxEREeXOr/Wnh02fPl1Tp051v3a5XDp58qQiIyNls1n3CQXVkZeXp7i4OB08ePCyvQQO9QO9CKugF2EV9CKsgl68wBij/Px8tWrVqsLlfAotUVFRCg4O1tGjRz2mHz16VC1atChzHYfDIYfD4TGtadOmvuy23goPDw/oJoR10IuwCnoRVkEvwiroRVX4CUuJIF82GBISop49e2rjxo3uaS6XSxs3blTfvn19rxAAAAAAKuHz5WFTp07V2LFj1atXLyUkJGjBggU6c+aMxo0bVxv1AQAAAAhwPoeWkSNH6vjx43r22Wd15MgRde/eXR999FGpm/MDmcPh0IwZM0pdFgfUNXoRVkEvwiroRVgFvegbn7+nBQAAAADqkk/3tAAAAABAXSO0AAAAALA0QgsAAAAASyO0AAAAALA0QksNW7x4sdq3b6+GDRuqT58++uKLL/xdEi5zqamp6t27t8LCwhQTE6OkpCTt37/fY5nCwkIlJycrMjJSTZo00d13313qS2KBmvbiiy/KZrMpJSXFPY1eRF05dOiQ7rvvPkVGRqpRo0a69tpr9eWXX7rnG2P07LPPqmXLlmrUqJEGDRqkb7/91o8V43JVXFysZ555RvHx8WrUqJE6duyo559/Xhc/C4t+rByhpQatWrVKU6dO1YwZM7Rz505169ZNQ4YM0bFjx/xdGi5jGRkZSk5O1rZt25Seni6n06lbb71VZ86ccS8zZcoUffDBB1q9erUyMjL0yy+/aNiwYX6sGpe77du3a9myZbruuus8ptOLqAunTp3SjTfeKLvdrg8//FB79uzRSy+9pGbNmrmXmTdvnl599VUtXbpUn3/+uRo3bqwhQ4aosLDQj5XjcjR37lwtWbJEixYt0t69ezV37lzNmzdPCxcudC9DP3rBoMYkJCSY5ORk9+vi4mLTqlUrk5qa6seqEGiOHTtmJJmMjAxjjDE5OTnGbreb1atXu5fZu3evkWS2bt3qrzJxGcvPzzdXXnmlSU9PN/379zeTJ082xtCLqDtPPfWU6devX7nzXS6XadGihZk/f757Wk5OjnE4HOYvf/lLXZSIAHLHHXeYBx980GPasGHDzJgxY4wx9KO3+KSlhpw7d047duzQoEGD3NOCgoI0aNAgbd261Y+VIdDk5uZKkpo3by5J2rFjh5xOp0dvdurUSW3btqU3USuSk5N1xx13ePScRC+i7rz//vvq1auXRowYoZiYGF1//fVasWKFe/6BAwd05MgRj16MiIhQnz596EXUuBtuuEEbN27UN998I0navXu3Nm/erKFDh0qiH73VwN8FXC6ys7NVXFys2NhYj+mxsbHat2+fn6pCoHG5XEpJSdGNN96orl27SpKOHDmikJAQNW3a1GPZ2NhYHTlyxA9V4nL21ltvaefOndq+fXupefQi6soPP/ygJUuWaOrUqfq3f/s3bd++XY8//rhCQkI0duxYd7+V9W82vYiaNm3aNOXl5alTp04KDg5WcXGxZs+erTFjxkgS/eglQgtwGUlOTlZWVpY2b97s71IQgA4ePKjJkycrPT1dDRs29Hc5CGAul0u9evXSnDlzJEnXX3+9srKytHTpUo0dO9bP1SHQvP322/qv//ovpaWlqUuXLtq1a5dSUlLUqlUr+tEHXB5WQ6KiohQcHFzqKThHjx5VixYt/FQVAsnEiRO1bt06bdq0SW3atHFPb9Gihc6dO6ecnByP5elN1LQdO3bo2LFj6tGjhxo0aKAGDRooIyNDr776qho0aKDY2Fh6EXWiZcuW6ty5s8e0a665Rj///LMkufuNf7NRF5544glNmzZNo0aN0rXXXqvf/va3mjJlilJTUyXRj94itNSQkJAQ9ezZUxs3bnRPc7lc2rhxo/r27evHynC5M8Zo4sSJWrt2rT755BPFx8d7zO/Zs6fsdrtHb+7fv18///wzvYkaNXDgQGVmZmrXrl3u/3r16qUxY8a4/59eRF248cYbSz36/ZtvvlG7du0kSfHx8WrRooVHL+bl5enzzz+nF1HjCgoKFBTk+ZY7ODhYLpdLEv3oLS4Pq0FTp07V2LFj1atXLyUkJGjBggU6c+aMxo0b5+/ScBlLTk5WWlqa3nvvPYWFhbmvf42IiFCjRo0UERGhhx56SFOnTlXz5s0VHh6uSZMmqW/fvvrVr37l5+pxOQkLC3PfS1WicePGioyMdE+nF1EXpkyZohtuuEFz5szRPffcoy+++ELLly/X8uXLJcn9/UEvvPCCrrzySsXHx+uZZ55Rq1atlJSU5N/icdlJTEzU7Nmz1bZtW3Xp0kVfffWV/vCHP+jBBx+URD96zd+PL7vcLFy40LRt29aEhISYhIQEs23bNn+XhMucpDL/e/31193LnD171kyYMME0a9bMhIaGmrvuusscPnzYf0UjYFz8yGNj6EXUnQ8++MB07drVOBwO06lTJ7N8+XKP+S6XyzzzzDMmNjbWOBwOM3DgQLN//34/VYvLWV5enpk8ebJp27atadiwoenQoYN5+umnTVFRkXsZ+rFyNmMu+jpOAAAAALAY7mkBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgBAnfrd736npKQkf5cBAKhHCC0AgDq1a9cude/e3d9lAADqEUILAKBO7d69m9ACAPAJoQUAUGf+8Y9/KDs72x1acnJylJiYqH79+unIkSP+LQ4AYFmEFgBAndm1a5eaNm2q9u3bKzMzU71791br1q21adMmtWjRwt/lAQAsitACAKgzu3btUrdu3ZSWlqb+/fvrySef1NKlS2W32/1dGgDAwmzGGOPvIgAAgWH48OH65JNPJEn//d//rb59+/q5IgBAfcAnLQCAOrNr1y4NGzZMhYWFysnJ8Xc5AIB6gk9aAAB1Ij8/XxEREdqxY4e++uorTZkyRVu2bFGXLl38XRoAwOIa+LsAAEBg2L17t4KDg9W5c2ddf/31ysrKUmJior744gtFRUX5uzwAgIVxeRgAoE7s2rVLnTp1ksPhkCTNnz9fV199tYYNG6Zz5875uToAgJVxeRgAAAAAS+OTFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACWRmgBAAAAYGmEFgAAAACW9v8B+/ST/c58UfkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 64  # length of input signal\n",
    "N = 8  # length of impulse response\n",
    "P = 24  # length of segments\n",
    "\n",
    "\n",
    "# generate input signal\n",
    "x = sig.windows.triang(L)\n",
    "# generate impulse response\n",
    "h = sig.windows.triang(N)\n",
    "\n",
    "# overlap-save convolution\n",
    "nseg = (L + N - 1) // (P - N + 1) + 1\n",
    "x = np.concatenate((np.zeros(N - 1), x, np.zeros(P)))\n",
    "xp = np.zeros((nseg, P))\n",
    "yp = np.zeros((nseg, P))\n",
    "y = np.zeros(nseg * (P - N + 1))\n",
