Decimation ratio in subband adaptive identification of a time-varying AR model

Abstract

This paper presents some conditions to determine decimation ratio in subband adaptive identification of a time-varying system. It has been reported in some experiments that a large decimation ratio is not suitable for subband identification of a time-varying system. However, theoretical conditions for a maximally decimated ratio in a time-varying system have not to date been reported. A short-time invariant model is the starting point for this research. The relation between a forgetting factor used in the recursive weighted least-squares (RWLS) algorithm and a time variation of the time-varying system are derived. Then, new forgetting factors are derived for the multirate processing case. Using a convergence property provided by these forgetting factors, theoretical conditions are obtained having parameters estimated from decimated signals that are as accurate as those from all observed signals. The propriety of these conditions is demonstrated using simulations.