Joint Representations in Quantum Mechanics and Signal Processing Theory: Why a Probability Function of Time and Frequency is Disallowed

摘要

A discussion is presented which attempts to clarify several misconceptions regarding the nature of distribution functions constructed as simultaneous functions of time and frequency. The problems associated with trying to interpret such densities as probability distributions are pointed out and the close correspondence between signal processing theory and quantum mechanics is exploited in order to address the problems raised. On the basis of the arguments presented, a preferred joint distribution is constructed, its properties outlined and its relevance to the representation of complex time-varying signals is discussed.