CRITICAL REVIEW OF THE FUNDAMENTAL IDEAS OF JOINT TIME-FREQUENCY DISTRIBUTIONS.

Abstract

The author reviews the basic ideas of joint time-frequency distributions and examines the concepts of instantaneous frequency, analytic signal, marginal distributions, expectation values, uncertainty principle, and other fundamental concepts that have been associated with the development of joint distributions. It is argued that many of these ideas have been improperly utilized, and it is concluded that we are far from a conceptual and practical understanding of what a joint time-frequency distribution is or should be, or of having a suitable candidate which meets expectations.