MULTIBAND DECOMPOSITION OF THE LINEAR PREDICTION ERROR APPLIED TO ADAPTIVE AR SPECTRAL ESTIMATION

A new structure for adaptive AR spectral estimation based on multi-ban d decomposition of the linear prediction error is introduced and the m athematical background for the solution of the related adaptive filter ing problem is derived. The presented structure gives rise to AR spect ral estimates that represent the true underlying spectrum with better fidelity than conventional LS methods by allowing an arbitrary trade-o ff between variance of spectral estimates and tracking ability of the estimator along the frequency spectrum. The linear prediction error is decomposed through a filter bank and components of each band are anal yzed by different window lengths, allowing long windows to track slowl y varying signals and short windows to observe fastly varying componen ts. The correlation matrix of the input signal is shown to satisfy bot h time-update and order-update properties for rectangular windowing fu nctions, and an RLS algorithm based on each property is presented. Ada ptive forward and backward relations are used to derive a mathematical framework that serves as a basis for the design of fast RLS algorithm s. Also, computer experiments comparing the performance of conventiona l and the proposed multi-band methods are depicted and discussed.