Using singular value decomposition for generalized linear autoregression of signals

Abstract

Autoregressive models (AR) are fundamental for analysis, representation, and prediction of signals. AR modelling uses the premise that past signal values infuence current ones. This infuence is causal and is modelled as a linear superposition, because a weighted addition of past values is used. The calculation of the required linear superposition parameters or weights can be done by the classical Yule-Walker approach or by least squares procedures. Here we show how to use singular value decomposition (SVD) for generalized linear autoregression (GLAR), i.e. using SVD to compute the weights of a linear combination of functions of given signal values and to check or optimize the GLAR model. The GLAR approach opens the possibility to take directly into account non-linear infuences from past to current signal values. The potential of this approach for analysis and representation is presented and demonstrated for simulated signals, i.e. pure and noisy sequences of non-linear recursions, and biomedical signals.