The discrete-time phase derivative as a definition of discrete instantaneous frequency and its relation to discrete time-frequency distributions

摘要

We compare two definitions of the instantaneous frequency of a discrete signal: the two-point symmetric phase difference and the discrete-time phase derivative. The phase derivative definition avoids the pitfalls associated with the two-point definition and is equal to the first moment w.r.t. frequency of a properly defined, alias-free time-frequency distribution of the signal, which is consistent with the continuous-time case.