Date of Award

Spring 2000

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Lihe Zou

Abstract

A scheme is presented to regain a finite number of lost samples from a Nyquist-rate-sampled band-limited signal f of finite energy by replenishing new sample values of the same number. The result can also be viewed as the solution to a special non-uniform sampling problem.

A scheme is also presented to recover a band-limited function f of finite energy from its sampling values on real sequences with an accumulation point. The result given here can also be viewed as an approach to the extrapolation problem of determination a band-limited function in terms of its given values on a finite interval. An error estimate is also obtained.

The existence of two kinds of frames, Weyl-Heisenberg frames and affine frames, is studied. The conditions given in this dissertation improve the known conditions and, in addition, are easy to verify.

A parallel algorithm for the two-dimensional forward fast wavelet transform is developed and implemented on the AP1000 multiprocessor system. The algorithm is carefully analyzed before implementation. Experiments are performed on different input sizes on different numbers of processors. The results from the experiments coincide with the theoretical analysis. The parallel algorithm gains expected speedup on the mesh architecture. Further work is suggested.

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