New efficient methods for Gabor analysis

Hans Georg Feichtinger; Ole Christensen

doi:10.1117/12.158015

22 October 1993 New efficient methods for Gabor analysis

Hans Georg Feichtinger, Ole Christensen

Proceedings Volume 2094, Visual Communications and Image Processing '93; (1993) https://doi.org/10.1117/12.158015
Event: Visual Communications and Image Processing '93, 1993, Cambridge, MA, United States

Abstract

In this paper we describe new methods to obtain (non-orthogonal) Gabor expansions of discrete and finite signals. By this we understand the expansion of a signal of a given length n into a (finite) series of coherent building blocks obtained from a Gabor atom through discrete time- and frequency-shift operators. Although bump-type atoms are natural candidates the approach is not restricted to such building blocks. Also the set of time/frequency shift operators does not have to be a (product) lattice but just an ordinary (additive) subgroup of the time/frequency-plane which is naturally identified with the two-dimensional n X n cyclic group. In contrast, other non-separable subgroups turn out to be more interesting for the efficient determination of a suitable set of coefficients for the coherent expansion. For this purpose it is enough to determine the so-called dual Gabor atom. The existence and basic properties of this dual atom are known in the case of lattice groups from the ordinary frame theory. But more importantly, we demonstrate that the use of the conjugate gradient method reduces the computational complexity of determining it drastically. The required Gabor coefficients are simply obtained as short time Fourier coefficients of the given signal with the dual atom being the moving window.

Citation Download Citation

Hans Georg Feichtinger and Ole Christensen "New efficient methods for Gabor analysis", Proc. SPIE 2094, Visual Communications and Image Processing '93, (22 October 1993); https://doi.org/10.1117/12.158015

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