LTI - Transfer Function Estimation - Impulse Step Response - Zero Pole - ROC.ipynb

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    "colab": {
      "name": "part3.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QRgCj1Si5if7",
        "outputId": "4c960fac-e74e-4247-b1df-e119086d60f1"
      },
      "source": [
        "## BASICS\n",
        "import numpy as np  # linear algebra\n",
        "import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n",
        "import os\n",
        "import seaborn as sns\n",
        "import itertools\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "from matplotlib.patches import Circle, Wedge, Polygon\n",
        "from IPython.display import display, HTML\n",
        "\n",
        "## DSP\n",
        "! pip install control\n",
        "! pip install audiolazy\n",
        "! pip install PyDynamic\n",
        "from PyDynamic.identification.fit_filter import LSIIR\n",
        "from scipy import signal, fftpack\n",
        "import control\n",
        "import cmath\n",
        "import sympy\n"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: control in /usr/local/lib/python3.6/dist-packages (0.8.3)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from control) (1.4.1)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.6/dist-packages (from control) (3.2.2)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from control) (1.18.5)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->control) (0.10.0)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->control) (2.4.7)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->control) (1.3.1)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->control) (2.8.1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from cycler>=0.10->matplotlib->control) (1.15.0)\n",
            "Requirement already satisfied: audiolazy in /usr/local/lib/python3.6/dist-packages (0.6)\n",
            "Requirement already satisfied: PyDynamic in /usr/local/lib/python3.6/dist-packages (1.6.1)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.6/dist-packages (from PyDynamic) (3.2.2)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from PyDynamic) (1.18.5)\n",
            "Requirement already satisfied: pandas in /usr/local/lib/python3.6/dist-packages (from PyDynamic) (1.1.5)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from PyDynamic) (1.4.1)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->PyDynamic) (0.10.0)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->PyDynamic) (2.8.1)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->PyDynamic) (1.3.1)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->PyDynamic) (2.4.7)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas->PyDynamic) (2018.9)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from cycler>=0.10->matplotlib->PyDynamic) (1.15.0)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/PyDynamic/identification/fit_filter.py:29: DeprecationWarning: The module *identification* will be combined with the module *deconvolution* and renamed to *model_estimation* in the next major release 2.0.0. From version 1.4.1 on you should only use the new module *model_estimation* instead.\n",
            "  DeprecationWarning,\n",
            "/usr/local/lib/python3.6/dist-packages/PyDynamic/identification/fit_transfer.py:28: DeprecationWarning: The package *identification* will be combined with the package *deconvolution* and renamed to *model_estimation* in the next major release 2.0.0. From version 1.4.1 on you should only use the new package *model_estimation* instead.\n",
            "  DeprecationWarning,\n",
            "/usr/local/lib/python3.6/dist-packages/PyDynamic/uncertainty/interpolation.py:28: PendingDeprecationWarning: The module :mod:`PyDynamic.uncertainty.interpolation` will be renamed to :mod:`PyDynamic.uncertainty.interpolate` in the next major release 2.0.0. From version 1.4.3 on you should only use the new module instead.\n",
            "  PendingDeprecationWarning,\n",
            "/usr/lib/python3.6/importlib/_bootstrap.py:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 192 from C header, got 216 from PyObject\n",
            "  return f(*args, **kwds)\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h7KHZClV-JnN"
      },
      "source": [
        "sns.set_style(\"darkgrid\")"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wHZL_qlN5tLs"
      },
      "source": [
        "# **PART 3 🇸- Linear Time Invariant (LTI) System**\n",
