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Mathematical Problems in Engineering
Volume 2014, Article ID 497471, 9 pages
Research Article

Minimizing Design Costs of an FIR Filter Using a Novel Coefficient Optimization Algorithm

Department of Electronic Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung 824, Taiwan

Received 26 June 2014; Accepted 19 August 2014; Published 11 September 2014

Academic Editor: Teen-Hang Meen

Copyright © 2014 Ming-Chih Chen and Tsung-Ting Chen. 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.


This work presents a novel coefficient optimization algorithm to reduce the area and improve the performance of finite impulse response (FIR) filter designs. Two basic architectures are commonly used in filters—direct and transposed. The coefficients of a filter can be encoded in the fewest possible nonzero bits using canonic signed digit (CSD) expressions. The proposed optimization algorithm can share common subexpressions (CS) and reduce the number of replicate operations that involve the CSD coefficients of filters with a transposed architecture. The effectiveness of the algorithm is confirmed by using filters with the collision detection multiple access (CDMA) standard, the 121-tap high-pass band, and 105- and 325-tap low-pass bands as benchmarks. For example, the proposed algorithm used in the optimization of 105-tap filter has a 30.44% smaller combinational logic area and a 16.69% better throughput/area than those of the best design that has been developed to date. Experimental results reveal that the proposed algorithm outperforms earlier designs.