Optimum oversampling in the rectangular 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. For sufficiently dense sampling, the synthesis window (which appears in Gabor's reconstruction formula) may be constructed such that it resembles a rather arbitrarily given function; this function may or may not be proportional to the analysis window (which is used in the windowed Fourier transform). It is shown that the resemblance 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.
Original languageEnglish
Title of host publicationSignal Processing IX, Theories and Applications, Proc. EUSIPCO-98, Ninth European Signal Processing Conference, Rhodes, Greece
EditorsS. Theodoridis, I. Pitas, A. Stouraitis, N. Kalouptsidis
Place of PublicationPatras, Greece
PublisherTyporama Editions
Pages617-620
Volume2
ISBN (Print)960-7620-07-0
Publication statusPublished - 1998
Event9th European Signal Processing Conference (EUSIPCO 1998) - Rhodos, Greece
Duration: 8 Sep 199811 Sep 1998
Conference number: 9

Conference

Conference9th European Signal Processing Conference (EUSIPCO 1998)
Abbreviated titleEUSIPCO 1998
CountryGreece
CityRhodos
Period8/09/9811/09/98

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