filter_design/window_method.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Design of Digital 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": [
    "## Design of Non-Recursive Filters using the Window Method\n",
    "\n",
    "The design of non-recursive filters with a finite impulse response (FIR) is a frequent task in practical applications. The designed filter should approximate a desired frequency response as close as possible. First, the design of causal filters is considered. For many applications the resulting filter should have a linear phase characteristic since this results in a constant (and thus frequency independent) group delay. We therefore specialize the design to causal linear-phase filters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Causal Filters\n",
    "\n",
    "Let's assume that the desired frequency characteristics of the filter are given by its frequency response (i.e. discrete-time Fourier transform) $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. The corresponding impulse response is computed by its inverse discrete-time Fourier transform (IDTFT)\n",
    "\n",
    "\\begin{equation}\n",
    "h_\\text{d}[k] = \\frac{1}{2 \\pi} \\int\\limits_{- \\pi}^{\\pi} H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\, \\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega\\,k} \\; \\mathrm{d}\\Omega\n",
    "\\end{equation}\n",
    "\n",
    "In the general case, $h_\\text{d}[k]$ will not be a causal FIR. The [Paley-Wiener theorem](https://en.wikipedia.org/wiki/Paley%E2%80%93Wiener_theorem) states, that a causal system $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ can only have zeros at single frequencies. This is not the case for idealized filters, like e.g. the [ideal low-pass filter](https://en.wikipedia.org/wiki/Low-pass_filter#Ideal_and_real_filters). The basic idea of the window method is to truncate the impulse response $h_\\text{d}[k]$ in order to derive a causal FIR filter. This can be achieved by applying a window $w[k]$ of finite length $N$ to $h_\\text{d}[k]$\n",
    "\n",
    "\\begin{equation}\n",
    "h[k] = h_\\text{d}[k] \\cdot w[k]\n",
    "\\end{equation}\n",
    "\n",
    "where $h[k]$ denotes the impulse response of the designed filter and $w[k] = 0$ for $k < 0$. Its frequency response $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is given by the multiplication theorem of the discrete-time Fourier transform (DTFT)\n",
    "\n",
    "\\begin{equation}\n",
    "H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\frac{1}{2 \\pi} \\; H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\circledast W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\n",
    "\\end{equation}\n",
    "\n",
    "where $W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ denotes the DTFT of the window function $w[k]$. The frequency response $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ of the filter is given as the periodic convolution of the desired frequency response $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and the frequency response of the window function $W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. The frequency response $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is equal to the desired frequency response $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ only if $W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = 2 \\pi \\cdot \\delta(\\Omega)$. This would require that $w[k] = 1$ for $k = -\\infty, \\dots, \\infty$. Hence for a window $w[k]$ of finite length deviations from the desired frequency response are to be expected.\n",
    "\n",
    "In order to investigate the effect of truncation on the frequency response $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$, a particular window is considered. A straightforward choice is the rectangular window $w[k] = \\text{rect}_N[k]$ of length $N$. Its DTFT is given as\n",
    "\n",
    "\\begin{equation}\n",
    "W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\mathrm{e}^{-\\mathrm{j} \\, \\Omega \\,\\frac{N-1}{2}} \\cdot \\frac{\\sin(\\frac{N \\,\\Omega}{2})}{\\sin(\\frac{\\Omega}{2})}\n",
    "\\end{equation}\n",
    "\n",
    "The frequency-domain properties of the rectangular window have already been discussed for the [leakage effect](../spectral_analysis_deterministic_signals/leakage_effect.ipynb). The rectangular window features a narrow main lobe at the cost of relative high sidelobe level. The main lobe gets narrower with increasing length $N$. The convolution of the desired frequency response with the frequency response of the window function effectively results in smoothing and ringing. While the main lobe will smooth discontinuities of the desired transfer function, the sidelobes result in undesirable ringing effects. The latter can be alleviated by using other window functions. Note that typical [window functions](../spectral_analysis_deterministic_signals/window_functions.ipynb) decay towards their ends and are symmetric with respect to their center. This may cause problems for desired impulse responses with large values towards their ends."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Causal approximation of ideal low-pass\n",
    "\n",
    "The design of an ideal low-pass filter using the window technique is illustrated in the following example. For $|\\Omega| < \\pi$ the transfer function of the ideal low-pass is given as\n",
    "\n",
    "\\begin{equation}\n",
    "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\begin{cases}\n",
    "1 & \\text{for } |\\Omega| \\leq \\Omega_\\text{c} \\\\\n",
    "0 & \\text{otherwise}\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "where $\\Omega_\\text{c}$ denotes the corner frequency of the low-pass. An inverse DTFT of the desired transfer function yields\n",
    "\n",
    "\\begin{equation}\n",
    "h_\\text{d}[k] = \\frac{\\Omega_\\text{c}}{\\pi} \\cdot \\text{si}[\\Omega_\\text{c} \\, k]\n",
    "\\end{equation}\n",
    "\n",
    "The impulse response $h_\\text{d}[k]$ is not causal nor FIR. In order to derive a causal and FIR approximation a rectangular window $w[k]$ of length $N$ is applied\n",
    "\n",
    "\\begin{equation}\n",
    "h[k] = h_\\text{d}[k] \\cdot \\text{rect}_N[k]\n",
    "\\end{equation}\n",
    "\n",
    "The resulting magnitude and phase response is computed numerically in the following."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109019128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6a80f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6d5160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.signal as sig\n",
    "\n",
    "N = 32  # length of filter\n",
    "Omc = np.pi/2\n",
    "\n",
    "# compute impulse response\n",
    "k = np.arange(N)\n",
    "hd = Omc/np.pi * np.sinc(k*Omc/np.pi)\n",
    "# windowing\n",
    "w = np.ones(N)\n",
    "h = hd * w\n",
    "\n",
    "# frequency response\n",
    "Om, H = sig.freqz(h)\n",
    "\n",
    "# plot impulse response\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.stem(h)\n",
    "plt.title('Impulse response')\n",
    "plt.xlabel(r'$k$')\n",
    "plt.ylabel(r'$h[k]$')\n",
    "# plot magnitude responses\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.plot([0, Omc, Omc], [0, 0, -100], 'r--')\n",
    "plt.plot(Om, 20 * np.log10(abs(H)))\n",
    "plt.title('Magnitude response')\n",
    "plt.xlabel(r'$\\Omega$')\n",
    "plt.ylabel(r'$|H(e^{j \\Omega})|$ in dB')\n",