        "## **AGENDA**\n",
        "## > Given input $x[n]$, output $y[n]$ find transfer function $H(z)$\n",
        "### >> **MANUALLY**\n",
        "### >> **ESTIMATION**\n",
        "## > Difference equation $\\sum_{k = 0}^{N}a_ky[n-k] = \\sum_{k = 0}^{M}b_kx[n - k] $ : Find $a_k$,$b_k$\n",
        "## > Zero-Pole map & Region of Convergence (ROC)\n",
        "## > Find **impulse response** (time)  $h[n]$\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UOAPb6c75wth"
      },
      "source": [
        "\n",
        "## 1. Define the **Linear time-invariant (LTI)** system\n",
        "\n",
        "### **The System**\n",
        "$$x[n] = 0.25^{n}u[n] + 5^{n}u[-n-1]$$ \n",
        "$$y[n] = 2^{n}u[-n-1] - \\frac{2^{n + 2}}{3^{n}}u[n]$$\n",
        "\n",
        "\n",
        "### **Discrete LTI**\n",
        "In the contexts of digital control, computer simulations and system identification (based on discrete-time sensor signals) it might be more natural to work directly with **discrete time models of LTI systems.**\n",
        "\n",
        "In this case all signals are only defined at equally spaced points in time. We write for example $\\underline{x}_k$ instead of $\\underline{x}(k \\cdot \\Delta t)$ where $\\Delta t$ is the the sampling period or the inverse of the sampling frequency and $k \\geq 0$ is an integer that denotes a specific sample of the signal.\n",
        "\n",
        "In the discrete-time case the dynamical system is written as a system of **linear first order difference equations.**, but also in the following convolution formulation. **Convolution in time becomes multiplication in the Z-domain**\n",
        "\n",
        "$$y[n] = h[n] * x[n] $$\n",
        "\n",
        "$$\\Rightarrow$$\n",
        "$$Y(z) = H(z)\\cdot X(z) $$\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "### **Transfer Function H(z)**\n",
        "A very important category of LTI systems is described by difference equations of the following\n",
        "type \n",
        "\n",
        "$$\\sum_{k = 0}^{N}a_k y[n - k] = \\sum_{k = 0}^{M}b_k x[n - k]$$\n",
        "\n",
        "From which, through Z-transform we obtain \n",
        "\n",
        "$$H(z) = \\frac{N(z)}{D(z)} =  \\frac{\\sum\\limits_{k = 0}^{M}b_k z^{-k} }{\\sum\\limits_{k = 0}^{N}a_k z^{-k}}$$\n",
        "\n",
        "where H(z) is the transfer function of the system. \n",
        "\n",
        "\n",
        "### **NOTES 📌**\n",
        "1. We used 2*N + 1 = 11 samples to simulate input and output signals $x[n], y[n]$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 610
        },
        "id": "IVYv6up55yjp",
        "outputId": "862aa441-fb74-4721-ab09-fbf0d4daed04"
      },
      "source": [
        "## 1. Define `x[n]` and `y[n]`\n",
        "N = 40\n",
        "n = np.arange(-N, N + 1,1, dtype = float)\n",
        "# n = np.arange(0, N ,1, dtype = float)\n",
        "\n",
        "x = (0.25**n) * np.heaviside(n, 1) + (5**n) * np.heaviside(-n - 1, 1)\n",
        "y = (2**n) * np.heaviside(-n - 1, 1) - 4*(2/3)**n * np.heaviside(n, 1)\n",
        "\n",
        "## 2. Visualize\n",
        "fig, axs = plt.subplots(1,2, figsize = (16,8))\n",
        "axs[0].stem(n, x, linefmt = '-b',  markerfmt='bo', label = r\"Input Signal $x[n]$\")\n",
        "axs[0].set_title(r\"LTI :  input signal $x[n] = 0.25^{n}u[n] + 5^{n}u[-n-1]$ \", size = 16, style = 'italic')\n",
        "axs[1].stem(n, y, linefmt = '-b',  markerfmt='bo', label = r\"Output Signal $y[n]$\")\n",
        "axs[1].set_title(r\"LTI : output signal $y[n] = 2^{n}u[-n-1] - \\frac{2^{n + 2}}{3^{n}}u[n]$ \", size = 16, style = 'italic')\n",
        "\n",
        "for idx in range(2) : \n",
        "  axs[idx].set_xlabel('Discrete-time index [n]', fontsize = 12)\n",
        "  axs[idx].set_ylabel('Amplitude',  fontsize = 12)\n",
        "  axs[idx].grid(True, color = 'gray', alpha = 0.5)\n",
        "  axs[idx].legend(fancybox = True, prop = {'size': 15})\n",
        "  axs[idx].set_ylim(-5, 5)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:11: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n",
            "  # This is added back by InteractiveShellApp.init_path()\n",
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:13: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n",
            "  del sys.path[0]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 1152x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QU2IKLob54r4"
