On generalized Walsh functions and transform

Abstract

This paper is basically tutorial in nature. Hence, its purpose is to introduce the Walsh set of functions, Walsh transform and some of the basic properties of these two formulations. The method of defining Walsh functions as products of Rademacher functions is adopted here. These functions are then extended to the generalized Walsh functions; and consequently the Walsh transform is introduced. The notion of a delta function for Walsh analysis is developed along the lines of the classical Fourier analysis. And finally, relations connecting Walsh and Fourier transforms are derived.