Generalized Levinson algorithms and Ladder filters for nonstationary signal processing

The Levinson algorithm, implemented via a ladder filter, has been widely used in seismic signal processing and more recently in speech analysis. This algorithm was originally developed (in 1947) for prediction of stationary stochastic processes. It has been adapted to applications where only a single sample function (time-series) is available by the use of appropriate "window functions" to "simulate stationarity". Such windowing is often somewhat artificial and can introduce undesirable artefacts in situations where only a limited amount of data is available. However, more realistic "windowing" will destroy the analogy to the stationary stochastic process case and thus apparently prohibit use of the Levinson-ladder- filter implementations. In this talk, we shall first show how by using a concept of how close a given process is to being stationary, we can develop generalized Levinson algorithms and generalized ladder filters applicable to any stochastic process, stationary or not. The complexity of the algorithm and the filter is proportional to the distance from stationarity of the given process. We shall then show that this structure can include analyses of several windowing strategies for applications where only a single observed record is available, thus including results obtained earlier for such problems by Morf, Vieira and Lee. The present results are based on work with D. Lee and H. Lev-Ari.