    "plt.axis([0, np.pi, -20, 3])\n",
    "plt.grid()\n",
    "# plot phase responses\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.plot(Om, np.unwrap(np.angle(H)))\n",
    "plt.title('Phase')\n",
    "plt.xlabel(r'$\\Omega$')\n",
    "plt.ylabel(r'$\\varphi (\\Omega)$ in rad')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercises**\n",
    "\n",
    "* Does the resulting filter have the desired phase?\n",
    "* Increase the length `N` of the filter. What changes?\n",
    "\n",
    "Solution: The desired filter has zero-phase for all frequencies, hence $\\varphi_\\text{d}(\\Omega) = 0$. The phase of the resulting filter is not zero as can be concluded from the lower illustration. The small local variations (ripples) in the magnitude $|H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|$ of the transfer function of the resulting filter decrease with an increasing number `N` of filter coefficients. The achievable attenuation in the stop-band of the low-pass does not change."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zero-Phase Filters\n",
    "\n",
    "Above results show that an ideal-low pass cannot be realized very well by the window method. The reason is that an ideal-low pass has zero-phase, as most of the idealized filters.\n",
    "\n",
    "Lets assume a general zero-phase filter with transfer function $H_d(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ with amplitude $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})  \\in \\mathbb{R}$. Its impulse response $h_d[k] = \\mathcal{F}_*^{-1} \\{ H_d(e^{j \\Omega} \\}$ is conjugate complex symmetric\n",
    "\n",
    "\\begin{equation}\n",
    "h_d[k] = h_d^*[-k]\n",
    "\\end{equation}\n",
    "\n",
    "due to the symmetry relations of the DTFT. Removal of the anti-causal part by windowing will result in large deviations between the desired transfer function and the designed filter. Hence, zero-phase filters cannot be realized very well by simple windowing of the desired impulse response. This observation motivates to shift the desired impulse response to the center of the window in order to limit the effect of windowing. This can be achieved by replacing the zero-phase with a linear-phase, as illustrated in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Causal Linear-Phase Filters\n",
    "\n",
    "The design of non-recursive FIR filters with a linear phase is often desired due to their constant group delay. Let's assume a system with generalized linear phase. For $|\\Omega| < \\pi$ its transfer function is given as\n",
    "\n",
    "\\begin{equation}\n",
    "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\cdot \\mathrm{e}^{-\\mathrm{j} \\alpha \\Omega + \\mathrm{j} \\beta}\n",
    "\\end{equation}\n",
    "\n",
    "where $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\in \\mathbb{R}$ denotes the amplitude of the filter, $\\alpha$ its linear phase and $\\beta$ a constant phase offset. Such a system can be decomposed into two cascaded systems: a zero-phase system with transfer function $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and an all-pass with phase $\\varphi(\\Omega) = - \\alpha \\Omega + \\beta$. The linear phase term $- \\alpha \\Omega$ results in the desired constant group delay $t_g(\\Omega) = \\alpha$. \n",
    "\n",
    "The impulse response $h[k]$ of a linear-phase system shows a specific symmetry which can be deduced from the symmetry relations of the DTFT for odd/even symmetry of $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ as\n",
    "\n",
    "\\begin{equation}\n",
    "h[k] = \\pm h[N-1-k]\n",
    "\\end{equation}\n",
    "\n",
    "for $k=0, 1, \\dots, N-1$ where $N \\in \\mathbb{N}$ denotes the length of the (finite) impulse response. The transfer function of a linear phase filter is given by its DTFT\n",
