Segmentation of nonstationary signals

Introduction In practice most signals can be regarded as nonstationary, i.e., as output of a linear but time variant system. Some kinds of signals, e.g., speech signals, to some extent can be interpreted as output of a linear system with abruptly changing parameters. Problems arising in processing signals with such kind of properties are estimation of change points and dealing with the problem of unknown parameters. Statistical approach for the segmentation of such signals is discussed in this paper. Optimal segmentation methods [1] can be applied to segmentation of nonstationary signals. Segmentation of a non-stationary signals consists of assuming piecewise stationarity of the signal and of detecting the instants of change. Usually it is considered that all the data are available in the same time and a global segmentation is performed instead of a sequential procedure. In our investigations we use a similar approach [2]. It is assumed that the signal is described by autoregressive (AR) model. Maximum likelihood (ML) method is used for determination change points of piecewise stationary signal. It is assumed that number of change points is known in advance. Maximization of the likelihood function is based on dynamic programming [3]. Expectation maximization approach [4] is used to deal with the problem of unknown signal parameters. Statement of the problem for known AR model parameters We formulate the problem similar to that in [2]. Let us consider random sequence } ) ( , . . . ), 2 ( ), 1 ( { N x x x x = , which is an output of linear discrete time