{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# The $z$-Transform\n",
    "\n",
    "*This Jupyter notebook is part of a [collection of notebooks](../index.ipynb) in the bachelors module Signals and Systems, Comunications Engineering, Universität Rostock. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition\n",
    "\n",
    "The [$z$-transform](https://en.wikipedia.org/wiki/Z-transform) is a transform which represents a discrete signal $x[k]$ in the spectral domain. It bases on the complex exponential function $z^{-k}$ with $z \\in \\mathbb{C}$ as kernel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two-Sided $z$-Transform\n",
    "\n",
    "The two-sided (or bilateral) $z$-transform is defined as\n",
    "\n",
    "\\begin{equation}\n",
    "X(z) = \\sum_{k = -\\infty}^{\\infty} x[k] \\, z^{-k}\n",
    "\\end{equation}\n",
    "\n",
    "where $X(z) = \\mathcal{Z} \\{ x[k] \\}$ denotes the $z$-transform of $x[k]$. A complex signal $x[k] \\in \\mathbb{C}$ with discrete index $k \\in \\mathbb{Z}$ is represented by its complex valued $z$-transform $X(z) \\in \\mathbb{C}$ with complex dependent variable $z \\in \\mathbb{C}$. The variable $z$ can be interpreted as [complex frequency](../discrete_signals/standard_signals.ipynb#Complex-Exponential-Signal) $z = e^{\\Sigma + j \\Omega}$ with $\\Sigma, \\Omega \\in \\mathbb{R}$.\n",
    "\n",
    "Whether a $z$-transform $X(z) = \\mathcal{Z} \\{ x[k] \\}$ exists depends on the complex frequency $z$ and the signal $x[k]$ itself. All values $z$ for which the $z$-transform converges form a region of convergence (ROC). The $z$-transforms of two different signals may differ only with respect to their ROCs. Consequently, the ROC needs to be explicitly given for a unique inversion of the $z$-transform."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### One-Sided $z$-Transform\n",
    "\n",
    "Causal signals play an important role in the theory of signals and systems. For a causal signal with $x[k] = 0$ for $k <0$, the relation $x[k] = x[k] \\cdot \\epsilon[k]$ holds. Introducing this into the definition of the two-sided $z$-transform results in\n",
    "\n",
    "\\begin{equation}\n",
    "X(z) = \\sum_{k = -\\infty}^{\\infty} x[k] \\cdot \\epsilon[k] \\, z^{-k} = \\sum_{k = 0}^{\\infty} x[k] \\, z^{-k}\n",
    "\\end{equation}\n",
    "\n",
    "This motivates the definition of the one-sided (or unilateral) $z$-transform\n",
    "\n",
    "\\begin{equation}\n",
    "X(z) = \\sum_{k = 0}^{\\infty} x[k] \\, z^{-k}\n",
    "\\end{equation}\n",
    "\n",
    "In the literature both the one- and two-sided $z$-transform are termed as $z$-transform. For causal signals both give the same result. The one-sided $z$-transform is also useful for the solution of initial value problems, for instance as defined by [linear difference equations with constant coefficients](../discrete_systems/difference_equation.ipynb) where the initial values are e.g. defined for $k \\leq 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Signals of Finite Duration\n",
    "\n",
    "The $z$-transform of a generic signal $x[k]$ of finite duration $x[k] = 0$ for $\\{k : k < M_1 \\wedge k \\geq M_2\\}$ with $M_1 < M_2$ reads\n",
    "\n",
    "\\begin{equation}\n",
    "X(z) = \\sum_{k=M_1}^{M_2 - 1} x[k] \\, z^{-k} = x[M_1] \\, z^{-M_1} + x[M_1 + 1] \\, z^{- (M_1 + 1)} + \\dots + x[M_2 - 1] \\, z^{- (M_2-1)}\n",
    "\\end{equation}\n",
    "\n",
    "The transform of a generic finite-length signal is given as a polynomial in $z$. Depending on the particular limits $M_1$ and $M_2$, the polynomial may contain powers of $z$ and $z^{-1}$. For a causal finite-length signal, above result specializes to the case $M_1 = 0$ and $M_2 > 0$ as\n",
    "\n",
    "\\begin{equation}\n",
    "X(z) = x[0] + x[1] \\, z^{-1} + \\dots + x[M_2 - 1] \\, z^{- (M_2-1)}\n",
    "\\end{equation}\n",
    "\n",
    "The transform of a causal finite-length signal is given as a polynomial in $z^{-1}$. The ROC for this case is given as $z \\in \\mathbb{C} \\setminus \\{ 0 \\}$. Similar considerations yield the $z$-transform and ROC of an anticausal signal. The ROCs for a generic finite-length signal can be summarized as\n",
