Short-time spectral and autocorrelation analysis in the Walsh domain

Abstract

A short-time dyadic autocorrelation function (dacf) and a short-time Walsh energy spectrum of the first kind are defined in the Walsh-Fourier domain. The natural choice of the short-time functions does not lead to a Walsh-Fourier transform pair (dyadic Wiener-Khintchine theorem), and thus a second kind of short-time dacf and short-time Walsh energy spectrum are defined as the Walsh-Fourier transforms of the first kind. This leads to a meaningful and convenient Walsh transform pair between the first short-time Walsh energy spectrum and the second short-time dacf. The measurement procedures for both kinds of functions are discussed, and the mean values of these short-time functions are shown to be related to the corresponding long-time functions.