College of Information Science and Technology, Donghua University, Shanghai, China.
PLoS One. 2012;7(7):e40549. doi: 10.1371/journal.pone.0040549. Epub 2012 Jul 11.
Design of a digital infinite-impulse-response (IIR) filter is the process of synthesizing and implementing a recursive filter network so that a set of prescribed excitations results a set of desired responses. However, the error surface of IIR filters is usually non-linear and multi-modal. In order to find the global minimum indeed, an improved differential evolution (DE) is proposed for digital IIR filter design in this paper. The suggested algorithm is a kind of DE variants with a controllable probabilistic (CPDE) population size. It considers the convergence speed and the computational cost simultaneously by nonperiodic partial increasing or declining individuals according to fitness diversities. In addition, we discuss as well some important aspects for IIR filter design, such as the cost function value, the influence of (noise) perturbations, the convergence rate and successful percentage, the parameter measurement, etc. As to the simulation result, it shows that the presented algorithm is viable and comparable. Compared with six existing State-of-the-Art algorithms-based digital IIR filter design methods obtained by numerical experiments, CPDE is relatively more promising and competitive.
数字无限脉冲响应 (IIR) 滤波器的设计过程是合成和实现递归滤波器网络，以使一组规定的激励产生一组期望的响应。然而，IIR 滤波器的误差曲面通常是非线性和多模态的。为了真正找到全局最小值，本文提出了一种改进的差分进化 (DE) 算法，用于数字 IIR 滤波器设计。所提出的算法是一种具有可控概率 (CPDE) 种群大小的 DE 变体。它根据适应度多样性，通过非周期性的部分增加或减少个体，同时考虑收敛速度和计算成本。此外，我们还讨论了一些 IIR 滤波器设计的重要方面，如代价函数值、（噪声）扰动的影响、收敛速度和成功率、参数测量等。从仿真结果来看，该算法是可行且可比较的。与数值实验获得的六种现有的基于最先进算法的数字 IIR 滤波器设计方法相比，CPDE 更有前途和竞争力。
