{
 "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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",
      "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": [
       "(0.0, 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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27dql5557zuVVqiuzbNky/fWvf9WaNWu0YMEC/fGPf1SPHj102223OY5xJW414epzPfnkkzpy5IiuueYaLV++XEuXLtXw4cPVtGnT897j+eefV0lJifr376+FCxdq3bp1WrJkie64445qY+7qub762VxwwQW6+eablZaWppUrV2rSpEkKCPjP/1Y8ua87n113Pqu+/Jz68j4HDx7U1VdfrUsuuURLly5VcHCw5s+frxMnTlTowZDK6y5uu+02denSRQ8//LBL98jNzVVubq7jl/bJkyfrySef1P3336+lS5e61d6zXX/99UpLS9OCBQv06aef6tlnn9WUKVM8quvw5Ptmf057r7ddaWmptm/f7tj+yy+/6Ntvv1WPHj3UuXNnhYSEaPv27S4nLb6KJ9Bo1eUsAEBjUd2MML/++quJj483nTp1MqWlpcaY8hlrpk6datq0aWOCg4NNq1atzKBBg8y8efOMMeUzBN17772me/fuplmzZiYsLMxccsklJjk52Zw+fdrp+h9++KG57LLLTFhYmLnwwgvNiy++6NLsYcYYM3v2bBMXF2cCAgKMJLNu3bpqn3Pjxo1m2LBhpmnTpiYsLMwMGDDArFq1yumYmswetmXLFjNmzBgTHh5uIiIizPjx481PP/1U4fjzxe3sax49erTC+ZXFwNXnMsaYlStXmu7du5uQkBATHx9v5s+fXyHWVd1jz5495tZbbzUtWrRwnD958mSnmY2q4sq5rjxDVbGpqs3GGPPxxx8bSUaS+eqrryrsdzV2ld3D1c+uMZV/Vj35edYkFjV5dle+Dz/++KPp2LGj6dWrV4XZ8X7/+98bq9Xq1B6bzWbGjRtnbrjhBqeZCe2qmu1qxYoVRpLZsWOH0/Y//OEPJjQ01GzYsMFpu6szXZ04ccLcfffdJjo62jRp0sQMHjzYbNy40QwdOtQMHTrUcZy7MXfl+1aZqp5z+/btRpJZtmyZMcaYzz//3LRp08axPykpyTzxxBOmVatWJisry7HdW/E8+1mZPQyoyGKMMbWRHAGAu+bMmaO5c+fq6NGjXqk1ABqD3//+99q/f7/S09OdZteymzx5stavX6+vv/5aFovF7XVCjDGy2Wx6/fXXdffdd2vz5s0Vei0agtTUVK1evdqxIOj69es1efJkff/99yooKHAsFulpPKXGE1PAEwwPAwCggfjuu+/06quv6ssvv1TLli0VHh6u8PBwbdy4scJxwcHBLtdmnG3FihUKDg7W3Xff7a1m+6Xt27ere/fujveDBw/WqVOn1KlTJ0fCYudJPKXGE1PAE/S0APBb9LQA3nfw4EHHxA1hYWHq2rWrW+efPHlSX3/9teN9ly5d1KRJE6+2sT7xNJ4SMQVcQdICAAAAwK95NDwsJSVFFotFs2bN8lJzAAAAAMBZjZOWzZs365VXXnEa7wkAAAAA3lajpOWXX37RnXfeqYULFyoqKsrbbQIAAAAAh6CanDR9+nSNHj1aV199tebNm1ftsUVFRSoqKnK8Lysr0/Hjx9WiRQuvLeIFAAAAoP4xxqigoEBxcXFOCxSfy+2kZcmSJdq6das2b97s0vEpKSmaO3euu7cBAAAA0EgcPnxYbdu2rXK/W0nL4cOHNXPmTH388ceVLlhVmdmzZyspKcnxPj8/X/Hx8Tr8wANqZrW6c/uGZ/ZsSZKtzGjLwRM6+kuhWoWHqneHKAUG0AsFAACAhu3UqVNq166dIiIiqj3OraRly5YtysvLU+/evR3bbDabNmzYoBdffFFFRUUVVoK1Wq2yVpKcNLNaG0XSYjNSVlmE8hSsaJWoX0CBAu35SLNmSt+Vq7mr9ig3v9BxTmxkqJLHdNHIxNj/XKfMKOvAceUVFCo6IlT9EpqT2AAAAKBBOF/ZiFtJy/Dhw7Vz506nbVOmTFHnzp314IMPVkhYGrt0W5TmlrRTrv6TnMWqSMnBhzUy8ITSd+Vq2uKtOnehnCP5hZq2eKtSJ/TSyMRYlxMbAAAAoCFyK2mJiIhQYmKi07amTZuqRYsWFbY3dum2KE0r6VgxIVGIppV01EvmGz25ak+F/ZJkJFkkzV21R2Vl0vQ3z5/YAAAAAA2VR4tLonI2I80tafdbouHc1WV+e/9oabxTz8m5jKTc/EI9umJXlYmNVJ7Y2MrK39nKjDK/OaYVOT8o85tjju0AAABAfVajKY/Ptn79ei80o2HJKotwGhJ2LiOLjivEpWsdP11czXXKE5usA8eV/2sxQ8gAAADQINHT4gGbkTJtEVpha65MW4Rsv3Vs5Cm4VtuxZs8RTVu8tULPjX0IWfqu3FptDwAAAOBNHve0NFbVFdlHq8SlazRvGqITp4srHf5lkRTVNFjHT5//Wstzfjxvbcw1XWKYbQwAAAD1Ej0tNWAvss89Z4iXvcj+hAlSrIpkqTSVkCwyilWR5t2Y+Nv7c/eXm3djomIjQyvsP/u45k2DXR5CRs0LAAAA6iN6Wtx0viJ7i4yeLG2nx4IOa3ppR1lkHMX35WeUn5kcfFgju49VakAvJa/crZ9OFTmOiTmrFiUgwKJpi7fKIjmlQPYr3nxZG732+cHztnvNniNKeieHmhcAAADUO/S0uOk/RfaV938YWZQrq6IspUoN/qbCULEYFSs1+BuNDDwhSRqZGKu1SUMd+9Om9NVnDw5zJBIjE2OVOqGXops5F/bHRIYqdUIvXd0lxqV2/+/nB6l5AQAAQL1ET4ubXC2yz1Owbgw8rsst+epW3FuSlBa8T1cEnFLgOfnO2bUmla10PzIxVpdf1FLd5nxcfp0pfXVFp1YKDLDIVmYUGxmqI/mFVQxGkwIsUmUjwah5AQAAQH1AT4ubXC2ytx93doLSL+CXCgmLq6pKbAIDLEoe00VS1bUx1ZWunF3zAgAAAPgjkhY39QsocKnIvl9AQa21qbohZHdf3sGla+QVlA8do1gfAAAA/obhYW4KtJQX0U8rqb7IvqY9KjVV1RCyrAPHXSrUj44IVfquXBaoBAAAgN+hp6UGRgaecKnIvrZVNoSsX0Lz806bHBsZqhOni1mgEgAAAH6JpKUaVa14L5UnLmtDdjrepwXv02fWHXWWsFTFlZqXx0Zfqic/2FPlApVSebE+Q8UAAABQF0haqpBui9Lgou4aX9JZM0s6anxJZw0u6q50W5TjGG8V2fva+aZNjmpqrdDDcjaK9QEAAFCXqGmphH3F+3P7Fewr3qeq7oaA1VR10yavyPnBpWucXayfdeC48goKFR0RWuk0zQAAAIC3kLScw5UV7+eWtNM1AfUraZGqnjY5OiLUpfMp1gcAAEBdYHjYOVxd8T6rLKJ2G+ZDFOsDAADAn5G0nMOdFe8bCor1AQAA4M9IWs7h7or3DQXF+gAAAPBX1LScw77i/RGFOC0caWeRUYyK1S+gQEUNLOejWB8AAAD+iKTlHG6teN8AR0JRrA8AAAB/07C6CrzEX1e8r0sU6wMAAKCukLRUob6seF9bKNYHAABAXSFpqUZ9WfG+tni7WN9WZpT5zTGtyPlBmd8cI5kBAABApahpgVu8VaxP3QsAAABc1Wh7WmxGyrRFaIWtuTJtEbLxR36XeVqsf/DnM9S9AAAAwGWNsqcl3RaluSXtlKv/DHOKVZGSgw832poVb7AX6x/JL6y0rsUiqXUzq97KOlRl3YtF5XUv13SJYYpkAAAASGqEPS3ptihNK+moXIU4bT+iEE0r6ah0W1Qdtaz+c6VYf3y/eB05xSKVAAAAcF2jSlpsRppb0u63v/I7/1ptX49lbkk7hop54HzF+h1aNnXpOmcvUkmxPgAAQOPm1vCw1NRUpaam6uDBg5Kkrl276vHHH9eoUaN80TavyyqLcBoSdi4ji3JlVVZZhAYGFtRiyxqW6or1M7855tI1WKQSAAAAdm71tLRt21bz589Xdna2srOzNWzYMN14443avXu3r9rnVXkK9upxqFpVxfosUgkAAAB3uZW0jBkzRtddd50uvvhiXXzxxXrqqacUHh6uTZs2+ap9XnXuCveeHgf3sUglAAAA3FXjmhabzaYlS5bo9OnTGjhwYJXHFRUV6dSpU06vutIvoECxKpKl0l+HJYuMYlWkfgEMDfMlby9SCQAAgIbN7aRl586dCg8Pl9Vq1b333qv3339fXbp0qfL4lJQURUZGOl7t2rXzqMGeCLRIycGHJalC4mJ/nxx8WIHMtOtzIxNjtTZpqON92pS++uzBYRqZGOsowj+fvIJCCvUBAAAaAbfXabnkkkuUk5OjkydPaunSpZo0aZIyMjKqTFxmz56tpKQkx/tTp07VaeIyMvCEUvWNkkvi9dNZ0x7HqJh1WmqZNxapHPy3TynUBwAAaODcTlpCQkJ00UUXSZL69OmjzZs364UXXtD//M//VHq81WqV1Vr1jF11YWTgCV1uyVe34t6SpLTgfboi4BQ9LH7ClUUqI5sEa8Haryrstxfqp07oReICAADQQHi8TosxRkVFRd5oS606O0HpF/ALCYsfOV+xvj1RoVAfAACgcXAraXn44Ye1ceNGHTx4UDt37tQjjzyi9evX68477/RV+9BIVVes/8DVnXTyTNUzvFGoDwAA0LC4NTzsp59+0sSJE5Wbm6vIyEh1795d6enpuuaaa3zVPjRiVS1SuXrHjy6dby/ot5UZZR04rryCQkVHhDrVzwAAAMD/uZW0vPbaa75qB1Cpyor1XS3Uj44IVfquXM1dtYdifQAAgHrM45oWoLbZC/Wr6iuxqDwxOXG6WNMWb62w5ou9WD99V67P2woAAADPNcikxWakTFuEVtiaK9MWIRv12A3K+Qr1Jemx0ZfqyQ/2UKwPAADQADS4pCXdFqXBRd01vqSzZpZ01PiSzhpc1F3ptqi6bhq8qLpC/dQJvRTV1Fqhh+VsFOsDAADUH26v0+LP0m1RmlbSseLaHQrRtJKOStU3LB7ZgFRVqB8YYNGKnB9cugbF+gAAAP6vwSQtNiPNLWn3W8Li/MumkUUWGc0taadrAk6wJksDUlmhviSK9QEAABqQBjM8LKssQrmyqmKVQzkji3JlVVZZRO02DHWCYn0AAICGo8EkLXkK9upxqN8o1gcAAGg4GkzSEq2qV0ivyXGo/7xdrG8rM8r85phW5PygzG+OkcwAAADUkgZT09IvoECxKtIRhchUMijIIqMYFatfQEEdtA51xVvF+tS9AAAA1J0G09MSaJGSgw9LKk9QzmZ/nxx8mCL8RsjTYv2DP5+h7gUAAKAONZikRZJGBp5QavA3FYaAxahYqcFMdwxnrhTrxzSz6q2sQ9S9