Discrete-time instantaneous frequency and its computation

Classical results indicate that the means of the Fourier and instantaneous frequencies are exactly equal and the weighted variance of the Fourier frequency is greater than or equal to that of the instantaneous frequency. These results are investigated for the discrete case in which the signal and its spectrum are both assumed to be periodic. Specifically, the cases in which the discrete-time instantaneous frequency is defined as the forward, backward, and central differences are discussed. A simple algorithm for computing the discrete-time instantaneous frequency is presented whereby descriptors for the characterization of the signal are constructed. The application of this algorithm is discussed through examples