The relationship between instantaneous frequency and time-frequency representations

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The relationship between instantaneous frequency and time-frequency representations

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Title: The relationship between instantaneous frequency and time-frequency representations
Author: Lovell, B.C.; Williamson, R.C.; Boashash, Boualem
Abstract: The relationship between instantaneous frequency estimation based on the derivative of the phase of the analytic signal and the first moment of the general time-frequency representation from Cohen's (1989) class is given in the continuous- and discrete-time domains. Application of the standard linear definition of first moment to discrete-time-frequency representations leads to biased instantaneous frequency estimators with high variance. To correct this problem, it is shown that periodic (circular) definitions of moments must be used to account for the periodization of the frequency variable due to sampling.
Description: This old paper records some relationships between TFDs and IF; for a complete treatment, see the review paper on instantaneous frequency by Boashash in Proceedings of IEEE; 1992. (The most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia., and then continuously updated).
URI: http://hdl.handle.net/10576/10719
Date: 1993-03

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