Gabor transform: theory and computations

Jie Yao

doi:10.1117/12.162059

1 November 1993 Gabor transform: theory and computations

Jie Yao

Proceedings Volume 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing; (1993) https://doi.org/10.1117/12.162059
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

In this paper, the theory and computations for the Gabor transform are discussed. The Gabor coefficients can be computed with a biorthogonal function or the Zak transform. Relations between a window function and its biorthogonal function are discussed. The formulas derived for the continuous variable Gabor transform with Zak transforms can be applied to the discrete Gabor transform by replacing the Zak transforms with the discrete Fourier transforms. The generalized Gabor transform are also discussed. Relations between a window function and its biorthogonal functions are presented. In the case of the generalized Gabor transform, the biorthogonal functions are not unique. The optimal biorthogonal functions are discussed. A relation between a window function and its optimal biorthogonal function is presented based on the Zak transform when T/T' is rational. The finite discrete generalized Gabor transform is also derived. The relations between a window function and its optimal biorthogonal function derived for the continuous variable generalized Gabor transform can be extended to the finite discrete case.

Citation Download Citation

Jie Yao "Gabor transform: theory and computations", Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); https://doi.org/10.1117/12.162059

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