    "\n",
    "* $z \\in \\mathbb{C}$ for an anticausal signal ($M_1 < 0$, $M_2 \\leq 0$)\n",
    "* $z \\in \\mathbb{C}_\\infty$ if $x[k] = 0$ for $k \\neq 0$ ($M_1 = 0$, $M_2 = 1$)\n",
    "* $z \\in \\mathbb{C} \\setminus \\{ 0 \\}$ for a causal signal ($M_1 = 0$, $M_2 > 0$)\n",
    "\n",
    "where $\\mathbb{C}_\\infty = \\mathbb{C} \\cup \\{ \\infty \\}$ denotes the [set of extended complex numbers](https://en.wikipedia.org/wiki/Riemann_sphere)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation of the Rectangular Signal\n",
    "\n",
    "The rectangular signal $x[k] = \\text{rect}_N[k]$ is a causal signal of finite duration. Using above result its $z$-transform can be derived straightforward as\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{Z} \\{ \\text{rect}_N[k] \\} = \\sum_{k=0}^{N-1} z^{-k} = 1 + z^{-1} + \\dots + z^{-N + 1}\n",
    "\\end{equation}\n",
    "\n",
    "for $z \\in \\mathbb{C} \\setminus \\{ 0 \\}$. Above sum can also be interpreted as [finite geometrical series](https://en.wikipedia.org/wiki/Geometric_series) with common ratio $\\frac{1}{z}$, resulting in an alternative form of the $z$-transform of the rectangular signal\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{Z} \\{ \\text{rect}_N[k] \\} =  \\begin{cases}\n",
    "\\frac{1 - z^{-N}}{1 - z^{-1}} & \\text{for } z \\neq 1 \\\\\n",
    "N & \\text{for } z = 1\n",
    "\\end{cases}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation of the Dirac Impulse\n",
    "\n",
    "The transform $\\mathcal{Z} \\{ \\delta[k] \\}$ of the [Dirac impulse](../discrete_signals/standard_signals.ipynb#Dirac-Impulse) is derived by introducing $\\delta[k]$ into the definition of the two-sided $z$-transform and exploiting the sifting property of the Dirac impulse\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{Z} \\{ \\delta[k] \\} = \\sum_{k = -\\infty}^{\\infty} \\delta[k] \\, z^{-k} = 1\n",
    "\\end{equation}\n",
    "\n",
    "for $z \\in \\mathbb{C}$. The ROC covers the entire complex plane.\n",
    "\n",
    "The transform of the Dirac impulse is equal to one. Hence, all complex frequencies $z$ are present with equal weight. Since the Dirac impulse is used to characterize linear time-invariant (LTI) systems by their [impulse response](../discrete_systems/impulse_response.ipynb) $h[k] = \\mathcal{H} \\{ \\delta[k] \\}$, this constitutes an important property in the theory of discrete signals and systems, ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example**\n",
    "\n",
    "The $z$-transform of the Dirac impulse is computed by direct evaluation of its definition. The Dirac impulse is represented by the [Kronecker delta](https://en.wikipedia.org/wiki/Kronecker_delta) $\\delta[k] = \\delta_{k 0}$ in `SymPy`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sym\n",
    "sym.init_printing()\n",
    "%matplotlib inline\n",
    "\n",
    "k = sym.symbols('k', integer=True)\n",
    "z = sym.symbols('z', complex=True)\n",
    "\n",
    "X = sym.summation(sym.KroneckerDelta(k, 0) * z**(-k), (k, -sym.oo, sym.oo))\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Derive the two-sided $z$-transform of a shifted Dirac impulse $\\delta[t - \\kappa]$ for $\\kappa \\in \\mathbb{Z}$ by manual evaluation of its definition and by modification of above example. Provide the ROC for the three cases $\\kappa<0$, $\\kappa=0$ and $\\kappa>0$.\n",
    "\n",
    "* Derive the one-sided $z$-transform of a shifted Dirac impulse $\\delta[t - \\kappa]$. Hint: Differentiate between the cases $\\kappa < 0$ and $\\kappa \\geq 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation of the Causal Complex Exponential Signal\n",
    "\n",
    "The transform $X(z) = \\mathcal{Z} \\{ x[k] \\}$ of the causal complex exponential signal\n",
    "\n",
    "\\begin{equation}\n",
    "x[k] = \\epsilon[k] \\cdot z_0^k\n",
    "\\end{equation}\n",
    "\n",
