PARAMETRIC MODELING OF THE WIGNER HALF-KERNEL AND ITS APPLICATION TO SPECTRAL ESTIMATION

Parametric spectral estimation methods provide high frequency resolution and allow a compact representation. The Wigner-Ville distribution (WVD), on the other hand, presents high frequency concentration and temporal resolution, but produces spectral crossterms and abundant data. WVD autoregressive (AR) modeling combines the advantages of both techniques. Using the analytic signal to compute the WVD kernel cancels negative frequency crossterms and provides a low-order complex predictor, half the size of real AR models. Crossterms and potential kernel symmetry problems are avoided by modeling the Smoothed WVD (SWVD) half-kernel. The developed representation is analyzed and compared to real and analytic AR spectral estimators. It is shown that the SWVD half-kernel AR covariance poles produce precise frequency estimates for monocomponent signals, independent of data length and phase, just like real and analytic AR estimators, but with the advantage of excellent performance in noise. These properties are verified experimentally and extended to multicomponent signals in noise, showing that while the analytic AR estimator performs slightly better than its real counterpart, the SWVD half-kernel results in a frequency estimation error reduction of around two orders of magnitude.