AAAA1KEGlbRI5YnL2pCdjvdpwfv0mXUHCQsqcKVYf3y/eB05xSKVAAAAdanBJS2SnIaA9Qv4hSFhqNL5ivU7tGzq0nXOXqSSYn0AAADvajCF+EBNVVesn/nNMZeuwSKVAAAAvtMge1oAd1VVrM8ilQAAAHWv3iUtNiNl2iK0wtZcmbYI2Rh9Ax9ikUoAAIC6V6+SlnRblAYXddf4ks6aWdJR40s6a3BRd6Xbouq6aWjAvL1IJQAAANxTb2pa0m1RmlbSscJfs48oRNNKOipVTGkM3/HWIpW2MqOsA8eVV1Co6IhQp6FoAAAAqFy9SFpsRppb0u63hMX5FzwjiywymlvSTtcEnGCmMPiMNxapHPy3TynUBwAAcFO9GB6WVRahXFlVsaqgnJFFubIqqyyidhsGyLVi/QuaBGvB2q8o1AcAAKiBepG05CnYq8cB3nS+Yn37kEYK9QEAAGqmXiQt0Srx6nGAt1VXrP/A1Z108kzVn00K9QEAAKrnVzUtNlM+FCxPwYpWifoFFCjQIvULKFCsinREITKVDMKxyChGxeoXUFAHrQbKVVWsv3rHjy6dn1dQPnSMYn0AAABnfpO0pNuiNLek3W+1K+ViVaTk4MMaGXhCycGHNa2koywyTomL5bcBNsnBhynCR52rrFjf1UL96IhQpe/K1dxVeyjWBwAAOEudDQ/LsoU7Foa0T2ecqxCnY+zTGafbojQy8IRSg7+pMAQsRsVKDWa6Y/gvVwr1YyNDdeJ0saYt3kqxPgAAwDnqLGmZWnKxBhd114elUdVOZyyVT3dsM9LIwBNaG7LTsT8teJ8+s+4gYYFfO1+hviQ9NvpSPfnBHor1AQAAKlGnhfhHFKI/lXZ0azrjs4eA9Qv4hSFhqBeqK9RPndBLUU2tFXpYzkaxPgAAaMzqtKbFOE0IWz2mM0Z9V1WhfmCARStyfnDpGvZifQAAgMbErZ6WlJQU9e3bVxEREYqOjtZNN92kffv2edgE17pKmM4YDUFlhfqS3CrWBwAAaGzcSloyMjI0ffp0bdq0SWvWrFFpaalGjBih06dPe6Eplfe4WGQUqyKmM0aD5mqxfr+E5rXZLAAAAL/g1vCw9PR0p/eLFi1SdHS0tmzZoiFDhnjcGKYzRmNlL9aftnhrhUGT9o9+8pgurNcCAAAaJY8K8fPz8yVJzZtX/dffoqIinTp1yul1NntPystBTGeMxu18xfqs0wIAABqrGhfiG2OUlJSkwYMHKzExscrjUlJSNHfu3Er3nd2TMjLwhK4IyFe34t6SyqczviLgFD0saFSqK9YHAABorGrc0zJjxgzt2LFDb731VrXHzZ49W/n5+Y7X4cOHHfvO7UlhOmOg6mJ9AACAxqpGPS333XefVq5cqQ0bNqht27bVHmu1WmW1WitsTw3er5HWYhITAAAAANVyq6fFGKMZM2Zo2bJl+vTTT5WQkFDjG/emJwUAAACAC9zqaZk+fbrefPNNrVixQhERETpy5IgkKTIyUmFhYT5pIAAAAIDGza2eltTUVOXn5+vKK69UbGys4/X222/7qn0AAAAAGjm3elqMqXwBSAAAAADwFY/WaQEAAAAAXyNpAQAAAODXSFoAAAAA+DWSFgAAAAB+jaQFAAAAgF8jaQEAAADg10haAAAAAPg1khYAAAAAfo2kBQAAAIBfI2kBAAAA4NdIWgAAAAD4NZIWAAAAAH6NpAUAAACAXyNpAQAAAODXSFoAAAAA+DWSFgAAAAB+jaQFAAAAgF8jaQEAAADg10haAAAAAPg1khYAAAAAfo2kBQAAAIBfI2kBAAAA4NdIWgAAAAD4NZIWAAAAAH6NpAUAAACAXyNpAQAAAODXSFoAAAAA+DW