DATA-ADAPTIVE EVOLUTIONARY SPECTRAL ESTIMATION

In this paper. we present a novel data-adaptive estimator for the evol utionary spectrum of nonstationary signals. We model the signal at a f requency of interest as a sinusoid with a time-varying amplitude, whic h is accurately represented by an orthonormal basis expansion. We then compute a minimum mean-squared error estimate of this amplitude and u se it to estimate the time-varying spectrum at that frequency, all whi le minimizing the interference from the signal components at other fre quencies. Repeating the process over all frequencies, we obtain a powe r distribution that is consistent with the Wold-Cramer evolutionary sp ectrum and reduces to Capon's method for the stationary case. Our esti mator possesses desirable properties in terms of time-frequency resolu tion and positivity and is robust in the spectral estimation of noisy nonstationary data. We also propose a new estimator for the autocorrel ation of nonstationary signals. This autocorrelation estimate is neede d in the data-adaptive spectral estimation. We illustrate the performa nce of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time-fre quency distribution with exponential kernels.