Complete Orthonormal Set of Two-Dimensional Haar-Like Functions.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 10, 1973
- Accession Number
- AD0755432
Entities
People
- John E. Shore
Organizations
- United States Naval Research Laboratory