      },
      "source": [
        "## 2. Calculate the Transfer Function $H(z)$\n",
        "### **Define Transfer Function**\n",
        "$$H(z) = \\frac{N(z)}{D(z)} =  \\frac{\\sum\\limits_{k = 0}^{M}b_k z^{-k} }{\\sum\\limits_{k = 0}^{N}a_k z^{-k}}$$\n",
        "\n",
        "Both $N(z)$ and $D(z)$ are polynomials in z, with z ∈ C. The roots of both polynomials are very important\n",
        "in the behavior of H(z). The roots of the numerator N(z) are called the zeros of the transfer function. The roots of the denominator N(z) are called the poles of the transfer function.\n",
        "\n",
        "\n",
        "### **Z-Tranform**\n",
        "Recall that the DTFT is \n",
        "$$ X(e^{j\\omega}) = \\sum_{n = - \\infty}^{\\infty}x[n]e^{-j\\omega n}, \\qquad -\\pi \\leq \\omega \\leq \\pi$$ Observe that the expression $e^{j\\omega}$ is a complex number on the unit circle on the complex plane. We can replace it by a more general complex number z, which does not need to be on the unit circle, and obtain the z-transform:\n",
        "\n",
        "$$ X(z) = \\sum_{n = - \\infty}^{\\infty}x[n]z^{-n}, \\qquad z \\in unitCycle$$ \n",
        "\n",
        "However we mentioned that we simulated DTFT as a sampled edition of the DFT. Therefore the Z-transform will occur by sampling the unit cycle in the DFT.\n",
        "\n",
        "The z-transform is more powerful because it is more general. Using it we can also determine, for instance, if a system or a signal has damping on it. Also, we can compute the z-transform even for unstable signals or systems \n",
        "\n",
        "\n",
        "#### *INPUT $x[n]\\leftrightarrow X(z)$*\n",
        "\n",
        "* $0.25^{n}u[n] \\leftrightarrow \\frac{z}{z - 0.25} \\qquad \\quad |z| > 0.25$\n",
        "* $-5^{n} u[-n-1] \\leftrightarrow \\frac{z}{z - 5} \\qquad |z| < 5 $\n",
        "\n",
        "$$X(z) = \\frac{z}{z - 0.25} - \\frac{z}{z - 5} = \\frac{-4.75z}{z^2  - 5.25z + 1.25}, \\qquad 0.25 < |z| < 5 $$\n",
        "\n",
        "#### *OUTPUT $y[n]\\leftrightarrow Y(z)$*\n",
        "\n",
        "* $-2^{n} u[-n-1] \\leftrightarrow \\frac{z}{z - 2} \\qquad |z| < 2 $\n",
        "* $\\frac{2^{n + 2}}{3^{n}}u[n] = 4 \\left(\\frac{2}{3}\\right)^{n}u[n] \\leftrightarrow 4 \\left( \\frac{z}{z - \\frac{2}{3}} \\right) \\qquad |z| > \\frac{2}{3}$\n",
        "\n",
        "$$Y(z) =  - \\frac{z}{z - 2} - 4  \\left( \\frac{z}{z - \\frac{2}{3}} \\right) = \\frac{-15z^{2} + 26z}{3z^{2} - 8z + 4} \\qquad \\frac{2}{3} < |z| < 2$$\n",
        "\n",
        "\n",
        "### **1st method (manual) TRANSFER FUNCTION H(z)**\n",
        "\n",
        "$$H(z) = \\frac{\\frac{-15z^{2} + 26z}{3z^{2} - 8z + 4}}{\\frac{-4.75z}{z^2  - 5.25z + 1.25}} = \\frac{-15z^3+104.75z^2-155.25z+32.5}{-14.25z^2+38z-19} = z \\frac{ -15 +   104.75 z^{-1}  - 155.25 z^{-2}  + 32.5z^{-3}  }{- 14.25 + 38z^{-1} -19 z^{-2} } = \\frac{1 - 4.777z + 3.223 z^{2} - 0.462z^{3}}{-0.585 + 1.169 z - 0.438 z^{2}}$$\n",
        "\n",
        "### **2nd method (estimation) TRANSFER FUNXTION H(z)**\n",
        "We are starting from numerical data and want to estimate an analytical expression for it, then we will have to perform some sort of model fit to the data. For signal modeling, we could use **least squares, Pade approximations, Prony's**\n",
        "\n",
        "We know that the frequency response of an 𝑁-th order linear discrete-time system can be written as $H(ω) = H(z)|_{z = e^{jω}}$. Therefore we see that \n",
        "$$\\sum_{k = 0}^{N}b_{k}e^{-jkω} - H(ω)(1 + \\sum_{k =1}^{N}a_ke^{-jkω}) = 0$$\n",
        "\n",
        "This equation is linear in the $2N+1$ unknown system difference equation coefficients $b_k$ and $a_k$. Given a desired frequency response 𝐻(𝜔), we would like to find coefficients that meet the above equation exactly for all values of 𝜔. For the general case, that's hard. So instead, we will search for a set of coefficients for a system whose frequency response approximates the desired response at a discrete set of frequencies.\n",
        "\n",
        "In order to solve for an appropriate set of coefficients using the **linear least squares method(LLS)**, we will use the function `LSIIR()` from `PyDynamic.model_estimation.fit_filter` which :\n",
        "* Input : $H(ω), \\text{No. of nominator coeffs} = 4-1 = 3, \\text{No. of denominator coeffs} = 3-1 = 2, f, f_s$\n",
        "* Output : b, a\n",
        "\n",