3k5YNGzZozJgxiouLk8Vi0fLly33QLAAAAAAo53bScvr0afXo0UMvvviiL9oDAAAAAE6C3D1h1KhRGjVqlC/aAgAAAAAVuJ20uKuoqEhFRUWO96dOnfL1LQEAAAA0ID4vxE9JSVFkZKTj1a5dO1/fEgAAAEAD4vOkZfbs2crPz3e8Dh8+7OtbAgAAAGhAfD48zGq1ymq1+vo2AAAAABoo1mkBAAAA4Nfc7mn55Zdf9PXXXzveHzhwQDk5OWrevLni4+O92jgAAAAAcDtpyc7O1lVXXeV4n5SUJEmaNGmS0tLSvNYwAAAAAJBqkLRceeWVMsb4oi0AAAAAUAE1LQAAAAD8GkkLAAAAAL9G0gIAAADAr5G0AAAAAPBrJC0AAAAA/BpJCwAAAAC/RtICAAAAwK+RtAAAAADwayQtAAAAAPwaSQsAAAAAv0bSAgAAAMCvkbQAAAAA8GskLQAAAAD8GkkLAAAAAL9G0gIAAADAr5G0AAAAAPBrJC0AAAAA/BpJCwAAAAC/RtICAAAAwK+RtAAAAADwayQtAAAAAPwaSQsAAAAAv0bSAgAAAMCvkbQAAAAA8GskLQAAAAD8GkkLAAAAAL9G0gIAAADAr5G0AAAAAPBrNUpaXn75ZSUkJCg0NFS9e/fWxo0bvd0uAAAAAJBUg6Tl7bff1qxZs/TII49o27ZtuuKKKzRq1CgdOnTIF+0DAAAA0MgFuXvC888/r7vvvlv33HOPJGnBggX66KOPlJqaqpSUFJevU1ZqU1lpqfM2EyBraVH5fweWqsxSVvE8PzrG42ucOVO+vbj0P8ecOaOy0oo/Fm8cU1v34Zm8115jTIX9AAAAjY3FuPFbUXFxsZo0aaJ3331XN998s2P7zJkzlZOTo4yMjArnFBUVqaioyPE+Pz9f8fHx+vTCCxUeEOhh84GGrc0nnyr8gmZ13QwAAACfOHXqlNq1a6eTJ08qMjKyyuPc6mn5+eefZbPZ1Lp1a6ftrVu31pEjRyo9JyUlRXPnzq2wfdi337pza6Bxat+urlsAAADgcwUFBd5LWuwsFovTe2NMhW12s2fPVlJSkuP9yZMn1b59ex06dKjahqFm7Nnq4cOH1awZf6H3NuLrW8TXt4ivbxFf3yK+vkV8fYv4Vs0Yo4KCAsXFxVV7nFtJS8uWLRUYGFihVyUvL69C74ud1WqV1WqtsD0yMpIfmg81a9aM+PoQ8fUt4utbxNe3iK9vEV/fIr6+RXwr50pHhluzh4WEhKh3795as2aN0/Y1a9Zo0KBB7rUOAAAAAFzg9vCwpKQkTZw4UX369NHAgQP1yiuv6NChQ7r33nt90T4AAAAAjZzbScvtt9+uY8eO6YknnlBubq4SExP14Ycfqn379i6db7ValZycXOmQMXiO+PoW8fUt4utbxNe3iK9vEV/fIr6+RXw959aUxwAAAABQ29yqaQEAAACA2kbSAgAAAMCvkbQAAAAA8GskLQAAAAD8Wq0mLS+//LISEhIUGhqq3r17a+PGjbV5+wZjw4YNGjNmjOLi4mSxWLR8+XKn/cYYzZkzR3FxcQoLC9OVV16p3bt3101j66GUlBT17dtXERERio6O1k033aR9+/Y5HUOMay41NVXdu3d3LLA1cOBA/etf/3LsJ7belZKSIovFolmzZjm2EeOamzNnjiwWi9MrJibGsZ/Yeu6HH37QhAkT1KJFCzVp0kSXXXaZtmzZ4thPjGuuQ4cOFT6/FotF06dPl0RsPVVaWqpHH31UCQkJCgsL04UXXqgnnnhCZWVljmOIsQdMLVmyZIkJDg42CxcuNHv27DEzZ840TZs2Nd99911tNaHB+PDDD80jjzxili5daiSZ999/32n//PnzTUREhFm6dKnZuXOnuf32201sbKw5depU3TS4nrn22mvNokWLzK5du0xOTo4ZPXq0iY+PN7/88ovjGGJccytXrjQffPCB2bdvn9m3b595+OGHTXBwsNm1a5cxhth6U1ZWlunQoYPp3r27mTlzpmM7Ma655ORk07VrV5Obm+t45eXlOfYTW88cP37ctG/f3kyePNl8+eWX5sCBA2bt2rXm66+/dhxDjGsuLy/P6bO7Zs0aI8msW7fOGENsPTVv3jzTokULs3r1anPgwAHz7rvvmvDwcLNgwQLHMcS45motaenXr5+59957nbZ17tzZPPTQQ7XVhAbp3KSlrKzMxMTEmPnz5zu2FRYWmsjISPPPf/6zDlpY/+Xl5RlJJiMjwxhDjH0hKirKvPrqq8TWiwoKCkynTp3MmjVrzNChQx1JCzH2THJysunRo0el+4it5x588EEzePDgKvcTY++aOXOm6dixoykrKyO2XjB69GgzdepUp21jx441EyZMMMbw+fVUrQwPKy4u1pYtWzRixAin7SNGjNAXX3xRG01oNA4cOKAjR444xdpqtWro0KHEuoby8/MlSc2bN5dEjL3JZrNpyZIlOn36tAYOHEhsvWj69OkaPXq0rr76aqftxNhz+/fvV1xcnBISEjRu3Dh9++23koitN6xcuVJ9+vTRrbfequjoaPXs2VMLFy507CfG3lNcXKzFixdr6tSpslgsxNYLBg8erE8++URfffWVJGn79u367LPPdN1110ni8+upoNq4yc8//yybzabWrVs7bW/durWOHDlSG01oNOzxrCzW3333XV00qV4zxigpKUmDBw9WYmKiJGLsDTt37tTAgQNVWFio8PBwvf/+++rSpYvjH21i65klS5Zo69at2rx5c4V9fH49079/f73++uu6+OKL9dNPP2nevHkaNGiQdu/eTWy94Ntvv1VqaqqSkpL08MMPKysrS/fff7+sVqvuuusuYuxFy5cv18mTJzV58mRJ/NvgDQ8++KDy8/PVuXNnBQYGymaz6amnntL48eMlEWNP1UrSYmexWJzeG2MqbIN3EGvvmDFjhnbs2KHPPvuswj5iXHOXXHKJcnJydPLkSS1dulSTJk1SRkaGYz+xrbnDhw9r5syZ+vjjjxUaGlrlccS4ZkaNGuX4727dumngwIHq2LGj/u///k8DBgyQRGw9UVZWpj59+ujpp5+WJPXs2VO7d+9Wamqq7rrrLsdxxNhzr732mkaNGqW4uDin7cS25t5++20tXrxYb775prp27aqcnBzNmjVLcXFxmjRpkuM4YlwztTI8rGXLlgoMDKzQq5KXl1ch24Rn7LPYEGvP3XfffVq5cqXWrVuntm3bOrYTY8+FhITooosuUp8+fZSSkqIePXrohRdeILZesGXLFuXl5al3794KCgpSUFCQMjIy9N///d8KCgpyxJEYe0fTpk3VrVs37d+/n8+vF8TGxqpLly5O2y699FIdOnRIEv/+est3332ntWvX6p577nFsI7ae+8tf/qKHHnpI48aNU7du3TRx4kQ98MADSklJkUSMPVUrSUtISIh69+6tNWvWOG1fs2aNBg0aVBtNaDQSEhIUExPjFOvi4mJlZGQQaxcZYzRjxgwtW7ZMn376qRISEpz2E2PvM8aoqKiI2HrB8OHDtXPnTuXk5Dheffr00Z133qmcnBxdeOGFxNiLioqKtHfvXsXGxvL59YLLL7+8whTzX331ldq3by+Jf3+9ZdGiRYqOjtbo0aMd24it586cOaOAAOdfrQMDAx1THhNjD9VWxb99yuPXXnvN7Nmzx8yaNcs0bdrUHDx4sLaa0GAUFBSYbdu2mW3bthlJ5vnnnzfbtm1zTB