New insights into delayless subband adaptive filters

The adaptive filter is an important workhorse of digital signal processing having a vast variety of applications in almost every branch of modern electronics. Today there is an abundance of algorithms with different performance and computational characteristics. In this paper we address the class of delayless subband adaptive filters (SAF). Although this class of adaptive filters have been popular for some time, there are still aspects related to convergence speed and filter bank design for such adaptive filters that are not fully understood nor fully explored. The aim of this paper is to present a first step in closing this knowledge gap by developing explicit and general equation sets, directly related to the Wiener-Hopf equation, that the delayless SAFs attempt to solve. By doing so we provide a firm basis for algorithm analysis and parameter selection that can now be undertaken in much the same way as the analysis of simpler adaptive filtering algorithms.