        "Note that $H(ω)$ was calculated as seen in the end of section (Frequency response $H(e^{jω})$.\n",
        "\n",
        "While there may not be a good way to estimate a priori what the required system order is to meet our design constraints. We could extend this method a bit to use weighted least-squares optimization if needed;.\n",
        "\n",
        "Moreover we noticed that the problem with this potential solution is, **since the phase is unknown about an existing transfer function, LS may converge on the wrong solution for the phase (see the chart)**\n",
        "\n",
        "### **3rd method (estimation) TRANSFER FUNXTION H(z)**\n",
        "\n",
        "We calculated the transfer function by adapting the following methodology\n",
        "1. Calculate $X(z)$ and $Y(z)$ by using the `sympy.Poly()` function\n",
        "2. Retrieve the coefficients $b_k, a_k$ by using `coeffs()` function on the calculated $X(z), Y(z)$\n",
        "3. Last but not least, we used function `signal.TransferFunction()` to calculate the $H(z)$ based on these coefficients\n",
        "\n",
        "Probably not the best method\n",
        "\n",
        "### **Difference Equation**\n",
        "$$X(z)(-15 +   104.75 z^{-1}  - 155.25 z^{-2}  + 32.5z^{-3}) = Y(z)(- 14.25 + 38z^{-1} -19 z^{-2} ) \\leftrightarrow$$\n",
        "\n",
        "$$-14.25 Y(z) + 38Y(z)z^{-1} - 19Y(z)z^{-2} = -15X(z) +104.75X(z)z^{-1} - 155.25X(z)z^{-2} + 32.5X(z)z^{-3} \\leftrightarrow$$\n",
        "\n",
        "$$-14.25y[n] + 38 y[n-1] +19 y[n-2] = -15x[n] +104.75x[n-1] -155.25x[n-2] + 32.5x[n-3] \\leftrightarrow$$\n",
        "\n",
        "$$y[n] = 1.017x[n] - 7.35 x[n-1] + 10.895x[n-2] - 2.28x[n-3] + 2.667 y[n-1] + 1.334 y[n-2]$$\n",
        "\n",
        "\n",
        "### **Frequency Response $H(e^{jω})$ of IIR filter with transfer function H(z)** \n",
        "* Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input\n",
        "\n",
        "$$ H(e^{jΩ}) = \\frac{Y(e^{jΩ})}{X(e^{jΩ})}$$\n",
        "\n",
        "* This extra analysis in the **continuous frequency** domain is executed for reasons of completeness, to check the **pass regions** of the filter\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fm4I-Isx5yoW"
      },
      "source": [
        "\n",
        "def display_tf(b, a, mode):\n",
        "  b = [round(x,3) for x in b]\n",
        "  a = [round(x,3) for x in a]\n",
        "  if mode == \"inverse\" :  b = b[::-1] ; a = a[::-1]\n",
        "  print()\n",
        "  print(\" \"* 7, end = \" \")\n",
        "  print(b[0], end = \" \")\n",
        "  for z_idx in range(1, len(b)):\n",
        "    if b[z_idx] > 0 : print(\"+\", end = \" \")\n",
        "    if mode == \"inverse\" :\n",
        "      print(\"{}z^({}) \".format(b[z_idx], -z_idx), end = \" \")\n",
        "    else:\n",
        "      print(\"{}z^({}) \".format(b[z_idx], z_idx), end = \" \")\n",
        "    \n",
        "  print()\n",
        "  print(\"H(z) = \" + \"-\"*max( len(b), len(a) ) * 13)\n",
        "  print(\" \"* 7, end = \" \")\n",
        "  print(a[0], end = \" \")\n",
        "  for z_idx in range(1, len(a)):\n",
        "    if a[z_idx] > 0 : print(\"+\", end = \" \")\n",
        "    if mode == \"inverse\" :\n",
        "      print(\"{}z^({}) \".format(a[z_idx], -z_idx), end = \" \")\n",
        "    else:\n",
        "      print(\"{}z^({}) \".format(a[z_idx], z_idx), end = \" \")\n",
        "  print()\n",
        "  print()\n",
        "\n",
        "# Calculate db\n",
        "def db(x):\n",
        "  return 20 * np.log10(np.abs(x) / np.abs(x).max())\n",
        "  "
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cTVsyqPZ5yxY",
        "outputId": "2601f175-25d7-4983-da37-a65ffaf5385e"
      },
      "source": [
        "## 1st METHOD H(z)✅\n",
        "b1 = [-15, 104.75, -155.25, 32.5]\n",
        "a1 = [-14.25, 38, -19]\n",
        "H1 = signal.TransferFunction(b1, a1)\n",
        "\n",
        "## 2nd METHOD H(z)✅\n",
        "H2w = (np.fft.rfft(y[N:])/np.fft.rfft(x[N:])) *(1/N)\n",
        "f = fftpack.fftfreq(N//2 + 1)\n",
        "b2, a2, tau = LSIIR(H2w, Nb = 3,Na = 2, f = f, Fs = 1 )\n",
        "H2 = signal.TransferFunction(b2, a2)\n",
        "\n",
        "## 3rd METHOD H(z)✅\n",
        "# 1. Calculate Z-transform for both input X(z), output Y(z) signals\n",
        "# [*] Both x, y have n-th index as defined before [-N, ..., 0 , ... , N]. We will only use x[N:], y[N:] to \n",
