On the discrete version of Gabor's signal expansion, the Gabor transform, and the Zak transform

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Samenvatting

Gabors expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e., the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of which Gabors expansion coefficients can be determined. The restriction to a signal and an analysis window that both have finite-support, leads to the concept of a discrete Gabor expansion and a discrete Gabor transform. After introduction of the discrete Fourier transform and the discrete Zak transform, it is possible to express the discrete Gabor expansion and the discrete Gabor transform as matrix-vector products. Using these matrix-vector products, a relationship between the analysis window and the synthesis window is derived. It is shown how this relationship enables us to determine the optimum synthesis window in the sense that it has minimum L_2 norm, and it is shown that this optimum synthesis window resembles best the analysis window.
Originele taal-2Engels
TitelProc. ProRISC/IEEE-Benelux Workshop on Circuits, Systems and Signal Processing, Mierlo, Netherlands
RedacteurenJ.P. Veen
Plaats van productieUtrecht, Netherlands
UitgeverijSTW Technology Foundation
Pagina's67-72
ISBN van geprinte versie90-73461-09-X
StatusGepubliceerd - 1996
Evenement1996 ProRISC/IEEE-Benelux Workshop on Circuits, Systems and Signal Processing - Mierlo
Duur: 1 jan 199628 nov 1996

Congres

Congres1996 ProRISC/IEEE-Benelux Workshop on Circuits, Systems and Signal Processing
Verkorte titelProRISC/IEEE 1996
StadMierlo
Periode1/01/9628/11/96
AnderProc. ProRISC/IEEE-Benelux Workshop on Circuits, Systems and Signal Processing, Mierlo, Netherlands, 27-28 November 1996

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  • Citeer dit

    Bastiaans, M. J. (1996). On the discrete version of Gabor's signal expansion, the Gabor transform, and the Zak transform. In J. P. Veen (editor), Proc. ProRISC/IEEE-Benelux Workshop on Circuits, Systems and Signal Processing, Mierlo, Netherlands (blz. 67-72). STW Technology Foundation.