Time-frequency signal analysis and instantaneous frequency estimation: methodology, relationships and implementations

A procedure is described for the time-frequency analysis of signals, based on time-frequency distributions (TFDs) and instantaneous frequency (IF) estimation. First, a suitable TFD is used to determine the number of signal components. Then, if the signal is monocomponent, the IF law can be estimated directly. For multicomponent signals, two-dimensional windowing in the time-frequency domain (a form of time-varying filtering) is used to isolate each component; IF estimation is then applied to the individual components. The periodic first moment of a TFD is used to estimate the IF. A suitable definition and of the periodic first moment is proposed, and the relationship of these estimators to others based on the central finite difference of the phase of the analytic signal is given. A TFD such as the Wigner-Ville distribution can be used to represent both IF and amplitude variations in the individual signal components at each stage of the analysis