Date of Award

12-1992

Document Type

Thesis

Degree Name

Master of Science in Electrical Engineering

Department

Department of Mathematics and Statistics

First Advisor

Gregory T. Warhola, PhD

Abstract

The multiresolution analysis (MRA) developed by Mallat and Meyer and further discussed by Daubechies is a useful tool in the analysis of sampled signals such as images and speech. This thesis develops the theory and implementation of a rational-resolution analysis (RRA) as an extension of the dyadic MRA for arbitrary rational dilation factors. We present a method to calculate families of compactly-supported scaling functions and wavelets based on arbitrary integer dilation factors and provide examples. The perfect- reconstruction properties of the RRA are discussed and it is demonstrated that the compactly-supported scaling functions and wavelets do not yield perfect- reconstruction. However, the approximation-reconstruction is demonstrated and families of basis function which do lead to perfect reconstruction are characterized. Finally, comparisons are made between RRAs and conventional MRAs and illustrated with speech signals.

AFIT Designator

AFIT-GE-ENC-92D-1

DTIC Accession Number

ADA259040

Comments

The author's Vita page is omitted.

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