ARMA estimation using the general order two channel fast transversal filter (FTF) algorithm

The general order, multichannel FTF algorithm is a generalization of the multichannel FTF algorithm in which the orders of the input channels can be independently specified. The algorithm is applied to a special case of a two-input-channel, joint process estimator. One of the input channels is defined as the unit-delayed joint process signal; the configuration is an `equation error´ form for least squares (LS) pole-zero ARMA (autoregressive moving-average) system identification. This form is also used in decision-directed equalization and echo cancellation. For this special two-channel case, a computational savings of 2N+1 operations per recursive update is identified, where N is the total number of filter taps. The saving is proven using the concepts of projection onto a vector space. The reduction is available with any of the order-N `fast´ LS algorithms including the fast Kalman (FK) and FAEST algorithms; this had not been recognized for similar application of the FK algorithm to decision-directed equalization. A summary of the modified algorithm is given, with an operations count for each step