天牛须搜索算法实现小波滤波器直接频域逼近  

Direct frequency-domain approximation of wavelet filter using beetle antennae search algorithm

作　　者：童耀南 曹鹂晨 赵舜楠 Tong Yaonan;Cao Lichen;Zhao Shunnan(School of Science and Engineering,Hunan Institute of Science and Technology,Yueyang 414006,China)

机构地区：[1]湖南理工学院信息科学与工程学院,岳阳414006

出　　处：《电子测量与仪器学报》2021年第3期56-63,共8页Journal of Electronic Measurement and Instrumentation

基　　金：湖南省科技计划项目(2017SK2164,2019TP1014);湖南省教育厅优秀青年科研项目(16B114);湖南理工学院科研创新团队项目(2019-TD-10);湖南省普通高校教学改革研究项目(湘教通[2019]291号)资助。

摘　　要：针对频域法构造小波滤波器方法较少、稳定性无法保证、逼近精度不高等问题,基于天牛须搜索算法提出了一种小波滤波器直接频域逼近方法。首先根据小波滤波器电路的基本要求设计逼近有理式,然后加入电路实现所需的稳定性、正实性和初值为零的约束条件,建立小波滤波器逼近的频域优化模型。再以高斯小波和Marr小波为例,使用天牛须搜索算法求解频域逼近的数学模型得到滤波器有理式参数。在时域和频域上分别将该方法和其他频域方法进行对比,仿真和计算结果表明在相同条件下,频域逼近法具有更优的效果,五阶高斯小波和七阶Marr小波的逼近均方误差仅为3.446 8×10^(-4)和7.346 2×10^(-4)。In this paper, a direct frequency domain approximation method of wavelet filter was proposed based on the beetle antennae search algorithm(BAS), aiming at the problems of less methods to construct wavelet filter in frequency domain, no guarantee of filter stability and low approximation accuracy. Firstly, the approximation rational formula was designed according to the basic requirements of the wavelet filter circuit. Then, based on the rational formula, a frequency domain optimization model of wavelet filter approximation was established considering the constraint conditions of filter circuit stability, positive reality and zero initial value. Finally, Gaussian and Marr wavelet were taken as examples, in which the BAS algorithm was used to solve the optimization mathematical model to obtain rational parameters. The approximation results are compared with other frequency-domain methods in time and frequency domain. The simulation and calculation results show that the proposed approach has a good approximation effect under the same conditions. The mean square errors(MSE) of the fifth-order Gaussian wavelet and seventh-order Marr wavelet are only 3.446 8×10^(-4) and 7.346 2×10^(-4) respectively.

关 键 词：小波变换 小波滤波器 滤波器逼近 天牛须搜索算法 

分 类 号：TN929.52[电子电信—通信与信息系统]