DELTA LEVINSON AND SCHUR-TYPE RLS ALGORITHMS FOR ADAPTIVE SIGNAL-PROCESSING

In this paper, we develop delta operator based Levinson and Schur type on-tine RLS algorithms. Such algorithms have the potential of improve d numerical behavior for ill-conditioned input data. These new algorit hms are obtained by a unified transformation on the existing q operato r based ones. We first show that the conventional lattice structure ca n be naturally derived when the backward delta operator is used. With this operator, Levinson and Schur algorithms for the stationary stocha stic model in q-domain can easily be transformed into the delta domain . Then, same transformation will be applied to the q-domain on-line Le vinson and Schur type RLS algorithms to obtain the delta-domain counte rparts. Their normalized versions as well as a systolic array architec ture implementing the new delta Schur RLS algorithm are proposed. Exte nsion to the equal length multichannel case is also given. Computer si mulations show the expected numerical advantages of the delta-based al gorithms for fast-sampled data in real time, over the q-domain ones un der finite precision implementation.