    "with complex frequency $z_0 \\in \\mathbb{C}$ is derived by evaluation of the definition of the one-sided $z$-transform\n",
    "\n",
    "\\begin{equation}\n",
    "X(z) = \\sum_{k=0}^{\\infty} z_0^k \\cdot z^{-k} = \\sum_{k=0}^{\\infty} \\left( \\frac{z_0}{z} \\right)^k = \\frac{z}{z - z_0}\n",
    "\\end{equation}\n",
    "\n",
    "The last equality has been derived by noting that the sum constitutes an [infinite geometrical series](https://en.wikipedia.org/wiki/Geometric_series) with common ratio $\\frac{z_0}{z}$ which converges for $\\left| \\frac{z_0}{z} \\right| < 1$. The ROC is consequently given as\n",
    "\n",
    "\\begin{equation}\n",
    "|z| > |z_0|\n",
    "\\end{equation}\n",
    "\n",
    "Combining above results, the transformation of the causal complex exponential signal reads\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{Z} \\{ \\epsilon[k] \\cdot z_0^k \\} = \\frac{z}{z - z_0} \\qquad \\text{for } |z| > |z_0|\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example**\n",
    "\n",
    "The $z$-transform of the causal complex exponential signal $x[k] = z_0^k \\cdot \\epsilon[k]$ with $z_0 \\in \\mathbb{C}$ is computed by direct evaluation of its definition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\begin{cases} \\frac{1}{1 - \\frac{z_{0}}{z}} & \\text{for}\\: \\left|{\\frac{z_{0}}{z}}\\right| < 1 \\\\\\sum_{k=0}^{\\infty} z^{- k} z_{0}^{k} & \\text{otherwise} \\end{cases}$"
      ],
      "text/plain": [
       "⎧     1             │z₀│    \n",
       "⎪   ──────      for │──│ < 1\n",
       "⎪       z₀          │z │    \n",
       "⎪   1 - ──                  \n",
       "⎪       z                   \n",
       "⎪                           \n",
       "⎪  ∞                        \n",
       "⎨ ___                       \n",
       "⎪ ╲                         \n",
       "⎪  ╲    -k   k              \n",
       "⎪  ╱   z  ⋅z₀    otherwise  \n",
       "⎪ ╱                         \n",
       "⎪ ‾‾‾                       \n",
       "⎪k = 0                      \n",
       "⎩                           "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z0 = sym.symbols('z0')\n",
    "\n",
    "X = sym.summation(z0**k * z**(-k), (k, 0, sym.oo))\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the sum is returned in case that it cannot be evaluated. It hence can be concluded that the series converges only for $|\\frac{z_0}{z}| < 1$. This is in line with the analytic result derived above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence\n",
    "\n",
    "The definition of the $z$-transform constitutes an infinite series. A sufficient but not necessary condition for the convergence of an infinite series is that its elements are absolutely summable. Applying this to the definition of the two-sided $z$-transform $X(z) = \\mathcal{Z} \\{ [k] \\}$ of a given signal $x[k]$ yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{k = -\\infty}^{\\infty} | x[k] \\cdot z^{- k} | = \\sum_{k = -\\infty}^{\\infty} | x[k] | \\cdot | z |^{- k}  < \\infty\n",
    "\\end{equation}\n",
    "\n",
    "It can be concluded from this result that the ROC is determined solely by the magnitude $|z|$ of the complex frequency. It follows further that the ROC is given as a ring in the $z$-plane which may include $z=0$ and/or $z=\\infty$. The phase $\\Omega$ of the complex frequency $z$ has no effect in terms of convergence, as $z = e^{\\Sigma} \\cdot e^{j \\Omega}$.\n",
    "\n",
    "For a right-sided signal of infinite length with $x[k] = 0$ for $k < M$, the ROC is given in the form of $|z| > a$ with $a \\in \\mathbb{R}^+$. This can be concluded from the decay of the term $| z |^{- k}$ for $k \\to \\infty$, which ensures convergence for a given $a$. However this holds only for signals $x[k]$ with [exponential growth](https://en.wikipedia.org/wiki/Exponential_growth). Please refer to the $z$-transform of the causal exponential signal derived above. \n",
    "\n",
    "The same reasoning leads to the ROCs of a left-sided and two-sided signal. The resulting ROCs are illustrated in the following\n",
    "\n",
