About Wiener’s Generalized Harmonic Analysis

Abstract

Harmonic analysis, probability and statistics were among the fields Wiener was most interested in. In his generalized harmonic analysis he introduced, for a signal with finite square modulus mean value, its spectral distribution which is linked to what can be called the integral Fourier transform of the signal. Wiener demonstrated, in a refined way, an interesting property of this integral Fourier transform which can be also established, very directly, with the help of what we call “epsilon distribution” which, in a way, is the antithesis of the delta distribution of Dirac.

Citation

Vallée, R. (1994), "About Wiener’s Generalized Harmonic Analysis", Kybernetes, Vol. 23 No. 6/7, pp. 65-70. https://doi.org/10.1108/03684929410795094