Abstract
Evolutionary optimization algorithms have been recently applied to optimal digital IIR filter design. In this paper, we apply a Bandwidth Adaptive Harmony Search (BAHS) algorithm to the design of 1-dimensional IIR filters. Harmony Search is an evolutionary algorithm, which emulates the improvisation process of musicians. We have modified the algorithm by setting the bandwidth equal to the standard deviation of the vectors in the harmony memory, and by introducing a penalty function to ensure IIR filter stability. The proposed variant has been applied to the design of low-pass, high-pass, band pass and band stop filters, by minimizing the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> norm approximation errors and the maximum pass band and stop band ripples. The algorithm has been compared with the TIA approach. The harmony search variant has been found to outperform the TIA approach in designing IIR filters having near-desired frequency responses.
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