89f/58ExkZaZYtW2Z27txpxo8fz3R6bpg2bZqJjIw069evd5oa8syZM45jiHHNzZ4922zYsMEcOHDA7Nixwzz88MMmICDAfPzxx8YYYusLZ88eZgwx9sSf//xns379evPtt9+aTZs2meuvv95EREQ4/l9GbD2TlZVlgoKCzFNPPWX2799v3njjDdOkSROzePFixzHE2DM2m83Ex8ebBx98sMI+YuuZSZMmmTZt2jimPF62bJlp2bKl+etf/+o4hhjXXK0lLcYY89JLL5n27dubkJAQ06tXL8cUsnDPunXrjKQKr0mTJhljyqfUS05ONjExMcZqtZohQ4aYnTt31m2j65HKYivJLFq0yHEMMa65qVOnOv4daNWqlRk+fLgjYTGG2PrCuUkLMa45+5oKwcHBJi4uzowdO9bs3r3bsZ/Yem7VqlUmMTHRWK1W07lzZ/PKK6847SfGnvnoo4+MJLNv374K+4itZ06dOmVmzpxp4uPjTWhoqLnwwgvNI488YoqKihzHEOOasxhjTJ108QAAAACAC2qlpgUAAAAAaoqkBQAAAIBfI2kBAAAA4NdIWgAAAAD4NZIWAAAAAH6NpAUAAACAXyNpAQAAAODXSFoAAAAA+DWSFgAAAAB+jaQFAFCr/vznP2vMmDF13QwAQD1C0gIAqFU5OTm67LLL6roZAIB6hKQFAFCrtm/frp49e9Z1MwAA9QhJCwCg1hw+fFjHjh1z9LScPHlSY8aM0aBBg5Sbm1u3jQMA+C2SFgBArcnJyVFkZKQSEhK0c+dO9e3bV7GxsVq/fr1iY2PrunkAAD9F0gIAqDU5OTnq0aOH3nrrLQ0ZMkT/7//9P73yyisKCQmp66YBAPyYxRhj6roRAIDG4ZZbbtG6deskSatXr9agQYPquEUAgPqAnhYAQK3JycnRLbfcosLCQp08ebKumwMAqCfoaQEA1IqCggJFRkZqy5Yt2r59u2bOnKkvvvhCXbt2reumAQD8XFBdNwAA0Djk5OQoMDBQXbp0Uc+ePbV7926NGTNGWVlZatmyZV03DwDgxxgeBgCoFdu3b1fnzp1ltVolSX/729/UpUsXjR07VsXFxXXcOgCAP2N4GAAAAAC/Rk8LAAAAAL9G0gIAAADAr5G0AAAAAPBrJC0AAAAA/BpJCwAAAAC/RtICAAAAwK+RtAAAAADwayQtAAAAAPwaSQsAAAAAv0bSAgAAAMCvkbQAAAAA8Gv/H9cxOfYWXXW1AAAAAElFTkSuQmCC",
      "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"
    }
   ],
   "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",
    "    plt.stem(yp[p, :])\n",
    "    plt.axvspan(0, N - 1 + 0.5, 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.axis([0, L + P, 0, 4])\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10, 2))\n",
    "plt.stem(y)\n",
    "plt.title(r\"Result $y[k] = x[k] * h[k]$\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$y[k]$\")\n",
    "plt.axis([0, 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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