    "\n",
    "\\begin{equation}\n",
    "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\sum_{k=0}^{N-1} h[k] \\, \\mathrm{e}^{\\,-\\mathrm{j}\\,\\Omega\\,k}\n",
    "\\end{equation}\n",
    "\n",
    "Introducing the symmetry relations of the impulse response $h[k]$ into the DTFT and comparing the result with above definition of a generalized linear phase system reveals four different types of linear-phase systems. These can be discriminated with respect to their phase and magnitude characteristics\n",
    "\n",
    "| Type | Length $N$ | Impulse Response $h[k]\\;$ | Group Delay $\\alpha$ in Samples| Constant Phase $\\beta$ | Transfer Function $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ |\n",
    "| :---:  | :---: | :---: | :---:| :---: | :---: |\n",
    "| 1 | odd | $h[k] = h[N-1-k]$ | $\\alpha = \\frac{N-1}{2} \\in \\mathbb{N}$ | $\\beta = \\{0, \\pi\\}$ | $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{-\\,\\mathrm{j}\\,\\Omega})$, all filter characteristics|\n",
    "| 2 | even| $h[k] = h[N-1-k]$ | $\\alpha = \\frac{N-1}{2} \\notin \\mathbb{N}$ | $\\beta = \\{0, \\pi\\}$ | $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{-\\,\\mathrm{j}\\,\\Omega})$, $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\pi}) = 0$, only lowpass or bandpass|\n",
    "| 3 | odd | $h[k] = -h[N-1-k]$ | $\\alpha = \\frac{N-1}{2} \\in \\mathbb{N}$ | $\\beta = \\{ \\frac{\\pi}{2}, \\frac{3 \\pi}{2} \\} $ | $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = - A(\\mathrm{e}^{-\\,\\mathrm{j}\\,\\Omega})$, $A(\\mathrm{e}^{\\,\\mathrm{j}\\,0}) = A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\pi}) =  0$, only bandpass|\n",
    "| 4 | even | $h[k] = -h[N-1-k]$ | $\\alpha = \\frac{N-1}{2} \\notin \\mathbb{N}$ | $\\beta = \\{ \\frac{\\pi}{2}, \\frac{3 \\pi}{2} \\} $ | $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = - A(\\mathrm{e}^{-\\,\\mathrm{j}\\,\\Omega})$, $A(\\mathrm{e}^{\\,\\mathrm{j}\\,0}) = 0$, only highpass or bandpass|\n",
    "\n",
    "These relations have to be considered in the design of a causal linear phase filter. Depending on the desired frequency characteristics $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ the suitable type is chosen. The odd/even length $N$ of the filter and the phase (or group delay) is chosen accordingly for the design of the filter. It is also abovious that a filter with zero-phase $\\alpha = 0$, e.g. an ideal low-pass, would result in $N=1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Causal linear-phase approximation of ideal low-pass\n",
    "\n",
    "We aim at the design of a causal linear-phase low-pass using the window technique. According to the previous example, the desired frequency response has an even symmetry $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{\\,-\\mathrm{j}\\,\\Omega})$ with $A(\\mathrm{e}^{\\mathrm{j}\\,0}) = 1$. This could be realized by a filter of type 1 or 2. We choose type 1, since the resulting filter then exhibits an integer group delay of $t_g(\\Omega) = \\frac{N-1}{2}$ samples. Consequently the length of the filter $N$ has to be odd. \n",
    "\n",
    "The impulse response $h_\\text{d}[k]$ is given by the inverse DTFT of $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ as\n",
    "\n",
    "\\begin{equation}\n",
    "h_\\text{d}[k] = \\frac{\\Omega_\\text{c}}{\\pi} \\cdot \\text{si} \\left[ \\Omega_\\text{c} \\left(k-\\frac{N-1}{2} \\right) \\right]\n",
    "\\end{equation}\n",
    "\n",
    "The impulse response fulfills the desired symmetry for $k=0,1, \\dots, N-1$. A causal and FIR approximation is obtained by applying a window function of length $N$ to the impulse response $h_\\text{d}[k]$\n",