    "![Region of convergence for left-/two-/right-sided signals](ROC.png)\n",
    "\n",
    "The gray areas denote the values $z$ for which the $z$-transform converges. The borders $a$ of these areas (dashed lines) depend on the signal $x[k]$. In case that the $z$-transform $X(z)$ is given in terms of a rational function in $z$, the ROC has to be chosen such that it does not include zeros of the denominator polynomial. A more detailed discussion of the ROCs for the $z$-transform can be found in the literature, e.g. [[Girod et al.](index.ipynb#Literature)]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relation to the Laplace Transform of a Sampled Signal\n",
    "\n",
    "The link between the Laplace transform of a sampled signal $x_\\text{s}(t)$ and the $z$-transform of its discrete counterpart $x[k] = x(k T)$ is established in the following. Under the assumption of [ideal sampling](../sampling/ideal.ipynb#Model-of-Ideal-Sampling), the sampled signal reads\n",
    "\n",
    "\\begin{equation}\n",
    "x_\\text{s}(t) = \\sum_{k = -\\infty}^{\\infty} x(k T) \\cdot \\delta(t - k T) = \\sum_{k = -\\infty}^{\\infty} x[k] \\cdot \\delta(t - k T)\n",
    "\\end{equation}\n",
    "\n",
    "where $x(t)$ denotes the continuous signal and $T$ the sampling interval. Introducing the sampled signal into the [definition of the Laplace transform](../laplace_transform/definition.ipynb) yields the transform of the sampled signal\n",
    "\n",
    "\\begin{equation}\n",
    "X_\\text{s}(s) = \\int_{-\\infty}^{\\infty} \\sum_{k = -\\infty}^{\\infty} x[k] \\cdot \\delta(t - k T) \\, e^{- s t} \\; dt = \\sum_{k = -\\infty}^{\\infty} x[k] \\, e^{-s k T}\n",
    "\\end{equation}\n",
    "\n",
    "where the last equality has been derived by changing the order of summation/integration and exploiting the [sifting property of the Dirac impulse](../continuous_signals/standard_signals.ipynb#Dirac-Impulse). Comparison with the definition of the $z$-transform yields\n",
    "\n",
    "\\begin{equation}\n",
    "X_\\text{s}(s) = X(z) \\big\\rvert_{z = e^{s T}}\n",
    "\\end{equation}\n",
    "\n",
    "The spectrum of the sampled signal $X_\\text{s}(s)$ is equal to the $z$-transform of the discrete Signal $X(z)$ for $z = e^{s T}$. The resulting mapping from the $s$-plane to the $z$-plane is illustrated by the shading and the colors in the following figure\n",
    "\n",
    "![Mapping of the $s$-plane onto the $z$-plane](mapping_s_z_plane.png)\n",
    "\n",
    "The Laplace transform of a sampled signal is peridoic with respect to the frequency $\\omega$. It sufficient to consider the strip $-\\frac{\\pi}{T} < \\Im \\{ s \\} < \\frac{\\pi}{T}$ of the $s$-plane for the mapping. The left half-plane of the $s$-plane is mapped into the unit circle of the $z$-plane. The corresponding right half-plane is mapped to the outside of the unit circle. The imaginary axis of the $s$-plane is mapped onto the unit circle $|z|=1$. The frequency $s=0$ is mapped onto $z=1$ and the frequencies $s=\\pm j \\frac{\\pi}{T}$ are mapped onto $z=-1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representation\n",
    "\n",
    "The $z$-transform $X(z) = \\mathcal{Z} \\{ x[k] \\}$ depends on the complex frequency $z \\in \\mathbb{C}$ and is in general complex valued $X(z) \\in \\mathbb{C}$. It can be illustrated by plotting its magnitude $|X(z)|$ and phase $\\varphi(z)$ or real $\\Re \\{ X(z) \\}$ and imaginary $\\Im \\{ X(z) \\}$ part in the complex $z$-plane. The resulting three-dimensional plots are often not very illustrative.\n",
    "\n",
    "However, many $z$-transforms of interest in the theory of signals and systems are [rational functions](https://en.wikipedia.org/wiki/Rational_function) in $z$. The polynomials of the numerator and denominator can be represented by their complex [roots](https://en.wikipedia.org/wiki/Zero_of_a_function#Polynomial_roots) and a constant factor. The roots of the numerator are termed as *zeros* while the roots of the denominator a termed as *poles* of $X(z)$. The polynomial and the zero/pole representation of a rational $z$-transform are equivalent\n",