    "\n",
    "for p in range(nseg):\n",
    "    xp[p, :] = x[p * (P - N + 1) : p * (P - N + 1) + P]\n",
    "    yp[p, :] = np.fft.irfft(np.fft.rfft(xp[p, :]) * np.fft.rfft(h, P))\n",
    "    y[p * (P - N + 1) : p * (P - N + 1) + P - N + 1] = yp[p, N - 1 :]\n",
    "y = y[0 : N + L]\n",
    "\n",
    "plt.figure(figsize=(10, 2))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.stem(x[N - 1 :])\n",
    "plt.title(r\"Signal $x[k]$\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$x[k]$\")\n",
    "plt.axis([0, L, 0, 1])\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.stem(h)\n",
    "plt.title(r\"Impulse response $h[k]$\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$h[k]$\")\n",
    "plt.axis([0, L, 0, 1])\n",
    "\n",
    "for p in np.arange(nseg):\n",
    "    plt.figure(figsize=(10, 2))\n",
    "    ky = np.arange(p*(P-N+1)-(N-1), p*(P-N+1)-(N-1)+P)\n",
    "    plt.stem(ky, yp[p, :])\n",
    "    plt.axvspan(p*(P-N+1)-(N-1),p*(P-N+1), facecolor=\"r\", alpha=0.5)\n",
    "    plt.title(r\"Result of periodic convolution of $x_%d[k]$ and $h_N[k]$\" % (p))\n",
    "    plt.xlabel(r\"$k$\")\n",
    "    plt.grid()\n",
    "    plt.axis([-N+1, L + P, 0, 4])\n",
    "\n",
    "plt.figure(figsize=(10, 2))\n",
    "plt.stem(y)\n",
    "plt.title(r\"Result $y[k] = x[k] * h[k]$\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.grid()\n",
    "plt.axis([-N+1, L + P, 0, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Change the length `N` of the impulse response and the length `P` of the segments. What changes?\n",
    "* How many samples of the output signal $y[k]$ are computed per segment for a particular choice of these two values?\n",
    "* What would be a good choice for the segment length `P` with respect to the length `N` of the impulse response?\n",
    "\n",
    "Solution: Decreasing the segment length $P$ or increasing the length of the impulse response $N$ decreases the number of valid output samples per segment which is given as $P-N+1$. The computation of $L$ output samples requires $\\frac{L}{P-N+1}$ cyclic convolutions of length $P$ each. Regarding the total number of multiplications, an optimal choice for the segment length is $P = 2 N - 2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Practical Aspects and Extensions\n",
    "\n",
    "* For both the overlap-add and overlap-save algorithm the length $P$ of the segments influences the lengths of the convolutions, FFTs and the number of output samples per segment. The segment length is often chosen as\n",
    "\n",
    "    * $P=N$ for overlap-add and \n",
    "    * $P = 2 N$ for overlap-save. \n",
    "\n",
    "For both algorithms this requires FFTs of length $2 N$ to compute $P$ output samples. The overlap-add algorithm requires $P$ additional additions per segment in comparison to overlap-save.\n",
    "\n",
    "* For real-valued signals $x_L[k]$ and impulse responses $h_N[k]$ real-valued FFTs lower the computational complexity significantly. As alternative, the $2 N$ samples in the FFT can be distributed into the real and complex part of a FFT of length $N$ [[Zölzer](../index.ipynb#Literature)].\n",
    "\n",
    "* The impulse response can be changed in each segment in order to simulate time-variant linear systems. This is often combined with an overlapping computation of the output in order to avoid artifacts due to instationarities.\n",
    "\n",
    "* For long impulse responses $h_N[k]$ or low-delay applications, algorithms have been developed which base on an additional segmentation of the impulse response. This is known as *partitioned convolution*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
 ],
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