Oversampling in Gabor's signal expansion by an integer factor

M.J. Bastiaans

doi:10.1109/TFSA.1994.467239

Oversampling in Gabor's signal expansion by an integer factor

M.J. Bastiaans

Signal Processing Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

2 Citations (Scopus)

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Abstract

Gabor's (1946) expansion of a signal into a discrete set of shifted and modulated versions of an elementary signal is reviewed and its relation to sampling of the sliding-window spectrum is shown. It is indicated how Gabor's expansion coefficients can be found as samples of the sliding-window spectrum, where the window function, which still has to be determined, is related to the elementary signal. Gabor's critical sampling as well as the case of oversampling by an integer factor are considered. The Zak (1967) transform is introduced and its intimate relationship to Gabor's signal expansion is demonstrated. It is shown how the Zak transform can be helpful in determining Gabor's expansion coefficients and how it can be used in finding window functions that correspond to a given elementary signal. An arrangement is described which is able to generate Gabor's expansion coefficients of a rastered, one-dimensional signal by coherent-optical means.

Original language	English
Title of host publication	Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 25-28 October 1994, Philadelphia, PA
Place of Publication	New York
Publisher	Institute of Electrical and Electronics Engineers
Pages	280-283
Number of pages	4
ISBN (Print)	0-7803-2127-8
DOIs	https://doi.org/10.1109/TFSA.1994.467239
Publication status	Published - 1994
Event	conference; Proc. 1994 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, PA, 25-28 October 1994; 1994-10-25; 1994-10-28 - Duration: 25 Oct 1994 → 28 Oct 1994

Conference

Conference	conference; Proc. 1994 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, PA, 25-28 October 1994; 1994-10-25; 1994-10-28
Period	25/10/94 → 28/10/94
Other	Proc. 1994 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, PA, 25-28 October 1994

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10.1109/TFSA.1994.467239

Cite this

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title = "Oversampling in Gabor's signal expansion by an integer factor",

abstract = "Gabor's (1946) expansion of a signal into a discrete set of shifted and modulated versions of an elementary signal is reviewed and its relation to sampling of the sliding-window spectrum is shown. It is indicated how Gabor's expansion coefficients can be found as samples of the sliding-window spectrum, where the window function, which still has to be determined, is related to the elementary signal. Gabor's critical sampling as well as the case of oversampling by an integer factor are considered. The Zak (1967) transform is introduced and its intimate relationship to Gabor's signal expansion is demonstrated. It is shown how the Zak transform can be helpful in determining Gabor's expansion coefficients and how it can be used in finding window functions that correspond to a given elementary signal. An arrangement is described which is able to generate Gabor's expansion coefficients of a rastered, one-dimensional signal by coherent-optical means.",

author = "M.J. Bastiaans",

year = "1994",

doi = "10.1109/TFSA.1994.467239",

language = "English",

isbn = "0-7803-2127-8",

pages = "280--283",

booktitle = "Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 25-28 October 1994, Philadelphia, PA",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "conference; Proc. 1994 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, PA, 25-28 October 1994; 1994-10-25; 1994-10-28 ; Conference date: 25-10-1994 Through 28-10-1994",

}

Bastiaans, MJ 1994, Oversampling in Gabor's signal expansion by an integer factor. in Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 25-28 October 1994, Philadelphia, PA. Institute of Electrical and Electronics Engineers, New York, pp. 280-283, conference; Proc. 1994 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, PA, 25-28 October 1994; 1994-10-25; 1994-10-28, 25/10/94. https://doi.org/10.1109/TFSA.1994.467239

Oversampling in Gabor's signal expansion by an integer factor. / Bastiaans, M.J.
Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 25-28 October 1994, Philadelphia, PA. New York: Institute of Electrical and Electronics Engineers, 1994. p. 280-283.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - Gabor's (1946) expansion of a signal into a discrete set of shifted and modulated versions of an elementary signal is reviewed and its relation to sampling of the sliding-window spectrum is shown. It is indicated how Gabor's expansion coefficients can be found as samples of the sliding-window spectrum, where the window function, which still has to be determined, is related to the elementary signal. Gabor's critical sampling as well as the case of oversampling by an integer factor are considered. The Zak (1967) transform is introduced and its intimate relationship to Gabor's signal expansion is demonstrated. It is shown how the Zak transform can be helpful in determining Gabor's expansion coefficients and how it can be used in finding window functions that correspond to a given elementary signal. An arrangement is described which is able to generate Gabor's expansion coefficients of a rastered, one-dimensional signal by coherent-optical means.

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M3 - Conference contribution

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BT - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 25-28 October 1994, Philadelphia, PA

PB - Institute of Electrical and Electronics Engineers

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T2 - conference; Proc. 1994 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, PA, 25-28 October 1994; 1994-10-25; 1994-10-28

Y2 - 25 October 1994 through 28 October 1994

ER -

Oversampling in Gabor's signal expansion by an integer factor

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