    "\n",
    "\\begin{equation}\n",
    "X(z) = \\frac{\\sum_{m=0}^{M} \\beta_m \\, z^{-m}}{\\sum_{n=0}^{N} \\alpha_n \\, z^{-n}} = K \\cdot \\frac{\\prod_{\\mu=0}^{Q} (z - z_{0 \\mu})}{\\prod_{\\nu=0}^{P} (z - z_{\\infty \\nu})}\n",
    "\\end{equation}\n",
    "\n",
    "where $M$ and $N$ denote the order of the numerator/denominator polynomial, $z_{0 \\mu}$ and $z_{\\infty \\nu}$ the $\\mu$-th zero/$\\nu$-th pole of $X(z)$, and $Q = M-1$ and $P = N-1$ the total number of zeros and poles, respectively. For $M=N$ the factor $K = \\frac{\\beta_M}{\\alpha_N}$. If \n",
    "\n",
    "* $M > N$ at least one pole is located at $|z| = \\infty$,\n",
    "* $M < N$ at least one pole is located at $z = 0$.\n",
    "\n",
    "It is common to illustrate the poles and zeros in a [pole-zero plot](https://en.wikipedia.org/wiki/Pole%E2%80%93zero_plot). Here the locations of the complex poles and zeros, their degrees and the factor $K$ are plotted in the $z$-plane. It is common to include the unit circle $|z| = 1$ in the plot due to its relevance in the theory of discrete signals and systems. An example for a pole-zero plot is shown in the following\n",
    "\n",
    "![Exemplary pole-zero plot](pz_plot.png)\n",
    "\n",
    "The locations of the poles and zeros provide insights into the composition of a signal. For instance, the $z$-transform of the [complex exponential signal](#Transformation-of-the-Causal-Complex-Exponential-Signal) has a zero at $z=0$ and a pole at $z = z_0$. A signal which is composed from a superposition of complex exponential signals will have multiple poles whose positions are related to the complex frequencies of the signals it is composed of."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Derive $X(z)$ together with its ROC from above pole-zero plot under the assumption that it represents a right-sided signal $x[k]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example**\n",
    "\n",
    "The $z$-transform of the causal complex exponential signal\n",
    "\n",
    "\\begin{equation}\n",
    "X(z) = \\frac{z}{z - z_0} \\qquad \\text{for } |z| > |z_0|\n",
    "\\end{equation}\n",
    "\n",
    "derived above is illustrated by plotting its magnitude $|X(z)|$ over the $z$-plane for $z_0 = 1 + j$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 614.4x460.8 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "rez, imz = sym.symbols('rez imz', real=True)\n",
    "\n",
    "X = z / (z - z0)\n",
    "X1 = X.subs({z: rez+sym.I*imz, z0: 1+sym.I})\n",
    "\n",
    "sym.plotting.plot3d(abs(X1), (rez, -2, 2), (imz, -2, 2),\n",
    "                    xlabel=r'$\\Re\\{z\\}$', ylabel=r'$\\Im\\{z\\}$', title=r'$|X(z)|$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, the $z$-transform $X(z)$ is illustrated by its pole-zero plot. First the poles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ z_{0} : 1\\right\\}$"
      ],
      "text/plain": [
       "{z₀: 1}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poles = sym.roots(sym.denom(X), z)\n",
    "poles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and zeros are computed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ 0 : 1\\right\\}$"
      ],
      "text/plain": [
       "{0: 1}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeros = sym.roots(sym.numer(X), z)\n",
    "zeros"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above dictionaries are composed from the poles and zeros, and their degrees. \n",
    "\n",
    "In order to illustrate the location of poles and zeros in the $z$-plane, the pole-zero plot is shown for $z_0 = 1 + j$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pole_zero_plot import pole_zero_plot\n",
    "\n",
    "X2 = X.subs(z0, 1+sym.I)\n",
    "pole_zero_plot(sym.roots(sym.denom(X2), z), sym.roots(sym.numer(X2), z))"
   ]
  },
  {
   "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, Continuous- and Discrete-Time Signals and Systems - Theory and Computational Examples*."
   ]
  }
 ],
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