    "\n",
    "\\begin{equation}\n",
    "h[k] = h_\\text{d}[k] \\cdot w[k]\n",
    "\\end{equation}\n",
    "\n",
    "Note that the window function $w[k]$ also has to fulfill the desired symmetries.\n",
    "\n",
    "As already outlined, the chosen window determines the properties of the transfer function $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. The [spectral properties of commonly applied windows](../spectral_analysis_deterministic_signals/window_functions.ipynb) have been discussed previously. The width of the main lobe will generally influence the  smoothing of the desired transfer function $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$, while the sidelobes influence the typical ringing artifacts. This is illustrated in the following."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAADiCAYAAADOIvrCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAIABJREFUeJzt3Xu8XGV97/HP10A0KhKRlEIAoYpRFDQ1wkG81UuDtpUc6wWqFms90HPEam1R8HisxVpQrG1tOa3UoqhVoErTVGmjlYraeiEY5HpSI3LJBiGAEdAoJPzOH2ttHLb7MjvZe8/Mns/79cors9Z6Zp7f8+w1s37zPGutSVUhSZKkwfGgXgcgSZKk6TGBkyRJGjAmcJIkSQPGBE6SJGnAmMBJkiQNGBM4SZKkAWMCJ81TSV6T5Cu9jmOQJTk4ybok6XUssynJdUmeP8d1PjPJhp14fiV57AzG84Yk75mp15NmmwmcNMt6cXDUjHkX8L6ahRtmznQCMmiq6stVtazXcXT4W+CVSX6u14FI3TCBk7TDkuzS6xhmS5K9gV8CVk+wfd62vVvzqQ+q6sfAvwC/2etYpG6YwElzqJ3W/I8kf5ZkS5Jrkzy9XX9jkluTHNdR/iNJ/ibJ55PcleTiJI9utx3QjuLs0lH+i0leN069aeu8NcmdSa5I8qR224OTvC/JDUluaetb1EX8twPvbNe/Nsk1Sb6fZG1HjJPVO2Hb2u1PT3JJkh+0/z99TDvf1cZyV5LPJdmz3faQJB9Pcnvbx5ck2avdtnuSv0tyc5KRJH+cZMEEf64XAN9sD+yj9V6X5K1JLgd+mGSXJPsk+XSSzUm+m+R3O8ovSPK2JN9p47w0yX5JvtQW+VaSu5O8Iskjk3ymfZ3vt4/37abN7fbfTHJ92+7/k46R37av/7ij7HOSbJrgb3xYkq+2fXdzkr9KsrBjeyV5fZJvA98e5/nnJPn99vHS0fLt8mOS3JHkQWNjaOP9gySXt3/z85I8pGP7SW08NyV57Zg6d0/y0bbvrk/y9iQParddn+Sp7eNXtvE8sV3+7SSdCfoXgV8Zr1+kfmMCJ829w4HLgUcBnwDOBZ4GPBZ4FfBXSR7eUf6VNFN5ewKXAX+/A3X+MvAs4HHA7sDLgdvbbae365/SxrAUeMcU8V8L7AW8O8nRwNuAlwBLgC8Dn+yi3gnblmQP4LPAB2j66f3AZ5M8quO5vwH8FvBzwELgD9r1x7V17dc+93eAre22jwDb2nYub+P7mYS3dQgw3jlax9Ic5BcD9wH/DHyLpt+eB7wpycq27Jvb8i8CHgG8FvhRVT2r3f7kqnp4VZ1H83n8YeDRwP5tzH81pu5x25zkYOD/0vTn3m37l07QrqlsB36P5m9yRNum/zWmzCqa/eDgcZ5/MfCc9vGzafaVZ3Usf7mq7pug7pcDRwEHAocCrwFIchRNW18AHASMPSXhL2na/AttHb9J00/dxHNxx+tcAzx5gtikvmICJ82971bVh6tqO3AeTaJxalX9pKo+B9xDk2CM+mxVfamqfgL8b+CIJPtNs857gd2AxwOpqmuq6uYkAY4Hfq+q7qiqu4A/AY6Z5LVuqqq/rKptVbWVJkE6rX3Nbe3zn9KOpo1bbxdt+xXg21X1sbaeTwL/D/i1jud+uKr+q43hfJoEdLStjwIeW1Xbq+rSqrqzHYV7EfCmqvphVd0K/NkkbV0M3DXO+g9U1Y1tvU8DllTVqVV1T1VdS3Mu1ehrvg54e1VtqMa3qur2cV6Tqrq9qj5dVT9q/w7vpkkwOk3U5pcC/1xVX6mqe2gS8B06b6/tr6+1/X4d8MFx4jit3V+2/uwrcDHwjHYE7FnAe4Ej221jE6axPlBVN1XVHTSJ8Wj7Xk7T9iur6oe0I7/QjHLS9PcpVXVXG/OfAq/uiGc0/mcCp3Usj43nLppEUOp7JnDS3Lul4/FWgKoau65zBO7G0QdVdTdwB7DPdCqsqotoRnPOBG5NclaSR9CMmD0UuLSdMtsC/Gu7fiI3jll+NPAXHc+/AwiwdJJ6p2rbPsD1Y+q5ngeOKn2v4/GP+GmffQxYC5zbTre9N8mubZy7Ajd3xPpBmtGs8XyfJvmcrP2PBvYZfb32Nd9GMzoJTXL+nQle/wGSPDTJB9spvzuBLwGLx0zxTtTmfXhgX/6IB450di3J49rp2++1cfwJzWhcp7H7wP2q6jvAD2mSr2cCnwFuSrKMqRO4rtrHA/eNPWn+rteP2T66r1wMPDPNOY0LaBLfI5McQJOsXdbxvN2AH0wSn9Q3TOCk/nf/aFs7tboHcBPNQRKaBGzUz0/0IlX1gap6Ks201+OAk4DbaBLGJ1bV4vbf7lX18Ileh58d2bkROKHj+YuralFV/eck9U7VtptokqNO+wMjk8Q12s57q+qPqupg4OnAr9JMqd0I/ATYsyPOR1TVEyd4qcvbeCdr/400I6qdbd+tql7Usf0xU8Xc+n1gGXB4VT2Cn07zdXMLk5uBzvPlFtGMQo76IV3uJ8Bf04x2HtTG8bZxYphqdO9imlHBhVU10i4fBzySByZM3bqZjn2FZl8YdRvNqOujx2wfAaiqjTTJ4BuAL1XVnTSJ4vHAV8ZM5z6BZjpc6nsmcFL/e1GSZ7Qnkr8L+Fo7hbeZ5iD1qvZk+dcyQbKQ5GlJDm9Hon4I/Bi4rz14/S3wZ2lvn9CeeL5yvNeZwN8Ap3ScGL57kpdNVu9UbQMuBB6X5DfSXCjwCpoE8DNTBZPkl5Ic0o5c3UlzcL+vnbr9HPCnSR7Rnkj/mCRjpwdHfR74xc4T6cfxDeCuNBc2LGr/Dk9K8rR2+4eAdyU5KI1DO87ju4XmnK1Ru9Ek01vacwD/cKq2dvgU8GtpLvxYSDPF2Jl0XUbT13sk+XngTZO81m40/XZ3kscD/3MacYy6GDiRZhQRmosDTqRJmLbvwOudD7wmzX35HkpH37Svdz7N+Zi