• DocumentCode
    715479
  • Title

    Harmonic analysis of binary functions

  • Author

    Belfiore, Jean-Claude ; Yi Hong ; Viterbo, Emanuele

  • Author_Institution
    Commun. & Electron. Dept., Telecom ParisTech, Paris, France
  • fYear
    2015
  • fDate
    April 26 2015-May 1 2015
  • Firstpage
    1
  • Lastpage
    5
  • Abstract
    In this paper we introduce the two-modular Fourier transform of a binary function f : R → R defined over a finite commutative ring R = F2[X]/φ(X), where F2[X] is the ring of polynomials with binary coefficients and φ(X) is a polynomial of degree n, which is not a multiple of X. We also introduce the corresponding inverse Fourier transform. We then prove the corresponding convolution theorem.
  • Keywords
    Fourier transforms; convolution; group theory; harmonic analysis; inverse transforms; polynomials; binary coefficients; binary functions; convolution theorem; finite commutative ring; harmonic analysis; inverse Fourier transform; polynomials; two-modular Fourier transform; Additives; Convolution; Fourier transforms; Harmonic analysis; Indexes; Modules (abstract algebra); Polynomials; binary functions; binary groups; two-modular Fourier transform;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Information Theory Workshop (ITW), 2015 IEEE
  • Conference_Location
    Jerusalem
  • Print_ISBN
    978-1-4799-5524-4
  • Type

    conf

  • DOI
    10.1109/ITW.2015.7133147
  • Filename
    7133147
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=715479