On instantaneous frequency of multicomponent signals

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Instantaneous frequency (IF) of analytic signals has been extensively studied in the literature. The general perception is that it is meaningful only for narrowband or monocomponent signals. In this paper, new insights into IF's of multicomponent signals are provided; it is argued that an IF's erratic behavior is dictated by the proximity of the signal's complex zeros to the unit circle and not by the band occupancy of the signal's spectrum. A connection between product representation of signals and well-known ideas in linear systems literature are first established. Closed-form expressions for IF's of signals consisting of multiple complex sinewaves are then derived; it is shown that there exists a one-to-one correspondence between signals' Fourier coefficients and their IF's. Using them, IF's of some simple signals are first studied. Next, signals for which IF's tend to be impulsive are addressed. This is followed by discussions on intensity-weighted IF and signals having positive IF's. While IF and log-envelope are known to be time functions that typically have infinite spectral bandwidths, it is pointed out that their filtered versions sufficiently characterize a signal. Finally, issues related to computation of digital IF are addressed. ©[997 ]£££.

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IEEE Transactions on Signal Processing





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