The relationship between instantaneous frequency and time-frequency representations

The relationship between instantaneous frequency estimation based on the derivative of the phase of the analytic signal and the first moment of the general time-frequency representation from Cohen's (1989) class is given in the continuous- and discrete-time domains. Application of the standard linear definition of first moment to discrete-time-frequency representations leads to biased instantaneous frequency estimators with high variance. To correct this problem, it is shown that periodic (circular) definitions of moments must be used to account for the periodization of the frequency variable due to sampling.<
>