Sampling for shift-invariant and wavelet subspaces

Jeffrey A. Hogan; Joseph D. Lakey

doi:10.1117/12.408622

4 December 2000 Sampling for shift-invariant and wavelet subspaces

Jeffrey A. Hogan, Joseph D. Lakey

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408622
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

We investigate several issues surrounding the general question of when a function in a finitely generated shift invariant subspace of L²(R) can be determined by certain of its sample values just as a function band limited to (-1/2, ½) can be expressed in terms of its integer samples. The main theme here is how answers to this question depend on general properties of the generators of the shift invariant space, such as orthogonality properties, scaling relations, smoothness and so forth. One of the main issues that we address is the question of how to control aliasing error.

Citation Download Citation

Jeffrey A. Hogan and Joseph D. Lakey "Sampling for shift-invariant and wavelet subspaces", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408622

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