Abstract
The fundamental problem ofdiscrete Gabor transforms is to compute a set ofGabor coefficients in efficient ways. Recent study on the subject is an indirect approach: in order to compute the Gabor coefficients, one needs to find an auxiliary bi-orthogonal window function γ.
We are seeking a direct approach in this paper. We introduce concepts ofGabor-Gram matrices and investigate their structural properties. We propose iterative methods to compute theGabor coefficients. Simple solutions for critical sampling, certain oversampling, and undersampling cases are developed.
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Communicated by Joshua Zeevi
Acknowledgements and Notes. The author was with University of Connecticut, Storrs, CT 06269-3009.
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Qiu, S. Discrete Gabor transforms: The Gabor-Gram matrix approach. The Journal of Fourier Analysis and Applications 4, 1–17 (1998). https://doi.org/10.1007/BF02475925
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DOI: https://doi.org/10.1007/BF02475925