Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals

Abstract

The concept of instantaneous frequency (IF), its definitions, and the correspondence between time-frequency signal analysis and the various mathematical models formulated for representation of IF are discussed. The extent to which the IF corresponds to the intuitive expectation of reality is also considered. A historical review of the successive attempts to define the IF is presented. The relationships between the IF and the group-delay, analytic signal, and bandwidth-time (BT) product are explored, as well as the relationship with time-frequency distributions. The notions of mono-component and multi-component signals and instantaneous bandwidth are discussed, and its relationship to Time-Frequency distributions clarified. It is shown that these notions are well described in the context of the theory presented.