Title :
Harmonic analysis of binary functions
Author :
Belfiore, Jean-Claude ; Yi Hong ; Viterbo, Emanuele
Author_Institution :
Commun. & Electron. Dept., Telecom ParisTech, Paris, France
fDate :
April 26 2015-May 1 2015
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;
Conference_Titel :
Information Theory Workshop (ITW), 2015 IEEE
Conference_Location :
Jerusalem
Print_ISBN :
978-1-4799-5524-4
DOI :
10.1109/ITW.2015.7133147
