Standard deviation of instantaneous frequency

Explicit expressions are derived for the standard deviation of instantaneous frequency (local bandwidth) at a particular time using the short-time Fourier transform and the general class of bilinear distributions. Examples are given. Application to the characterization and description of a multicomponent signal is discussed. The theorem of Fink (1966) and Mandel (1974), which states that the bandwidth of a signal is always greater than the global deviation of the derivative of the phase from the average frequency, is generalized for the short-time Fourier transform. The difference in the two standard deviations is found to be precisely the average of the local bandwidth as calculated with the bilinear distributions.<
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