EVOLUTIONARY PERIODOGRAM FOR NONSTATIONARY SIGNALS

In this paper, we present a novel estimator for the time-dependent spectrum of a nonstationary signal. By modeling the signal, at any given frequency, as having a time-varying amplitude accurately represented hy an orthonormal basis expansion, we are able to compute a minimum mean-squared error estimate of this time-varying amplitude. Repeating the process over all frequencies, we obtain a power distribution as a function of time and frequency that is consistent with the Wold-Cramer evolutionary spectrum. Based on the model assumptions, we develop the evolutionary periodogram (EP) for nonstationary signals, an estimator analogous to the periodogram used in the stationary case. We also derive the time-frequency resolution of the new estimator. Our approach is free of some of the drawbacks of the bilinear distributions and of the short-time Fourier transform spectral estimates. It is guaranteed to produce nonnegative spectra without the cross-term behavior of the bilinear distributions, and it does not require windowing of data in the time domain. Examples illustrating the new estimator are given.