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 Walsh-Hadamard 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