Accession Number : ADA311766

Title :   Frames and Orthonormal Bases for Variable Windowed Fourier Transforms.

Descriptive Note : Technical rept. 1 Oct 95-30 Jun 96,

Corporate Author : COLORADO UNIV AT BOULDER DEPT OF ELECTRICAL AND COMPUTER ENGINEERING

Personal Author(s) : Ueng, Neng-Tsann ; Scharf, Louis L.

PDF Url : ADA311766

Report Date : 29 JUL 1996

Pagination or Media Count : 8

Abstract : We generalize the windowed Fourier transform to the variable windowed Fourier transform. This generalization brings the Gabor transform and the wavelet transform under the same framework. Using frame theory we characterize frames and orthonormal bases for the variable windowed Fourier series (VWFS). These characterizations are formulated explicitly in terms of window functions. Therefore they can serve as guidelines for designing windows for the VWFS. We introduce the notion of 'complete orthogonal support' and, with the help of this notion, we construct a class of orthonormal VWFS bases for L(sq)(R+).

Descriptors :   *SIGNAL PROCESSING, *VISUAL SIGNALS, FOURIER TRANSFORMATION, THEORY, ORTHOGONALITY.

Subject Categories : Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE