Application of Walsh Transform to Statistical Analysis

1 April 1971

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Systems, Man, and Cybernetics

Vol. SMC-1 (2) , 111-119
https://doi.org/10.1109/tsmc.1971.4308267

Abstract

Harmonic analysis of probability distribution functions has long served an important function in the treatment of stochastic systems. The tasks of generating moments and distributions of sums have been effectively executed in the Fourier spectrum. The properties of the Walsh-Hadamard transform of probability functions of discrete random variables is explored. Many analogies can be drawn between Fourier and Walsh analysis. In particular, it is shown that moments can be generated taking the Gibb's derivative of the Walsh spectrum and that products of Walsh spectra yield the distribution of dyadic sums. Stochastic systems with dyadic symmetry would benefit most from the properties of Walsh analysis and the computational advantages it offers. Some applications in the areas of information theory and pattern recognition are demonstrated.

Keywords

This publication has 4 references indexed in Scilit:

A Generalized Technique for Spectral Analysis
IEEE Transactions on Computers, 1970
Transmission of Information by Orthogonal Functions
Published by Springer Nature ,1969
Hadamard transform image coding
Proceedings of the IEEE, 1969
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Transactions of the American Mathematical Society, 1949