On optimum oversampling in the Gabor scheme

M.J. Bastiaans

doi:10.1109/ICASSP.1997.599449

On optimum oversampling in the Gabor scheme

M.J. Bastiaans

Signal Processing Systems

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

3 Citaten (Scopus)

Samenvatting

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.

Originele taal-2	Engels
Titel	Proc. ICASSP 97, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, München, Germany
Plaats van productie	Los Alamitos, CA
Uitgeverij	IEEE Computer Society
Pagina's	2101-2104
ISBN van geprinte versie	0-8186-7919-0
DOI's	https://doi.org/10.1109/ICASSP.1997.599449
Status	Gepubliceerd - 1997
Evenement	1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1997) - Munich, Duitsland Duur: 21 apr. 1997 → 24 apr. 1997

Congres

Congres	1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1997)
Verkorte titel	ICASSP 1997
Land/Regio	Duitsland
Stad	Munich
Periode	21/04/97 → 24/04/97
Ander	Proc. ICASSP 97, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, München, Germany, 21-24 April 1997

Toegang tot document

10.1109/ICASSP.1997.599449

Citeer dit

@inproceedings{a17a2369392741178caf6ffd1850af70,

title = "On optimum oversampling in the Gabor scheme",

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.",

author = "M.J. Bastiaans",

year = "1997",

doi = "10.1109/ICASSP.1997.599449",

language = "English",

isbn = "0-8186-7919-0",

pages = "2101--2104",

booktitle = "Proc. ICASSP 97, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, M{\"u}nchen, Germany",

publisher = "IEEE Computer Society",

address = "United States",

note = "1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1997), ICASSP 1997 ; Conference date: 21-04-1997 Through 24-04-1997",

}

Bastiaans, MJ 1997, On optimum oversampling in the Gabor scheme. in Proc. ICASSP 97, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, München, Germany. IEEE Computer Society, Los Alamitos, CA, blz. 2101-2104, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1997), Munich, Beieren, Duitsland, 21/04/97. https://doi.org/10.1109/ICASSP.1997.599449

TY - GEN

T1 - On optimum oversampling in the Gabor scheme

AU - Bastiaans, M.J.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

U2 - 10.1109/ICASSP.1997.599449

DO - 10.1109/ICASSP.1997.599449

M3 - Conference contribution

SN - 0-8186-7919-0

SP - 2101

EP - 2104

BT - Proc. ICASSP 97, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, München, Germany

PB - IEEE Computer Society

CY - Los Alamitos, CA

T2 - 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1997)

Y2 - 21 April 1997 through 24 April 1997

ER -

On optimum oversampling in the Gabor scheme

Samenvatting

Congres

Toegang tot document

Vingerafdruk

Citeer dit