
Accession Number : AD0713194
Title : APPLICATION OF WALSH TRANSFORM TO STATISTICAL ANALYSIS,
Corporate Author : CALIFORNIA UNIV LOS ANGELES SCHOOL OF ENGINEERING AND APPLIED SCIENCE
Personal Author(s) : Pearl,Judea
Report Date : AUG 1970
Pagination or Media Count : 43
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 effectively been executed in the Fourier spectrum. This paper explores the properties of the WalshHadamard transform of probability functions of discrete random variables. 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 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. (Author)
Descriptors : (*STATISTICAL ANALYSIS, TRANSFORMATIONS(MATHEMATICS)), (*INFORMATION THEORY, PATTERN RECOGNITION), FOURIER ANALYSIS, GROUPS(MATHEMATICS), SET THEORY, S MATRIX, STATISTICAL DISTRIBUTIONS, HARMONIC ANALYSIS, INTEGRAL TRANSFORMS
Subject Categories : Statistics and Probability
Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE