Analysis and Minimization of l2-Sensitivity for Block-State Realization of IIR Digital Filters

Akimitsu DOI  Takao HINAMOTO  Wu-Sheng LU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A    No.2    pp.447-459
Publication Date: 2018/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.447
Type of Manuscript: PAPER
Category: Digital Signal Processing
block-state realization,  l2-scaling constraints,  l2-sensitivity analysis,  l2-sensitivity minimization,  state-space digital filters,  

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Block-state realization of state-space digital filters offers reduced implementation complexity relative to canonical state-space filters while filter's internal structure remains accessible. In this paper, we present a quantitative analysis on l2 coefficient sensitivity of block-state digital filters. Based on this, we develop two techniques for minimizing average l2-sensitivity subject to l2-scaling constraints. One of the techniques is based on a Lagrange function and some matrix-theoretic techniques. The other solution method converts the problem at hand into an unconstrained optimization problem which is solved by using an efficient quasi-Newton algorithm where the key gradient evaluation is done in closed-form formulas for fast and accurate execution of quasi-Newton iterations. A case study is presented to demonstrate the validity and effectiveness of the proposed techniques.