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Proceedings Paper

Class of discrete Gabor expansion
Author(s): Shidong Li; Dennis M. Healy
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Paper Abstract

We present a new approach to studying a discrete Gabor expansion (DGE). We show that, in general, DGE is not the usual biorthogonal decomposition, but belongs to a larger and looser decomposition scheme which we call pseudo frame decomposition. It includes the DGE scheme proposed as a special case. The standard dual frame decomposition is also a special case. We derive algorithms using techniques for Gabor sequences to compute 'biorthogonal' sequences through proper matrix representation. Our algorithms involve solutions to a linear system to obtain the 'biorthogonal' windows. This approach provides a much broader mathematical view of the DGE, and therefore, establishes a wider mathematical foundation towards the theory of DGE. The general algorithm derived also provides a whole class of discrete Gabor expansions, among which 'good' ones can be generated. Simulation results are also provided.

Paper Details

Date Published: 15 March 1994
PDF: 12 pages
Proc. SPIE 2242, Wavelet Applications, (15 March 1994); doi: 10.1117/12.170082
Show Author Affiliations
Shidong Li, Dartmouth College (United States)
Dennis M. Healy, Dartmouth College (United States)

Published in SPIE Proceedings Vol. 2242:
Wavelet Applications
Harold H. Szu, Editor(s)

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