        "#     calculate correclty the coefficients of the Z transform in the formation : a0 + a1* z^{-1} + ... + aN * z^{-N}\n",
        "z = sympy.symbols('z')\n",
        "X = sympy.Poly(np.flipud(x[N  :]), z**(-1))\n",
        "Y = sympy.Poly(np.flipud(y[N  :]), z**(-1))\n",
        "# 2. Calculate Transfer Function H(z)\n",
        "# [*] method : We will use `signal.TransferFunction(b, a)`, where\n",
        "#     a = { coefficients of X } , b = { coefficients of Y }\n",
        "b3 = np.array( Y.coeffs(), dtype = float)\n",
        "a3 = np.array( X.coeffs(), dtype = float )\n",
        "H3 = signal.TransferFunction(b3, a3)\n",
        "\n",
        "\n",
        "# 3. Display input, output data, n-index and H(z) to visualize the variable (1/z) matching\n",
        "data = pd.DataFrame(np.vstack([x,y]).T, columns = [\"Input x[n]\", \"Output y[n]\"], index = n).T\n",
        "data.index.name = \"n-th index\"\n",
        "print(\"============================== 1st METHOD ================================\")\n",
        "display_tf(b1,a1, \"inverse\")\n",
        "print(\"============================== 2nd METHOD ================================\")\n",
        "display_tf(b2,a2, \"inverse\")\n",
        "print(\"============================== 3rd METHOD ================================\")\n",
        "display_tf(b3,a3, \"inverse\")\n",
        "\n"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Least-squares fit of an order 3 digital IIR filter\n",
            "to a frequency response given by 21 values.\n",
            "\n",
            "Least squares fit finished after 1 iterations (tau=0).\n",
            "Final rms error = 4.494431e-02 \n",
            "\n",
            "\n",
            "============================== 1st METHOD ================================\n",
            "\n",
            "        32.5 -155.25z^(-1)  + 104.75z^(-2)  -15z^(-3)  \n",
            "H(z) = ----------------------------------------------------\n",
            "        -19 + 38z^(-1)  -14.25z^(-2)  \n",
            "\n",
            "============================== 2nd METHOD ================================\n",
            "\n",
            "        -0.002 -0.001z^(-1)  + 0.015z^(-2)  -0.101z^(-3)  \n",
            "H(z) = ----------------------------------------------------\n",
            "        -0.01 -0.449z^(-1)  + 1.0z^(-2)  \n",
            "\n",
            "============================== 3rd METHOD ================================\n",
            "\n",
            "        -4.0 -2.667z^(-1)  -1.778z^(-2)  -1.185z^(-3)  -0.79z^(-4)  -0.527z^(-5)  -0.351z^(-6)  -0.234z^(-7)  -0.156z^(-8)  -0.104z^(-9)  -0.069z^(-10)  -0.046z^(-11)  -0.031z^(-12)  -0.021z^(-13)  -0.014z^(-14)  -0.009z^(-15)  -0.006z^(-16)  -0.004z^(-17)  -0.003z^(-18)  -0.002z^(-19)  -0.001z^(-20)  -0.001z^(-21)  -0.001z^(-22)  -0.0z^(-23)  -0.0z^(-24)  -0.0z^(-25)  -0.0z^(-26)  -0.0z^(-27)  -0.0z^(-28)  -0.0z^(-29)  -0.0z^(-30)  -0.0z^(-31)  -0.0z^(-32)  -0.0z^(-33)  -0.0z^(-34)  -0.0z^(-35)  -0.0z^(-36)  -0.0z^(-37)  -0.0z^(-38)  -0.0z^(-39)  -0.0z^(-40)  \n",
            "H(z) = -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
            "        1.0 + 0.25z^(-1)  + 0.062z^(-2)  + 0.016z^(-3)  + 0.004z^(-4)  + 0.001z^(-5)  0.0z^(-6)  0.0z^(-7)  0.0z^(-8)  0.0z^(-9)  0.0z^(-10)  0.0z^(-11)  0.0z^(-12)  0.0z^(-13)  0.0z^(-14)  0.0z^(-15)  0.0z^(-16)  0.0z^(-17)  0.0z^(-18)  0.0z^(-19)  0.0z^(-20)  0.0z^(-21)  0.0z^(-22)  0.0z^(-23)  0.0z^(-24)  0.0z^(-25)  0.0z^(-26)  0.0z^(-27)  0.0z^(-28)  0.0z^(-29)  0.0z^(-30)  0.0z^(-31)  0.0z^(-32)  0.0z^(-33)  0.0z^(-34)  0.0z^(-35)  0.0z^(-36)  0.0z^(-37)  0.0z^(-38)  0.0z^(-39)  0.0z^(-40)  \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 864
        },
        "id": "k9DBhcu25y3-",
        "outputId": "6e263d77-e3cb-4c5b-971d-cfabbb21a0fc"
      },
      "source": [
        "# 4. Calculate Frequency Response\n",
        "\n",
        "def plot_freq_response(w, Y,  method = \"\"):\n",
        "  magnitude = db(abs(Y))\n",
        "  angles    = np.unwrap(np.angle(Y))\n",
        "  fig = plt.figure()\n",
        "  ax1 = fig.add_subplot(111)\n",
        "  plt.title(method + r' Digital filter frequency response $H(e^{jΩ})$')\n",
        "  plt.plot(w, magnitude , 'b', label = \"magnitude (1st Method)\")\n",
        "  plt.ylabel('Amplitude [dB]', color='b')\n",
        "  plt.xlabel('Normalized Frequency [rad/sample]')\n",
        "  ax2 = ax1.twinx()\n",
        "  plt.plot(w, angles, 'g')\n",
        "  plt.ylabel('Angle (radians)', color = 'g')\n",
