Accession Number : AD0755432

Title :   Complete Orthonormal Set of Two-Dimensional Haar-Like Functions.

Descriptive Note : Interim rept.,

Corporate Author : NAVAL RESEARCH LAB WASHINGTON D C

Personal Author(s) : Shore,John E.

Report Date : 10 JAN 1973

Pagination or Media Count : 27

Abstract : A set of two-dimensional functions is defined. Expansions of two dimensional functions f(x, y) in terms of this set have convergence properties analogous to those of one-dimensional Haar series. The Nth partial sum (P sub N)(x, y) is a step function of 2 sup (2N) square steps each of area 1/2 sup (2N). The value of (P sub N)(x, y) on any step is the mean value of f(x, y) over the area covered by the step. If f(x, y) is continuous or has a finite number of discontinuities along binary-rational line segments, then (P sub N)(x, y) converges uniformly. If f(x, y) has a finite number of discontinuities along binary-irrational line segments, then (P sub N))x, y) converges pointwise, except along the discontinuities. Accuracy of the estimate (P sub N) and the convergence rate are analogous to those for one-dimensional Haar series. (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), THEOREMS), SERIES(MATHEMATICS), CONVERGENCE, FOURIER ANALYSIS, BINARY ARITHMETIC, CODING, PATTERN RECOGNITION, TRANSFORMATIONS(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE