Optimal kernels for Wigner-Ville spectral estimation

Current theories of a time-varying spectrum of a nonstationary process all involve, either by definition or by implementation, an assumption that the signal statistics vary slowly over time. This restrictive quasi-stationarity assumption limits the use of existing estimation techniques to a small class of nonstationary processes. We overcome this limitation by deriving a statistically optimal kernel, within Cohen's class of time-frequency representations, for estimating the Wigner-Ville Spectrum of a nonstationary process. Both time-frequency invariant and time-frequency varying kernels are derived. It is shown that, in the presence of any noise, optimal performance requires a nontrivial kernel, and that optimal estimation may require smoothing filters very different from those based on a quasi-stationarity assumption. An example illustrates that the optimal estimators can potentially yield tremendous improvements in performance over existing methods.