        "  plt.grid()\n",
        "  plt.axis('tight')\n",
        "  plt.show()\n",
        "\n",
        "## 1st METHOD H(z)✅\n",
        "w1, Y1 = signal.freqz(b1, a1)\n",
        "plot_freq_response(w1, Y1, \"1st Method - \")\n",
        "\n",
        "## 2nd METHOD H(z)✅\n",
        "w2, Y2 = signal.freqz(b2, a2)\n",
        "plot_freq_response(w2, Y2)\n",
        "\n",
        "## 3rd METHOD H(z)✅\n",
        "w3, Y3 = signal.freqz(b3, a3)\n",
        "plot_freq_response(w3, Y3,\"3rd Method - \")\n",
        "\n"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nObKl_y59WmR"
      },
      "source": [
        "## 3. Zero - Pole diagram & Region of Convergence (ROC)\n",
        "\n",
        "### **Poles & Zeros**\n",
        "A pole-zero plot shows the location in the complex plane of the poles and zeros of the transfer function of a dynamic system,. By convention, the poles of the system are indicated in the plot by an X while the zeros are indicated by a circle or O.\n",
        "\n",
        "We will use function `scipy.signal.tf2zpk()` that returns **zero, pole, gain**(z, p, k) representation from a numerator, denominator representation of a linear filter.\n",
        "\n",
        "#### Zeros\n",
        "$$ z = b_{k} \\text{ such that } N(z)|_{z = b_{k}} = 0$$\n",
        "\n",
        "#### Poles\n",
        "$$ z = a_{k} \\text{ such that } D(z)|_{z = a_{k}} = 0$$\n",
        "\n",
        "we will only plot the zeros-poles for the 1st and the 2nd method. The 3rd method was just an idea of how to find many $a_k, b_k$.\n",
        "\n",
        "\n",
        "### **Region of Convergence (ROC) (1st Method)**\n",
        "\n",
        "#### Input X(Z)\n",
        "* **Poles** : $z \\in \\{ 0.25, 5\\}$\n",
        "* **Zeros** : $z = 0$\n",
        "$$0.25 < |z| < 5 \\quad \\text{(two-sided)}$$\n",
        "\n",
        "#### Output Y(Z)\n",
        "* **Poles** : $z \\in \\{ 0.666, 2\\}$\n",
        "* **Zeros** : $z \\in \\{ 0, 1.7333\\}$\n",
        "$$\\frac{2}{3} < |z| < 2 \\quad \\text{(two-sided)}$$\n",
        "\n",
        "#### System H(z) = Y(z) / X(z) (unstable, non-causal)\n",
        "\n",
        "* **ZERO & POLES** : \n",
        "  * **Poles** : $z \\in \\{0.25, 1.733, 5 \\}$\n",
        "  * **Zeros** : $z \\in \\{0, 0.666, 2 \\}$\n",
        "  * We see that the poles of the output became zeros for the system $\\mathcal{S}$ and its zeros became poles for the system \n",
        "  * Since the *order of the numerator* $N = 4$ and the *order of the numerator* $M = 3$ , $N > M$, there extra $N - M = 4 - 3 = 1$ zero at $z = \\infty$. So, in order to properly use the `zplot()` function from the `audiolazy` library we will exclude this extra $z$.\n",
        "\n",
        "* **ROC & CAUSALITY**\n",
        "  * Now we know that the ROC of the multiplication of two $\\mathcal{Z}$-transforms equals the intersection of the ROCs of the individual $\\mathcal{Z}$-transforms, unless there is pole-zero cancellation, in which case the resulting ROC can be bigger than the intersection\n",
        "  * Both $x[n]$ and $y[n]$ are **non-causal** signals since they have non-negative values for some $n < 0$, and this is why both ROCs are two-sided. \n",
        "  * In order to fulfill both restrictions the only ROC which is accepted is \n",
        "$$ \\frac{2}{3} < |z| < 2 \\quad \\text{(two-sided)}$$\n",
        "which also **includes the unit circle**, Moreover the system will be **non-causal**. Furthemore, this ROC does not include any poles.\n",
        "  * We can also see that the *order of the numerator* $N = 4$ is **greater** than the *order of the denominator* $M = 3$ , and we could conclude that the system is **non-causal**.\n",
        "$$N > M$$\n",
        "\n",
        "* **STABILITY**\n",
        "\n",
        "  * Last but not least, the system will be **stable** since the ROC includes the unit circle $|z| = 1$\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 628
        },
        "id": "IzsRDgTV5y8z",
        "outputId": "d7df2c21-5f89-4fc7-e12c-c87eee81b3d4"
      },
      "source": [
        "from audiolazy import z;\n",
        "## 1. Calculate both zeros and poles of the LTI system\n",
        "# 1st METHOD H(z)✅\n",
        "zeros1, poles1, _ = signal.tf2zpk(b1, a1)\n",
        "# 2nd METHOD H(z)✅\n",
        "zeros2, poles2, _ = signal.tf2zpk(b2, a2)\n",
        "\n",
        "zeros = [zeros1, zeros2]\n",
        "poles = [poles1, poles2]\n",
