Minimum-variance evolutionary spectral estimation of nonstationary signals

A novel unbiased estimator for the time-dependent spectrum of a nonstationary signal is presented. The signal is modeled at a given frequency, as having a time-varying amplitude accurately represented by an orthonormal basis expansion. After a minimum-variance estimate of this time-varying amplitude is computed, and depending on assumptions made on the signal model, different time-varying estimators analogous to the ones used in the stationary case are developed. Presented is the time-varying periodogram estimator. By repeating the process over all frequencies, a power distribution is obtained as a function of time and frequency that is consistent with the evolutionary spectrum. The approach is guaranteed to produce nonnegative spectra without the cross-term behavior of the Wigner distribution, and it does not require windowing of data in the time domain, as the short time Fourier transform does. Examples illustrating the estimator are given