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Proceedings Paper

Local Bandwidth And Optimal Windows For The Short Time Fourier Transform
Author(s): Leon Cohen; Chongmoon Lee
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Paper Abstract

The standard deviation of instantaneous frequency (local bandwidth) is derived for the short time Fourier transform. This is done by calculating the local moments of frequency for a given time instants using the spectrogram as a joint time-frequency distribution. By minimizing the local bandwidth optimal windows are obtained. We show that amplitude modulation has a very significant effect on the optimum window. We also show that to obtain the highest possible resolution, divergent windows which non the less lead to convergent short time Fourier transforms, must sometimes be used. Series expansions for the estimated instantaneous frequency and local bandwidth are derived in terms of the derivatives pf the phase. The theorem of Ville, Mandel and Fink, relating the global bandwidth to the excursions of the instantaneous frequency, is generalized to the short time Fourier transform. The bandwidth and duration of the spectrogram are related to those of the signal and window and a local uncertainty relationship for the spectrogram is derived. Also, the concept of local duration for a particular frequency is introduced and explicit formulas are given.

Paper Details

Date Published: 14 November 1989
PDF: 25 pages
Proc. SPIE 1152, Advanced Algorithms and Architectures for Signal Processing IV, (14 November 1989); doi: 10.1117/12.962295
Show Author Affiliations
Leon Cohen, Naval Underwater Systems Center (United States)
Chongmoon Lee, University of New Mexico (United States)

Published in SPIE Proceedings Vol. 1152:
Advanced Algorithms and Architectures for Signal Processing IV
Franklin T. Luk, Editor(s)

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