Abstract: The infinite impulse response digital notch filters are applied to eliminate or suppress one or some specific frequency components in digital signal. On the basis of the essential two order notch filter, pole-zero doublets are added to design a new single notch structure. The pole angles of the two poles and the new added zero are both designed to be equal to the pole angle of the original zero, the polar radius of the new added pole is designed to be equal to the pole radius of the original pole. Furtherly, transition-band gain can be increased by adjusting the polar radius of the new added zero, which can narrow the transition zone and improve the performance of notch filter. A novel design approach of digital multiple notch filters is proposed. By cascading improved single notch filter, optimizing the polar radius of the new added zero based on Kinetic-Molecular Theory based Optimization Algorithm（KMTOA）, this method can realize the optimized design of notch filters with stable characteristics and accelerate the calculation speed. The practicability and robustness of the presented approach are validated by a series of simulation experiments.

Key words: notch filter, kinetic-molecular theory optimization algorithm, pole and zero displacement

摘要： 数字无限脉冲响应陷波滤波器的作用是抑制或滤除数字信号中一些特定的频率分量。在基本的二阶陷波滤波器的基础上，通过增加零极点对，设计一种新的单频陷波滤波器，设置两个极点和新增加零点的极角等于原零点的极角，新增加极点的极径等于原极点极径，以此来弥补其过渡带；调整新增加零点的极径，增大过渡带增益，使其具有更窄的过渡带，陷波效果更好。提出一种数字多频陷波器的设计方法，通过级联改进的单频陷波器，用分子动理论优化算法优化新增加零点的极径，实现具有稳定特性的陷波系统并且加快计算速度。经过一系列仿真实验，验证了所提方法的鲁棒性和实用性。

关键词: 陷波滤波器, 分子动理论优化算法, 零极点配置