7tVP3bwY+Pk48o6N/XxyzPOrZNFeiSn3PBE7qf5+gOWDdATyV5kKHUf+DZkTrduCJwH9O8BqPoEnUvk8zvXQ7cEa77a3ARuBr7ZTZv9GMBHWlqv4ReA/NlOWdwJXAC7uod8K2teeJ/SrNqNTtwFuAX62q27oI6edpEpo7aU5Kv5hmWhWakbiFwNVtTJ+iOel/vHbdAlwEHD1J27e3cT4F+C7NaNCH+Ol5VO+nSS4+18bzd8DoFb7vBM5pp15fDvx5u+024Gs0U9ldqaqraEaYzqUZrbobuJVmxBGa9n8LuK6N5bxJXu4PaC6WuIvmbzdZ2YlcTJMIjiZwX6EZAfzShM+YRFX9C03/XESzr140psgbaL4gXNvW9Qng7EniGbtMm6i/CDhnR2KU5lpm4f6UkmZIko8Am6rq7b2OZaYNQtvaqzvPAQ6rAfqwbKejt9BMg3631/EMgiRvAParqrf0OhapG/PmJoySNNOq6mqaK037XpJfA75AM3X6PuAKmhE3daGq/rLXMUjT4RSqJM0PR/PTC0AOAo4ZpFFDSdPjFKokSdKAcQROkiRpwJjASZIkDZh5fxHDnnvuWQcccECvw5AkSZrSpZdeeltVTfZrOMAQJHAHHHAA69at63UYkiRJU0oy9mcEx+UUqiRJ0oAxgZMkSRowfZXAJTkqyYYkG5OcPM721yTZnOSy9t/rehGnpOG1ev0IR55+EQee/FmOPP0iVq8f6XVIkoZQ35wD1/7w9JnAC4BNwCVJ1rR3Qu90XlWdOOcBShp6q9ePcMoFV7D13ub32Ee2bOWUC64AYNXypb0MTdKQ6acRuMOAjVV1bVXdQ/OjzBP+iLQkzbUz1m64P3kbtfXe7ZyxdkOPIpI0rPopgVsK3NixvKldN9avJ7k8yaeS7DfeCyU5Psm6JOs2b948G7FKGkI3bdk6rfWSNFv6KYHrxj8DB1TVocDngXPGK1RVZ1XViqpasWTJlLdSkaSu7LN40bTWS9Js6acEbgToHFHbt113v6q6vap+0i5+CHjqHMUmSZy0chmLdl3wgHWLdl3ASSuX9SgiScOqnxK4S4CDkhyYZCFwDLCms0CSvTsWXwxcM4fxSRpyq5Yv5bSXHMLCBc1H59LFizjtJYd4AYOkOdc3V6FW1bYkJwJrgQXA2VV1VZJTgXVVtQb43SQvBrYBdwCv6VnAkobSquVL+eQ3bgDgvBOO6HE0koZV3yRwAFV1IXDhmHXv6Hh8CnDKXMclSZLUT/ppClWSJEldMIGTJEkaMCZwkiRJA8YETpIkacCYwEmSJA0YEzhJkqQBYwInSZI0YEzgJEmSBowJnCRJ0oAxgZMkSRowJnCSJEkDxgROkiRpwJjASZIkDRgTOEmSpAFjAidJkjRg+iqBS3JUkg1JNiY5eZJyv56kkqyYy/gkSZL6Qd8kcEkWAGcCLwQOBo5NcvA45XYD3gh8fW4jlCRJ6g99k8ABhwEbq+raqroHOBc4epxy7wLeA/x4LoOTJEnqF/2UwC0FbuxY3tSuu1+SXwT2q6rPzmVgkiRJ/aSfErhJJXkQ8H7g97soe3ySdUnWbd68efaDkyRJmkP9lMCNAPt1LO/brhu1G/Ak4ItJrgP+G7BmvAsZquqsqlpRVSuWLFkyiyFLkiTNvX5K4C4BDkpyYJKFwDHAmtGNVfWDqtqzqg6oqgOArwEvrqp1vQlXkiSpN/omgauqbcCJwFrgGuD8qroqyalJXtzb6CRJkvrHLr0OoFNVXQhcOGbdOyYo+5y5iEmSJKnf9M0InCRJkrpjAidJkjRgTOAkSZIGjAmcJEnSgDGBkyRJGjAmcJIkSQPGBE6SJGnAmMBJkiQNGBM4SZKkAWMCJ0mSNGBM4CRJkgaMCZwkSdKA6asfs5ek2bZ6/QhnrN3ATVu2ss/iRZy0chmrli8dmvolzQ8mcJKGxur1I5xywRVsvXc7ACNbtnLKBVcAzEkS1ev6Jc0fTqFKGhpnrN1wf/I0auu92zlj7YahqF/S/GECJ2lo3LRl67TWz7f6Jc0ffZXAJTkqyYYkG5OcPM7230lyRZLLknwlycG9iFPSYNpn8aJprZ9v9UuaP/omgUuyADgTeCFwMHDsOAnaJ6rqkKp6CvBe4P1zHKakAXbSymUs2nXBA9Yt2nUBJ61cNhT1S5o/+ukihsOAjVV1LUCSc4GjgatHC1TVnR3lHwbUnEYoaaCNXijwlk9dzj3b72PpHF8F2uv6Jc0f/ZTALQVu7FjeBBw+tlCS1wNvBhYCzx3vhZIcDxwPsP/++894oJIG16rlS/nkN24A4LwTjhi6+iXND30zhdqtqjqzqh4DvBV4+wRlzqqqFVW1YsmSJXMboCRJ0izrpwRuBNivY3nfdt1EzgVWzWpEkiRJfaifErhLgIOSHJhkIXAMsKazQJKDOhZ/Bfj2HMYnSZLUF/rmHLiq2pbkRGAtsAA4u6quSnIqsK6q1gAnJnk+cC/wfeC43kUsSZLUG32TwAFU1YXAhWPWvaPj8RvnPChJkqQ+009TqJIkSeqCCZwkSdKAMYGTJEkaMCZwkiRJA8YETpIkacCYwEmSJA0YEzhJkqQBYwInSZI0YEzgJEmSBowJnCRJ0oCZ8qe0kuzRxevcV1VbZiAeSZIkTaGb30K9qf2XScosAPafkYgkSZI0qW4SuGuqavlkBZKsn6F4JEmSNIVuzoE7YobKSJIkaQZMmcBV1Y8Bkvzx2G1JFnSWkSRJ0uybzlWoS5McO7qQ5OeAf5vJYJIclWRDko1JTh5n+5uTXJ3k8iRfSPLomaxfkiRpEEwngTsBOD7JYUmeBlwEvG+mAmlH884EXggcDByb5OAxxdYDK6rqUOBTwHtnqn5JkqRB0c1tRD4KfJMmeXo98AlgG7CqqjbOYCyHARur6tq23nOBo4GrRwtU1b93lP8a8KoZrF+SJGkgdDMC9xGaW4j8FvBx4ADg+8Crkrx0BmNZCtzYsbypXTeR3wb+ZQbrlyRJGghTjsBV1UU006UAJNkFeALwZOBwmqnMOZXkVcAK4NkTbD8eOB5g//29PZ0kSZpfurkP3ANU1Tbgivbfx2cwlhFgv47lfdt1D5Dk+cD/Bp5dVT+ZIMazgLMAVqxYUTMYoyRJUs9NOYWa5JszUaYLlwAHJTkwyULgGGDNmHqWAx8EXlxVt85AnZIkSQOnmxG4JyS5fJLtAXbf2UCqaluSE4G1ND/NdXZVXZXkVGBdVa0BzgAeDvxDEoAbqurFO1u3JEnSIOkmgXt8F2W272wgAFV1IXDhmHXv6Hj8/JmoR5IkaZB1cxHD9QBJngu8EtgCXAlcDlw50XlokiRJmh3TuYjhbOBNwK7AocAq4InAY2chLkmSJE1gOgnc9VW1un38D7MRjCRJkqbWzVWoH03yJuBrSd48BzFJkiRpEtP5JYa9gFcnuT7JmiTvSvKyWY1OkiRJP2Nnf4nhaTidKkmSNKd29pcYJEmSNMe6mUKVJElSHzGBkyRJGjAmcJIkSQPGBE6SJGnAmMBJkiQNGBM4SZKkAWMCJ0mSNGBM4CRJkgZMXyVwSY5KsiHJxiQnj7P9WUm+mWRbkpf2IkZJkqRe65sELskC4EzghcDBwLFJDh5T7AbgNcAn5jY6SZKk/jHtn9KaRYcBG6vqWoAk5wJHA1ePFqiq69pt9/UiQEmSpH7QNyNwwFLgxo7lTe06SZIkdeinBG7GJDk+ybok6zZv3tzrcCRJkmZUPyVwI8B+Hcv