        "\n",
        "## 2. Visualize zeros , poles\n",
        "def plot_pole_zero(zeros, poles, ROC, lim = 6):\n",
        "\n",
        "  fig, ax = plt.subplots(figsize = (10, 10))\n",
        "  circle = plt.Circle((0, 0), radius = 1, color = 'b', linestyle = '--', linewidth = 1, fill = False, label = r\"Unit Circle $|z| = 1$\")\n",
        "  ax.add_patch(ROC)\n",
        "  ax.add_patch(circle)\n",
        "  colors = [\"b\", \"r\"]\n",
        "  for z, c in zip(*[zeros, colors]) :\n",
        "    ax.scatter(z.real,z.imag, color = c , marker = 'o', s = 100, label = \"Zeros\")\n",
        "  for p, c in zip(*[poles, colors]) :\n",
        "    ax.scatter(p.real,p.imag, color = c , marker = 'x', s = 100, label = \"Poles\")\n",
        "  ax.axhline(y = 0, xmin = -5.0, xmax = 5.0, color='blue', linestyle = '--',alpha = 0.2)\n",
        "  ax.axvline(x = 0, ymin = -5.0, ymax = 5.0, color='blue', linestyle = '--',alpha = 0.2)\n",
        "  ax.set_title(r\"Pole-Zeros Map & ROC\", size = 16, style = 'italic')\n",
        "  ax.set_xlabel('Real Part (Re)', fontsize = 12)\n",
        "  ax.set_ylabel('Imaginary Part (Im)', fontsize = 12)\n",
        "  ax.set_xlim(-lim,lim)\n",
        "  ax.set_ylim(-lim,lim)\n",
        "  ax.grid(True, color = 'gray', alpha = 0.5)\n",
        "  ax.legend(fancybox = True, prop = {'size': 15})\n",
        "  plt.show()\n",
        "\n",
        "\n",
        "roc = Wedge((0,0), 2, 0, 360, width = 1.33, alpha = 0.5, label = r\"ROC $\\frac{2}{3} < |z| < 2$\")\n",
        "plot_pole_zero(zeros, poles, roc, lim = 6)\n"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AaIjGpDb9q1t"
      },
      "source": [
        "## 4. LTI Responses\n",
        "Having found the transfer function $H(z)$ we can calculate the **unit** and **impulse** response. In discrete time the unit impulse is the first difference of the unit step, and the unit step is the running sum of the unit impulse.\n",
        "$$\\delta[n] = u[n] - u [n - 1]$$\n",
        "\n",
        "$$u[n] = \\sum_{m = - \\infty}^{n}\\delta[m]$$\n",
        "\n",
        "### **Impusle Response (Input $x[n] = \\delta[n]$)**\n",
        "We would like to measure the impulse response of an LTI system,\n",
        "described by the impulse response h[n] (which is the inverse Z-transform of the transfer function)\n",
        "\n",
        "<a href=\"https://ibb.co/0j46JtV\"><img src=\"https://i.ibb.co/TBj7hLq/1.png\" alt=\"1\" border=\"0\"></a>\n",
        "\n",
        "This can be practically difficult because input amplitude is often limited. A\n",
        "very short pulse then has very little energy.\n",
        "\n",
        "$$y[n] = h[n] * x[n] \\rightarrow y[n] = h[n] * \\delta[n] \\rightarrow Y(z) = H(z) \\cdot 1 \\rightarrow Y(z) = H(Z) \\rightarrow y[n] = h[n]$$\n",
        "\n",
        "We know that\n",
        "\n",
        "$$H(z) = \\frac{-15z^3+104.75z^2-155.25z+32.5}{-14.25z^2+38z-19} = -15z + 64.75 + 15.75\\frac{1}{z-2} - 21.667 \\frac{1}{z - \\frac{2}{3}}$$\n",
        "\n",
        "Therefore, the inverse transform Z of $H(z)$ is\n",
        "$$h[n] = \\mathcal{Z}^{-1}\\{H(z)\\} = 64.75\\delta[n] - 15 \\delta[n+1] + 15.75 \\cdot 2^{n-1}u[n-1] + 21.677 \\cdot \\left(\\frac{2}{3}\\right)^{n-1}u[n-1]$$\n",
        "\n",
        "\n",
        "### **Step Response (Input $x[n] = u[n]$)**\n",
        "\n",
        "A common alternative is to measure the step response $s[n]$, the response\n",
        "to a unit step input $u[n]$\n",
        "<a href=\"https://ibb.co/Hh3hdjM\"><img src=\"https://i.ibb.co/wcjcsfb/Screen-Shot-2020-12-09-at-18-10-20.png\" alt=\"Screen-Shot-2020-12-09-at-18-10-20\" border=\"0\"></a>\n",
        "\n",
        "$$y[n] = h[n] * x[n] \\rightarrow y[n] = h[n] * u[n] \\rightarrow y[n] = s[n] = h[n] * u[n]$$\n",
        "\n",
        "\n",
        "### **NOTES**\n",
        "* Below we did 2 things : (1) defined manually $h[n]$ and plotted it (impulse responsed for ground truth)(2) used function `lfilter()` for the 3 methods (with the respective b,a) to calculate unit and impulse response.\n",
        "* We see that the 2nd method (that applies least square algorithm) fails to generate the necessary outcome. This is because of the wrong phase calculation we mentioned before. Interestingly , the 3rd method approximates better the ground truth result"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 464
        },
        "id": "7gvfqBp55zBn",
