Optimal time-frequency kernels for spectral estimation of locally stationary processes

This paper investigates the mean square error optimal time-frequency kernel for estimation of the Wigner-Ville spectrum of a certain class of nonstationary processes. The class of locally stationary processes have a simplified covariance structure which facilitates analysis. We give a formula for the optimal kernel in the ambiguity domain and conditions that are sufficient for the optimal time-frequency kernel to he a continuous function, decaying at infinity.