Tracking nonstationarities with a wavelet transform

Abstract

Nonstationary signal parameter estimation/detection is challenging on account of the underlying stationarity assumption in most of the classical techniques. The authors present a framework for a class of nonstationary processes via a multiscale analysis. This framework gives insight into the problem, and new results are obtained on multiscale autoregressive integrated moving average (ARIMA) processes. The possibility of inducing stationarity at different resolution levels of nonstationary processes by an appropriate wavelet transform is shown. This permits use of classical estimation/detection techniques. The approach is extended to wavelet package decompositions.<>