7tuumrarOqqoVVbViyZIlMxKcJElSv+inBO4S4KAkByZZCBwDrOlxTJIkSX2nbxK4qtoGnAisBa4Bzq+qq5KcmuTFAEmelmQT8DLgg0mu6l3EkiRJvdFPV6FSVRcCF45Z946Ox5fQTK1KkiQNrb4ZgZMkSVJ3+moETtLcWL1+hDPWbuCmLVvZZ/EiTlq5jFXLvWuPZp/7njQzTOCkIbN6/QinXHAFW+/dDsDIlq2ccsEVAB5INavc96SZ4xSqNGTOWLvh/gPoqK33bueMtRt6FJGGhfueNHNM4KQhc9OWrdNaL80U9z1p5pjASUNmn8WLprVeminue9LMMYGThsxJK5exaNcFD1i3aNcFnLRyWY8i0rBw35NmjhcxSENm9GTxt3zqcu7Zfh9LvRJQc8R9T5o5JnAaWsN8O4NVy5fyyW/cAMB5JxzR42g0TIZ53xvmzxzNPBM4DSVvZyBpLvmZo5lmAjfEhvnb4GS3MxiWPpA0d4b9M2eYjzezxQRuSA37t0FvZyBpLg3zZ86wH29mi1ehDqlhv6GmtzOQNJeG+TNn2I83s8UEbkgN87dB8HYGkubWMH/mDPvxZraYwA2pYf42CM2w/WkvOYSFC5q3wNLFizjtJYc4nC9pVgzzZ86wH29miwnckBrmb4OjVi1fyvL9F3P4gXvwHyc/dyg+SCX1zrB+5ni8mR19dRFDkqOAvwAWAB+qqtPHbH8w8FHgqcDtwCuq6rq5jrNTL6+s2Zm6Z+KGmr2+qmhQ+976B7/+Xup1233fDWf9Hm/67zOnbxK4JAuAM4EXAJuAS5KsqaqrO4r9NvD9qnpskmOA9wCvmPtoG728smYm6t6ZG2r2+qqiQe976x/c+nup1233fTec9Xu86c/PnFRVzyrvlOQI4J1VtbJdPgWgqk7rKLO2LfPVJLsA3wOW1CSNWLFiRa1bt25WYj7y9IsY2bKVEy7/J37hByP3r3/wLgtYvv/irl7jutt/CMABj3rYtOpef8MWfrJt+8+sn07dAFfffCcAB+/9iJ7UP4jtH+a2z2T9vWz/jra918+fD30Pvu9gsP72w9z2sfVfu/tSPnjo0UBzHuN/nPzcab1WN5JcWlUrpirXNyNwwFLgxo7lTcDhE5Wpqm1JfgA8Crits1CS44HjAfbff//ZinfCK2jG29Em8qN7ui/bTR3TqRvgoQsXTF1oFusfxPYPc9tnsv5etn9H297r58+Hvgffd72sf0faP8xtn6yeXl9F208jcC8Fjqqq17XLrwYOr6oTO8pc2ZbZ1C5/py1z23ivCXMzAjfWdLLyV3zwq8D0h5Rnou6dMVP1D2L7h7ntM1n/oLa/l4a574e57TNZ/460f5jbPpP1d6vbEbh+ugp1BNivY3nfdt24Zdop1N1pLmboiV5eWdPrq3qGuf5hbrv191av2+77bjjrH+a290P9E+mnKdRLgIOSHEiTqB0D/MaYMmuA44CvAi8FLprs/LfZNnry4o5embJ6/Qjrb9jCPdvv48jTL9qhq3p6dVXMMNc/zG23/t7qddt93w1n/fOh7YN8vJ1I30yhAiR5EfDnNLcRObuq3p3kVGBdVa1J8hDgY8By4A7gmKq6drLXnM0p1J0x9qoWaDL6Ybmx46gdHdKeD4a57WD7e2mY+36Y2w7D2f5BO94O4hQqVXVhVT2uqh5TVe9u172jqta0j39cVS+rqsdW1WFTJW/9zN+G++k3oq9/9w6OPP0iVq8fO2MuSZopw/qZO1+Pt32VwA2TYf9tuNFvRPdsvw/46X11huUDRZLm0jB/5s7X460JXI8M+2/DzddvRJLUj4b5M3e+Hm9N4HqkX69qmSvz9RuRJPWjYf7Mna/HWxO4Hlm1fCmnveQQli5eRGjuJ9OvJ1TOhvn6jahbw3ouitRLw/y+G+bP3Pl6vO2n24gMnVXLlw78DrSjTlq5bNyrggb9G1E3JjoXBeb/b3lKvTLs77th/syF+Xm8dQROPTFfvxF1Y5jPRZF6Zdjfd8P8mTtfOQKnnpmP34i6Mcznoki94vtueD9z5ytH4KQ5Nsznoki94vtO840JnDTH5usVUVI/832n+cYpVGmO9evv6knzme87zTcmcFIPeC6KNPd832k+cQpVkiRpwJjASZIkDRgTOEmSpAFjAidJkjRg+iKBS7JHks8n+Xb7/yMnKPevSbYk+cxcxyhJktQv+iKBA04GvlBVBwFfaJfHcwbw6jmLSpIkqQ/1SwJ3NHBO+/gcYNV4harqC8BdcxWUpNmxev0I62/Ywte/ewdHnn4Rq9eP9DqkoWHfS/NDvyRwe1XVze3j7wF79TIYSbNn9foRTrngCu7Zfh8AI1u2csoFV5hIzAH7Xpo/5iyBS/JvSa4c59/RneWqqoDaybqOT7IuybrNmzfvVNySZtYZazew9d7tD1i39d7tnLF2Q48iGh72vTR/zNkvMVTV8yfaluSWJHtX1c1J9gZu3cm6zgLOAlixYsVOJYOSZtZNW7ZOa71mjn0vzR/9MoW6BjiufXwc8E89jEXSLNpn8aJprdfMse+l+aNfErjTgRck+Tbw/HaZJCuSfGi0UJIvA/8APC/JpiQrexKtpB120splLNp1wQPWLdp1ASetXNajiIaHfS/NH33xY/ZVdTvwvHHWrwNe17H8zLmMS9LMG/0x8TPWbuCmLVvZZ/EiTlq5zB8ZnwP2vTR/pLlmYP5asWJFrVu3rtdhSJIkTSnJpVW1Yqpy/TKFKkmSpC6ZwEmSJA0YEzhJkqQBM+/PgUuyGbh+DqraE7htDuqZj+y7HWff7Tj7bufYfzvOvttxw9B3j66qJVMVmvcJ3FxJsq6bkw71s+y7HWff7Tj7bufYfzvOvttx9t1POYUqSZI0YEzgJEmSBowJ3Mw5q9cBDDD7bsfZdzvOvts59t+Os+92nH3X8hw4SZKkAeMInCRJ0oAxgdtJSY5KsiHJxiQn9zqeQZPkuiRXJLksib95NokkZye5NcmVHev2SPL5JN9u/39kL2PsVxP03TuTjLT73mVJXtTLGPtVkv2S/HuSq5NcleSN7Xr3vSlM0nfue11I8pAk30jyrbb//qhdf2CSr7fH3fOSLOx1rL3gFOpOSLIA+C/gBcAm4BLg2Kq6uqeBDZAk1wErqmq+39dnpyV5FnA38NGqelK77r3AHVV1evsF4pFV9dZextmPJui7dwJ3V9X7ehlbv0uyN7B3VX0zyW7ApcAq4DW4701qkr57Oe57U0oS4GFVdXeSXYGvAG8E3gxcUFXnJvkb4FtV9de9jLUXHIHbOYcBG6vq2qq6BzgXOLrHMWmeqqovAXeMWX00cE77+Byag4PGmKDv1IWqurmqvtk+vgu4BliK+96UJuk7daEad7eLu7b/Cngu8Kl2/dDueyZwO2cpcGPH8iZ8c05XAZ9LcmmS43sdzADaq6pubh9/D9irl8EMoBOTXN5OsToFOIUkBwDLga/jvjctY/oO3Pe6kmRBksuAW4HPA98BtlTVtrbI0B53TeDUa8+oql8EXgi8vp3q0g6o5nwIz4no3l8DjwGeAtwM/Glvw+lvSR4OfBp4U1Xd2bnNfW9y4/Sd+16Xqmp7VT0F2Jdm1uvxPQ6pb5jA7ZwRYL+O5X3bdepSVY20/98K/CPNG1Tdu6U9z2b0fJtbexzPwKiqW9qDw33A3+K+N6H2/KNPA39fVRe0q933ujBe37nvTV9VbQH+HTgCWJxkl3bT0B53TeB2ziXAQe0VMQuBY4A1PY5pYCR5WHtiL0keBvwycOXkz9IYa4Dj2sfHAf/Uw1gGymjy0frvuO+Nqz2R/O+Aa6rq/R2b3PemMFHfue91J8mSJIvbx4toLhi8hiaRe2lbbGj3Pa9C3Unt5d9/DiwAzq6qd/c4pIGR5BdoRt0AdgE+Yf9NLMkngecAewK3AH8IrAbOB/YHrgdeXlWerD/GBH33HJoprAKuA07oOKdLrSTPAL4MXAHc165+G825XO57k5ik747FfW9KSQ6luUhhAc2A0/lVdWp77DgX2ANYD7yqqn7Su0h7wwROkiRpwDiFKkmSNGBM4CRJkgaMCZwkSdKAMYGTJEkaMCZwkiRJA8YETpIkacCYwEmSJA0YEzhJmoYkz0vysV7HIWm4mcBJ0vQ8mebu75LUMyZwkjQ9TwbWJ3lwko8k+ZP2Ny8lac7s0usAJGnAHArcCqwFPlRVH+9xPJKGkL+FKkldSrIrcBvNj7efUFVf7XFIkoaUU6iS1L0nAJcA24DtPY5F0hAzgZOk7j0Z+E/gGODDSfbqcTyShpQJnCR178nAlVX1X8BbgfPbaVVJmlOeAydJkjRgHIGTJEkaMCZwkiRJA8YETpIkacCYwEmSJA0YEzhJkqQBYwInSZI0YEzgJEmSBowJnCRJ0oC7zd44AAAABklEQVT5/2q7SD6sXkitAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c9f6630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c7399b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6d5358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 33  # length of filter\n",
    "Omc = np.pi/2\n",
    "\n",
    "# compute impulse response\n",
    "k = np.arange(N)\n",
    "hd = Omc/np.pi * np.sinc((k-(N-1)/2)*Omc/np.pi)\n",
    "# windowing\n",
    "w1 = np.ones(N)\n",
    "w2 = np.blackman(N)\n",
    "h1 = hd * w1\n",
    "h2 = hd * w2\n",
    "\n",
    "# frequency responses\n",
    "Om, H1 = sig.freqz(h1)\n",
    "Om, H2 = sig.freqz(h2)\n",
    "\n",
    "# plot impulse response\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.stem(h1)\n",
    "plt.title('Impulse response (rectangular window)')\n",
    "plt.xlabel(r'$k$')\n",
    "plt.ylabel(r'$h[k]$')\n",
    "# plot magnitude responses\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.plot([0, Omc, Omc], [0, 0, -300], 'r--')\n",
    "plt.plot(Om, 20 * np.log10(abs(H1)), label='rectangular window')\n",
    "plt.plot(Om, 20 * np.log10(abs(H2)), label='Blackmann window')\n",
    "plt.title('Magnitude response')\n",
    "plt.xlabel(r'$\\Omega$')\n",
    "plt.ylabel(r'$|H(e^{j \\Omega})|$ in dB')\n",
    "plt.axis([0, np.pi, -120, 3])\n",
    "plt.legend(loc=3)\n",
    "plt.grid()\n",
    "# plot phase responses\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.plot(Om, np.unwrap(np.angle(H1)), label='rectangular window')\n",
    "plt.plot(Om, np.unwrap(np.angle(H2)), label='Blackmann window')\n",
    "plt.title('Phase')\n",
    "plt.xlabel(r'$\\Omega$')\n",
    "plt.ylabel(r'$\\varphi (\\Omega)$ in rad')\n",
    "plt.legend(loc=3)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercises**\n",
    "\n",
    "* Does the impulse response fulfill the required symmetries for a type 1 filter?\n",
    "* Can you explain the differences between the magnitude responses $|H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|$ for the different window functions?\n",
    "* What happens if you increase the length `N` of the filter?\n",
    "\n",
    "Solution: Inspection of the impulse response reveals that it shows the symmetry $h[k] = h[N-1-k]$ of a type 1 filter for odd `N`. The rectangular window features a narrow main lobe at the cost of a high level of the side lobes, the main lobe of the Blackmann window is wider but the level of the side lobes is lower compared to the rectangular window. This explains the behavior of the magnitude responses $|H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|$ in the stop-band of the realized low-passes. The distance between the local minima in the magnitude responses $|H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|$ decreases with increasing length `N` and the attenuation for frequencies towards the Nyquist frequency increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "\n",
    "**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, 2016-2017*."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}