Abstract: Focused on the issue that the traditional multiplierless Infinite Impulse Response (ⅡR) digital filters have fixed structure and poor performance, a random structure based design method for multiplierless ⅡR digital filters was proposed. Stable 2-order subsystems with shifters were directly used to design the multiplierless filter structure. Firstly, a set of encoding structures of the multiplierless digital filter were created randomly. Then, Differential Evolution with a Successful-Parent-Selecting Framework (SPS-DE) was used to optimize the multiplierless filter structure. The proposed method realized diversified structure design, and SPS-DE effectively balanced exploration and exploitation due to adopting a Successful-Parent-Selecting framework, which achieved good results in the optimization of the multiplierless filter structure. Compared with state-of-the-art design methods, the passband ripple of the multiplierless ⅡR filter designed in this paper is reduced by 43% and the stopband maximum attenuation is decreased by 40.4%. Simulation results show that the multiplierless ⅡR filter designed by the proposed method meets structural requirements and has good performance.

Key words: multiplierless design, digital filter, random structure, Differential Evolution (DE), subsystem

摘要： 针对现有的无乘法无限冲激响应（ⅡR）数字滤波器设计方法存在结构固定、滤波器性能不佳的问题，提出了一种基于随机结构的无乘法ⅡR数字滤波器设计方法。该方法使用加入移位器的稳定二阶子系统直接进行无乘法滤波器的结构设计。首先，无乘法数字滤波器的结构编码被随机创建；然后，利用一种加入成功父代选择框架的差分进化算法（SPS-DE）对生成的无乘法滤波器结构进行优化。该方法实现了无乘法滤波器结构的多样化设计，而且SPS-DE算法因采用成功父代选择框架机制，具有很好的种群开发与勘探能力，在无乘法滤波器的结构优化上取得了很好的效果。与现有的无乘法ⅡR数字滤波器设计方法相比，该方法设计的无乘法ⅡR滤波器通带波纹减小了43%，阻带最大衰减下降了40.4%。实验结果表明所提方法设计的无乘法ⅡR滤波器满足结构要求并且拥有优良的性能。

关键词: 无乘法设计, 数字滤波器, 随机结构, 差分进化, 子系统