Gabor representation with oversampling

Meir Zibulski; Yehoshua Y. Zeevi

doi:10.1117/12.131510

1 November 1992 Gabor representation with oversampling

Meir Zibulski, Yehoshua Y. Zeevi

Proceedings Volume 1818, Visual Communications and Image Processing '92; (1992) https://doi.org/10.1117/12.131510
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

An approach for characterizing the properties of the basis functions of the Gabor representation in the context of oversampling is presented. The approach is based on the concept of frames and utilizes the Piecewise Zak Transform (PZT). The frame operator associated with the Gabor-type frame, the so-called Weyl-Heisenberg frame, is examined for a rational oversampling rate by representing the frame operator as a matrix-valued function in the PZT domain. Completeness and frame properties of the Gabor representation functions are examined in relation to the properties of the matrix-valued function. The frame bounds are calculated by means of the eigenvalues of the matrix-valued function, and the dual-frame, which is used in calculation of the expansion coefficients, is expressed by means of the inverse matrix.

Citation Download Citation

Meir Zibulski and Yehoshua Y. Zeevi "Gabor representation with oversampling", Proc. SPIE 1818, Visual Communications and Image Processing '92, (1 November 1992); https://doi.org/10.1117/12.131510

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