Theoretical and numerical aspects of an SVD-based method for band-limiting finite-extent sequences

4 square-root Schur RLS adaptive filter with two-fold (inputand residual) normalization is presented. The algorithm has severalattractive features suchas a fully systolic structure based on elementaryhyperbolic plane rotations. All internal variables are bounded in theunit interval and fully utilize it in successive stages due to an inherent‘‘ autoscaling ” property of the algorithm. This work is presented in acondensed form because it extends the previous work of this author inthe area of SchurRLS adaptive filtering. I. ARBlTRARLLY WEIGHTED RLS USING SCHUR RECURSIONS Recursive least squares (RLS) adaptive filters based on Schur’srecursions [ l ] have been introduced in [2]-[6] as temporal adaptivefiltering techniques which allow the incorporation of arbitrarilyshaped windows or “forgetting functions” in a true RLS adaptationscheme. In its unnormdized form, a SchurRLS adaptive filtersolves, at each time step, the following weighted fonvard/backwardprediction error filtering problem in a true least squares sense: e,( t ) = ~ l / ~ z ( t )w~/’x,(~ l)a,,,(t), r , ( t ) =W’/2z(t m) W’”X,(t)b,(t)(la)