Computational frameworks for discrete Gabor analysis

Thomas Strohmer

doi:10.1117/12.279497

24 October 1997 Computational frameworks for discrete Gabor analysis

Thomas Strohmer

Proceedings Volume 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII; (1997) https://doi.org/10.1117/12.279497
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

The Gabor transform yields a discrete representation of a signal in the phase space. Since the Gabor transform is non-orthogonal, efficient reconstruction of a signal from its phase space samples is not straightforward and involves the computation of the so- called dual Gabor function. We present a unifying approach to the derivation of numerical algorithms for discrete Gabor analysis, based on unitary matrix factorization. The factorization point of view is notably useful for the design of efficient numerical algorithms. This presentation is the first systematic account of its kind. In particular, it is shown that different algorithms for the computation of the dual window correspond to different factorizations of the frame operator. Simple number theoretic conditions on the time-frequency lattice parameters imply additional structural properties of the frame operator.

Citation Download Citation

Thomas Strohmer "Computational frameworks for discrete Gabor analysis", Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); https://doi.org/10.1117/12.279497

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