Nonstationary Blind Source Separation Using Slepian Spectral Estimator

Abstract: Introduced by Priestley, evolutionary spectral theory generalizes the definition of spectrum for nonstationary signals while avoiding some of the shortcomings of bilinear time-frequency distributions. There have been different approaches to estimate Priesley’s evolutionary spectrum such as evolutionary periodogram. In this paper, we present an estimator of evolutionary spectrum for blind separation of nonstationary signals. Our estimator uses a transform based on discrete prolate spheroidal sequences. Also known as Slepian sequences, DPSS are defined to be sequences with maximum spectral concentration for a given duration and bandwidth. Using the connection between discrete evolutionary transform and evolutionary periodogram, we derive the estimator for the evolutionary spectrum and demonstrate its performance for blind source separation of time-varying autoregressive moving average signals