Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 560650, 15 pages
Research Article

CSD-Coded Genetic Algorithm on Robustly Stable Multiplierless IIR Filter Design

Department of Computer Science and Information Engineering, National University of Kaohsiung, No. 700, Kaohsiung University Road, Nanzih District, Kaohsiung 811, Taiwan

Received 6 October 2011; Revised 5 December 2011; Accepted 5 December 2011

Academic Editor: Jyh Horng Chou

Copyright © 2012 Shing-Tai Pan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A Canonic-Signed-Digit-(CSD-) coded genetic algorithm (GA) is proposed to find the optimal design of robustly stable infinite impulse response digital filter (IIR). Under the characteristics of the CSD structure, the circuit of the filter can be simplified and also the calculation speed can be raised to increase the hardware’s efficiency. However, the design of CSD has a big challenge: the CSD structure of the system parameters will be destroyed by an optimal design procedure. To solve this problem, in this research a CSD-coded GA is proposed so that the CSD structure can be maintained. Moreover, the robustly stable IIR filters design problem is included in this paper. The robustness of the IIR filters is achieved by ensuring that all poles of the filters are located inside a disk D(α,r) contained in the unit circle, in which α is the center, r is the radius of the disk, and |α|+r<1. Consequently, in this paper, a new and more efficient D(α,r)-stability criterion will be derived and then embedded in GA for the design of robust IIR filters. It is worthwhile to note that to design an IIR filter simultaneously with CSD-structured parameters and robust stability is difficult and is not well explored so far. An example will be presented to show the efficiency of the proposed strategy for design of IIR filters.