Discrete Gabor transforms: The Gabor-Gram matrix approach

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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