        "outputId": "df237096-0bdd-4261-c333-c5d02aa11d9a"
      },
      "source": [
        "## 1. Define `x[n]` and `y[n]`\n",
        "N = 100\n",
        "n = np.arange(0, N,1, dtype = float)\n",
        "h = 64.75 * signal.unit_impulse(N , 0) - 15 *  signal.unit_impulse(N,1) + 15.75 * 2**(n - 1)* np.heaviside(n - 1, 1) + 21.67* (2/3)**(n-1)* np.heaviside(n - 1, 1)\n",
        "\n",
        "## 2. Visualize\n",
        "def plot_response(y, exponent = None, N  = 100, dbScale = False, name = \"\", color = \"b\") :\n",
        "  n = np.arange(N)\n",
        "  if dbScale : y = y = db(np.abs(y))\n",
        "  fig, ax = plt.subplots(figsize = (10,6))\n",
        "  ax.stem(n, y, linefmt = '-{}'.format(color),  markerfmt = '{}o'.format(color), label = r\"Output Signal $y[n]$\")\n",
        "  if exponent is not None: plt.plot(n, 1.7368*(exponent)**n, \"r--\")\n",
        "  ax.set_title(r\"LTI : Input ${}$ / Output y[n]\".format(name), size = 16, style = 'italic')\n",
        "  ax.set_xlabel('Discrete-time index [n]', fontsize = 12)\n",
        "  ax.set_ylabel('Amplitude',  fontsize = 12, color = \"b\")\n",
        "  ax.grid(True, color = 'gray', alpha = 0.5)\n",
        "  ax.legend(fancybox = True, prop = {'size': 15})\n",
        "  plt.show()\n",
        "\n",
        "plot_response(y = h,  N  = 100, dbScale = False, name = \"x[n] = 0.25^{n}u[n] + 5^{n}u[-n-1]\")\n"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:11: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n",
            "  # This is added back by InteractiveShellApp.init_path()\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "BipQKLkX5zHU",
        "outputId": "5283e450-b363-4e42-b3ed-8f6ab8323fbe"
      },
      "source": [
        "## INPUT : x[n] = u[n] | OUTPUT : Step Reponse y[n] = s[n]\n",
        "# 1. Define the input `x[n] = δ[n]`\n",
        "L = 100\n",
        "n = np.arange(100)\n",
        "x = np.heaviside(n, 1)\n",
        "\n",
        "# 2. Now calculate the impulse response for the 3 methods\n",
        "# 1st METHOD h[n]✅\n",
        "y1 = signal.lfilter(b1[::-1], a1[::-1], x)\n",
        "plot_response(y1,  N  = L , dbScale = False, name = \"u[n]\", color = \"r\")\n",
        "\n",
        "# 2nd METHOD h[n]✅\n",
        "y2 = signal.lfilter(b2, a2, x)\n",
        "plot_response(y2,  N  = L , dbScale = False, name = \"u[n]\",  color = \"r\")\n",
        "\n",
        "# 3rd METHOD h[n]✅\n",
        "y3 = signal.lfilter(b3, a3, x)\n",
        "plot_response(y3,  N  = L , dbScale = False, name = \"u[n]\",  color = \"r\")"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:11: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n",
            "  # This is added back by InteractiveShellApp.init_path()\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:11: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n",
            "  # This is added back by InteractiveShellApp.init_path()\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:11: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n",
            "  # This is added back by InteractiveShellApp.init_path()\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hhFNAwX26BOv"
      },
      "source": [
        "## EXTRA\n",
        "---"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qSv8zwgj5zfg"
      },
      "source": [
        "## 1. Estimate H(z) with spectral density (https://github.com/dnvgl/qats/blob/24bdb5f61829611d79e8cda086fdf7ce5c3c3926/qats/signal.py )\n",
        "# from matplotlib.mlab import psd, csd\n",
        "# def tfe(x, y):\n",
        "#    \"\"\"estimate transfer function from x to y, see csd for calling convention\"\"\"\n",
        "#    f, Pxy  = signal.csd(x, y)  # Pxy is the cross power spectral density of x and y,\n",
        "#    _, Pxx = signal.welch(x)    # Pxx is the power spectral density of x, calculated using the welch method\n",
        "#    return f, Pxy / Pxx\n",
        "# f, H = tfe(x,y)\n",
        "# print(H)\n",
        "# plt.plot(1. / f[(0. < f) & (f <= 0.5)], abs(H[(0. < f) & (f <= 0.5)]))\n",
        "\n",
        "\n",
        "## 2. Zero-pole Map\n",
        "# [*] 1st method\n",
        "# H = control.TransferFunction(b, a)\n",
        "# control.pzmap(H)\n",
        "# [*] 2nd method\n",
        "# H = (-15*z**3 + 104.75*z**2 -155.25*z + 32.5)/ (-14.75 * z**3 + 38 * z**2 -19*z );\n",
        "# H.zplot();\n",
        "# H.plot();"
      ],
      "execution_count": 10,
      "outputs": []
    }
  ]
}