Frequency weighted optimal order reduction of digital filters

This paper focuses on the computation of an l(2) optimal reduced order filt er for a given stable discrete higher order filter in the presence of input and output frequency weightings. We first parameterize a set of stable red uced order filters through an orthogonal projection. We then propose two gr adient based algorithms, namely the continuous and iterative algorithms, fo r computing an optimal reduced order filter. The algorithms are shown to po ssess nice properties including convergence. Examples are given to demonstr ate the superior performance of the algorithms as compared with the convent ional frequency weighted balanced truncation method. (C) 1999 Elsevier Scie nce B.V. All rights reserved.