A modular prewindowing framework for covariance FTF RLS algorithms

In a companion paper, a fast transversal filter (FTF) algorithm was derived for solving multichannel multiexperiment recursive least-squares (RLS) problems arising in adaptive FIR filtering. By introducing sequential processing of the different channels and experiments, the multichannel multiexperiment algorithm was decomposed into a set of intertwined single-channel single-experiment algorithms, resulting in a modular algorithm structure. The algorithm was derived under the prewindowing assumption. However, using an embedding into multichannel and multiexperiment problems, we show how the conventional FTF algorithms for the growing-window and sliding-window covariance cases follow naturally from the modular prewindowed algorithm. Furthermore, taking the sequential processing one step of granularity further, we derive modular multichannel FTF algorithms for these covariance cases also.