Journal of Guangxi Normal University(Natural Science Edition) ›› 2021, Vol. 39 ›› Issue (5): 89-99.doi: 10.16088/j.issn.1001-6600.2020072503

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LS-FIR Filter Based on Least Square Method

WU Kangkang, ZHU Xufei, LU Ye*, ZHOU Peng, DONG Cui, DAI Qinxuan, ZHOU Runchang   

  1. College of Electronic Engineering, Guangxi Normal University, Guilin Guangxi 541004, China
  • Received:2020-07-25 Revised:2020-10-15 Online:2021-09-25 Published:2021-10-19

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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

CLC Number: 

  • TN713
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