14 November 1989 Local Bandwidth And Optimal Windows For The Short Time Fourier Transform
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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.
© (1989) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Leon Cohen, Leon Cohen, Chongmoon Lee, Chongmoon Lee, } "Local Bandwidth And Optimal Windows For The Short Time Fourier Transform", Proc. SPIE 1152, Advanced Algorithms and Architectures for Signal Processing IV, (14 November 1989); doi: 10.1117/12.962295; https://doi.org/10.1117/12.962295
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