RLS algorithms for adaptive AR spectrum analysis based on multi-band decomposition of the linear prediction error

A structure for adaptive AR spectral estimation based on multi-band decomposition of the linear prediction error is analyzed and two RLS algorithms to solve the related adaptive filtering problem are derived. The presented structure gives rise to spectral estimates that represent the true underlying spectrum with better fidelity than conventional LS methods by allowing an arbitrary trade-off between variance of spectral estimates and tracking ability of the estimator along the frequency domain. The linear prediction error is decomposed through a power complementary filter bank and components of each band are analyzed by different window lengths, allowing long windows to track slowly varying signals and short windows to observe fastly varying components. The correlation matrix of the input signal is shown to satisfy both time-update and order-update properties for rectangular windowing functions, and an RLS algorithm based on each property is presented. Also, simulations comparing the performance of conventional and the proposed multi-band LS methods are depicted and discussed.