Optimal estimation of time-frequency representations from corrupted observations

Statistical time-frequency analysis is potentially very useful for estimating the parameters of nonstationary signals from measurements corrupted by nonstationary noise or interference which is a common situation in many signal processing applications. However, most existing time-frequency estimation techniques are ad hoc and invoke the quasi-stationarity assumption, which severely limits their scope. We overcome these limitations by deriving a statistically optimal kernel, within Cohen's class of time-frequency representations (TFRs), for estimating a particular TFR of a realization of a random signal from a correlated observation. Both time-frequency invariant and time-frequency varying kernels are derived, and it is shown that optimal estimation may require smoothing filters very different from those based on a quasi-stationarity assumption. Examples illustrate the impressive performance of the proposed scheme. In particular, the ability of the optimal kernel to suppress interference is quite remarkable, thus making the proposed framework potentially useful for interference suppression via time-frequency filtering.