On optimum oversampling in the Gabor scheme

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Abstract

The windowed Fourier transform of a time signal is considered, as well as a way to reconstruct the signal from a sufficiently densely sampled version of its windowed Fourier transform using a Gabor representation; following Gabor, sampling occurs on a two-dimensional time-frequency lattice with equidistant time intervals and equidistant frequency intervals. In the limit of infinitely dense sampling, the optimum synthesis window (which appears in Gabor's reconstruction formula) becomes similar to the analysis window (which is used in the windowed Fourier transform). It is shown that this similarity can already be reached for a rather small degree of oversampling, if the sampling distances in the time and frequency directions are properly chosen. A procedure is presented with which the optimum ratio of the sampling intervals can be determined. The theory is elucidated by finding the optimum ratio in the cases of a Gaussian and an exponential analysis window.
Original languageEnglish
Title of host publicationProc. ICASSP 97, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, München, Germany
Place of PublicationLos Alamitos, CA
PublisherIEEE Computer Society
Pages2101-2104
ISBN (Print)0-8186-7919-0
DOIs
Publication statusPublished - 1997
Event1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1997) - Munich, Germany
Duration: 21 Apr 199724 Apr 1997

Conference

Conference1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1997)
Abbreviated titleICASSP 1997
CountryGermany
CityMunich
Period21/04/9724/04/97

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    Bastiaans, M. J. (1997). On optimum oversampling in the Gabor scheme. In Proc. ICASSP 97, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, München, Germany (pp. 2101-2104). IEEE Computer Society. https://doi.org/10.1109/ICASSP.1997.599449