基于最小二乘法的LS-FIR滤波器

doi:10.16088/j.issn.1001-6600.2020072503

摘要/Abstract

摘要： 本文提出一种基于最小二乘法的LS-FIR滤波器。根据色散补偿滤波器与有限长单位冲激响应的频域函数之间的关系构造线性方程组,线性方程组中独立方程的个数大于未知量个数,所以此方程组无解。但在最小范数意义下,能够找到一组解使得估计误差模的平方和最小,得到的解是最小二乘解。用所得到的最小二乘解作为滤波器的抽头权值,即是所要设计的滤波器。滤波器仿真结果表明:不同调制格式(QPSK、16QAM、64QAM)和信噪比(1~20)条件下,当全频带且滤波器的抽头数为315时,均方误差稳定于2.610 9×10^-6;当窄频带滤波器的抽头数为197时,均方误差稳定于2.556 6×10^-6;与FIR和Hm-FIR滤波器对比,LS-FIR滤波器算法具有较高的稳定度、较好的逼近效果,且滤波效果更佳。

关键词: LS-FIR滤波器, 最小范数, 估计误差, 最小二乘解, 抽头权值

Abstract: LS-FIR filter based on least square method is proposed in this paper. According to the relationship between dispersion compensation filter and frequency domain function of the finite length unit impulse response, the linear equations are constructed. Because the number of independent equations is larger than unknowns in the linear equations, the equations have no solution. However, in the sense of minimum norm, a set of solutions is found to minimize the sum of squares estimated error modes. These are the least square solutions, which are used as the tap weight of the filter, and then the filter that needs to be designed is obtained. The simulation results of filter show that under different modulation formats (QPSK, 16QAM, 64QAM) and different signal-to-noise ratios (1~20), in the whole frequency band, when the number of taps is 315, the mean square error reaches 2.610 9×10^-6; In the narrow band, when the number of taps is 197, the mean square error reaches 2.556 6×10^-6; Compared with filters of FIR and Hm-FIR, the algorithm of LS-FIR has higher stability, better approximation effect, and better filtering effect.

Key words: LS-FIR filter, minimum norm, estimation error, least square solution, tap weight

中图分类号:

TN713

武康康, 朱旭飞, 陆叶, 周鹏, 董翠, 戴沁璇, 周闰昌. 基于最小二乘法的LS-FIR滤波器[J]. 广西师范大学学报（自然科学版）, 2021, 39(5): 89-99.

WU Kangkang, ZHU Xufei, LU Ye, ZHOU Peng, DONG Cui, DAI Qinxuan, ZHOU Runchang. LS-FIR Filter Based on Least Square Method[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(5): 89-99.

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