Frame analysis of the discrete Gabor-scheme

Author

Zibulski, Meir ; Zeevi, Yehoshua Y.

Author_Institution

Dept. of Mater. Eng., Technion-Israel Inst. of Technol., Haifa, Israel

Volume

42

Issue

4

fYear

1994

fDate

4/1/1994 12:00:00 AM

Firstpage

942

Lastpage

945

Abstract

The properties of the discrete Gabor scheme are considered in the context of oversampling. The approach is based on the concept of frames and utilizes the piecewise finite Zak transform (PFZT). The frame operator is represented as a matrix-valued function in the PFZT domain, and its properties are examined in relation to this 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. DFT-based algorithms for computation of the expansion coefficients, and for the reconstruction of signals from these coefficients, are generalized for the case of oversampling of the Gabor space. The algorithms are implemented in an example of representation of a nonstationary signal

Keywords

eigenvalues and eigenfunctions; fast Fourier transforms; signal processing; DFT-based algorithms; PFZT domain; discrete Gabor scheme; dual frame; eigenvalues; expansion coefficients; frame analysis; frame bounds; frame operator; inverse matrix; matrix-valued function; nonstationary signal; oversampling; piecewise finite Zak transform; signal reconstruction; Discrete transforms; Eigenvalues and eigenfunctions; Hilbert space; Image reconstruction; Sampling methods; Signal processing; Space technology;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.285657

Filename

285657