Master's Theses

Date of Award

2013

Document Type

Thesis

Department

Computer Science

First Advisor

Izidor Gertner

Second Advisor

Douglas Troeger

Keywords

Gabor Analysis, Time frequency, Wilson basis

Abstract

Discrete orthonormal time-frequency basis functions are described and used for both analysis and synthesis of complex-valued signals. We derive expressions for complex-valued expansion coefficients in time-frequency lattices in the discrete one dimensional case. This derivation is based on Professor I. Gertner's previous construction of a complete orthonormal set of basis functions well localized in the temporal-spatial-frequency domain in the continuous case. We describe how these can be generalized to any number of dimensions. Example applications are presented in one and two dimensions. Three dimensional basis functions are visualized and discussed. Finally, a full a Matlab implementation of this work is provided. Chapter two of this thesis has been submitted for publication as a self-contained paper.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.