{
  "id": "1409.1727",
  "version": "v1",
  "published": "2014-09-05T10:22:52.000Z",
  "updated": "2014-09-05T10:22:52.000Z",
  "title": "Two Methods for Numerical Inversion of the Z-Transform",
  "authors": [
    "Farshad Merrikh-Bayat"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In some of the problems, complicated functions of the Z-transform variable, $z$, appear which either cannot be inverted analytically or the required calculations are quite tedious. In such cases numerical methods should be used to find the inverse Z-transform. The aim of this paper is to propose two simple and effective methods for this purpose. The only restriction on the signal (whose Z-transform is given) is that it must be absolutely summable (of course, this limitation can be removed by a suitable scaling). The first proposed method is based on the Discrete Fourier Transform (DFT) and the second one is based on solving a linear system of algebraic equations, which is obtained after truncating the signal whose Z-transform is known. Numerical examples are also presented to confirm the efficiency of the proposed methods. Functions in non-integer powers of $z$ are also briefly discussed and it is shown that such functions cannot be obtained by taking the Z-transform from any discrete-time signal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-05T10:22:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "numerical inversion",
      "discrete fourier transform",
      "non-integer powers",
      "cases numerical methods",
      "algebraic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.1727M"
    }
  }
}