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Internal Projections and $L_{2}$ $L_{2}$ Norm for Optimal Digital Filters Model Reduction: A Comparative Study

Amel B. H. Adamou-Mitiche

Electrical Engineering Department, University of Djelfa, B. P. 3047 Ain Chih, Djelfa 17000, Algeria

E-mail Address: amelmitiche@yahoo.fr

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and

Lahcène Mitiche

http://orcid.org/0000-0003-3526-368X

Electrical Engineering Department, University of Djelfa, B. P. 3047 Ain Chih, Djelfa 17000, Algeria

E-mail Address: l_mitiche@yahoo.fr

Corresponding author.

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https://doi.org/10.1142/S0218126619300010Cited by:5 (Source: Crossref)

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 $L_{2}$ $L_{2}$ norm, and the integral-squared error (ISE) allowed to conclude on the efficiency of the best approximation algorithm.

This paper was recommended by Regional Editor Emre Salman.

Keywords:

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