Class of discrete Gabor expansion

Shidong Li; Dennis M. Healy Jr.

doi:10.1117/12.170082

15 March 1994 Class of discrete Gabor expansion

Shidong Li, Dennis M. Healy Jr.

Proceedings Volume 2242, Wavelet Applications; (1994) https://doi.org/10.1117/12.170082
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States

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.

Citation Download Citation

Shidong Li and Dennis M. Healy Jr. "Class of discrete Gabor expansion", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); https://doi.org/10.1117/12.170082

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