Internal Projections and L2 Norm for Optimal Digital Filters Model Reduction: A Comparative Study

Abstract

A comparative study based on combined special projections and important frequency-weighted model order reduction (MOR) algorithms to compute optimal approximants for full order digital filters is achieved. It is about the gradient flow (GF) without frequency weighted, the frequency-weighted balanced truncation (FWBT), the GF with frequency weighted (FWGF) and the frequency cross-gramian (CGF) techniques, where special projections of frequency-weighted approximation are used. The obtained low order approximants are expected to follow the original digital filter behavior. With the aim of highlighting the best technique from their implementation, a comparative study is achieved when comparing with a robust MOR technique. Furthermore, two robust performance tools are used namely, the [Formula: see text] norm, and the integral-squared error (ISE) allowed to conclude on the efficiency of the best approximation algorithm.