Digital IIR Filter Design Using Differential Evolution Algorithm
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Digital IIR Filter Design Using Differential Evolution Algorithm Nurhan Karaboga Department of Electronic Engineering, Faculty of Engineering, Erciyes University, 38039 Melikgazi, Kayseri, Turkey Email: nurhan [email protected] Received 14 May 2004; Revised 3 December 2004; Recommended for Publication by Ulrich Heute Any digital signal processing algorithm or processor can be reasonably described as a digital filter. The main advantage of an infinite impulse response (IIR) filter is that it can provide a much better performance than the finite impulse response (FIR) filter having the same number of coefficients. However, they might have a multimodal error surface. Differential evolution (DE) algorithm is a new heuristic approach mainly having three advantages; finding the true global minimum of a multimodal search space regardless of the initial parameter values, fast convergence, and using a few control parameters. In this work, DE algorithm has been applied to the design of digital IIR filters and its performance has been compared to that of a genetic algorithm. Keywords and phrases: digital IIR filter, design, evolutionary algorithms, differential evolution, genetic algorithm.
1.
INTRODUCTION
Anything that contains information can be considered as a signal. Therefore, signals arise in almost every field of science and engineering. Two general classes of signals can be identified, namely, continuous-time and discrete-time signals. A discrete-time signal is one that is defined at discrete instants of time. The numerical manipulation of signals and data in discrete-time signals is called digital signal processing (DSP). The extraordinary growth of microelectronics and computing has had a major impact on DSP. Therefore, DSP has already moved from being primarily a specialist research topic to a one with practical applications in many disciplines. Almost any DSP algorithm or processor can reasonably be described as a filter. Filtering is a process by which the frequency spectrum of a signal can be modified, reshaped, or manipulated according to some desired specifications. Digital filters can be broadly classified into two groups: recursive and nonrecursive. The response of nonrecursive (FIR) filters is dependent only on present and previous values of the input signal. However, the response of recursive (IIR) filters depends not only on the input data but also on one or more previous output values. The main advantage of an IIR filter is that it can provide a much better performance than the FIR filter having the same number of coefficients. Design of a digital filter is the process of synthesizing and implementing a filter network so that a set of prescribed excitations results in a set of desired responses [1, 2]. However, there are some problems with the design of IIR filters [3, 4, 5]. The fundamental problem is that they might have a multimodal error surface. A further problem is the possibility of the filter
becoming unstable during the adaptation process. This second problem can be easily handled by limiting the par
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