Date of Award


Document Type


Degree Name

Master of Science


Department of Electrical and Computer Engineering

First Advisor

Bruce W. Suter, PhD


This thesis develops and evaluates a number of new concepts and tools for the analysis of signals using Malvar wavelets lapped orthogonal transforms . Windowing, often employed as a spectral estimation technique, can result in irreparable distortions in the transformed signal. By utilizing the Malvar wavelet, any signal distortion resulting from the transformation can be eliminated or cancelled during reconstruction. This is accomplished by placing conditions on the window and the basis function and then incorporating the window into the orthonormal representation. Paradigms for both a complex-valued and a real-valued Malvar wavelet are summarized. I-lie algorithms for the wavelets were implemented in the DOD standard language, Ada. The code was verified to ensure perfect reconstruction could be obtained and experiments were performed using the wavelet programs. Various compression techniques were investigated and evaluated using the Malvar wavelet in both homomorphic and non- homomorphic systems. The Malvar wavelet has the unique ability to overlap adjacent windows without increasing the number of transform coefficients. Various amounts of window overlap were investigated to determine if there is an optimal amount which should be used. In addition, the real-valued basis function was used to attempt real-valued deconvolution.

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The author's Vita page is omitted.