Uncertainty, information, and time-frequency distributions

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Abstract
The well-known uncertain principle is often invoked in signal processing. It is also often considered to have the same implications in signal analysis as does the uncertainty principle in quantum mechanics. The uncertainty principle is often incorrectly interpreted to mean that one cannot locate the time-frequency coordinates of a signal with arbitrarily good precision, since, in quantum mechanics, one cannot determine the position and momentum of a particle with arbitrarily good precision. Renyi information of the third order is used to provide an information measure on time-frequency distributions. The results suggest that even though this new measure tracks time-bandwidth results for two Gabor log-ons separated in time and/or frequency, the information measure is more general and provides a quantitative assessment of the number of resolvable components in a time frequency representation. As such, the information measure may be useful as a tool in the design and evaluation of time-frequency distributions.

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