Time‐Frequency Methods for Non‐stationary Statistical Signal Processing

Time‐frequency (TF) methods can be used to analyze and process non‐stationary random processes in an efficient and intuitive manner. This chapter presents some of the non‐parametric methods in this area. We first discuss two different definitions of a “TF spectrum” for non‐stationary processes. For the important subclass of underspread processes, it is demonstrated that the various TF spectra are effectively equivalent and approximately satisfy several desirable properties. Methods for estimating TF spectra are presented and studied. Finally, we discuss the use of TF spectra for processing non‐stationary random processes of the underspread type. Simple formulations of quasi‐optimum estimators and detectors are proposed, which generalize methods for the stationary case (such as, for instance, Wiener‐type filters) to the case of underspread non‐stationary random processes. These “TF estimators/detectors” have the advantage of allowing an intuitive interpretation and being numerically stable and efficient.