基于改进最小二乘法的滤波器设计
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摘要
为了克服最小二乘法设计的滤波器阻带衰减较小的缺陷,提出一种新的改进最小二乘法设计数字低通滤波器的方法,大幅改善了滤波器的阻带衰减。用MATLAB仿真了三种低通滤波器的改进最小二乘法、最小二乘法的设计方法并将设计滤波器的幅频特性和用凯塞窗设计的同阶滤波器的幅频特性做对比。仿真结果表明,最小二乘法和凯塞窗设计的滤波器的幅频特性的阻带最大增益近似相等。但是改进的最小二乘法设计的滤波器的幅频特性的阻带增益却大幅低于最小二乘法和凯塞窗设计的滤波器。
In order to overcome the drawback of the weak performance in stop band of the filter designed by the least square method,a novel digital low pass filter design method of ameliorated least square method is presented.MATLAB is used to simulate the new method and the least square method for three low pass filters.The amplitude frequency characteristics of designed filters are compared with the counterpart of the same order filter designed by Kaiser window.The results of the simulations show while the least square designed filter most gain in stop band is approximately equal to that of Kaiser window designed filter,ameliorated least square approach's gain in stop band is far lower than other two approaches'.
In order to overcome the drawback of the weak performance in stop band of the filter designed by the least square method,a novel digital low pass filter design method of ameliorated least square method is presented.MATLAB is used to simulate the new method and the least square method for three low pass filters.The amplitude frequency characteristics of designed filters are compared with the counterpart of the same order filter designed by Kaiser window.The results of the simulations show while the least square designed filter most gain in stop band is approximately equal to that of Kaiser window designed filter,ameliorated least square approach's gain in stop band is far lower than other two approaches'.
引文
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[5] TOLEDOPEREZ D C,MARTINEZPRADO M A,RODRIGUEZRESENDIZ J,et al.IIR digital filter design implemented on FPGA for myoelectric signals[C/OL]//Proceedings of 2017 XIII International Engineering Congress (CONIIN).New York:IEEE,2017:1-7.
[6] ZHAO C,ZHANG Y Z.Digital filter design and performance analysis of dynamic temperature signal denoise based on FPGA[C/OL]//Procedings of 10th International Conference on Sensing Technology (ICST).New York:IEEE,2016:1-7.
[7] WANG S,MARUYAMA T.An implementation method of the box filter on FPGA[C/OL]// Procedings of 26th International Conference on Field Programmable Logic and Applications (FPL).New York:IEEE,2016:1-8.
[8] VASKELAINEN L I.Iterative least-squares synthesis methods for conformal array antennas with optimized polarization and frequency properties[J/OL]IEEE Transaction on Antennas and Propagation,1997,45(7):1179-1185.
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[11] LI Y,ZOU L,TAKAHASHI K,et al.High resolution velocity analysis method using the e1 norm regularized least squares method for pavement inspection[J/OL]IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2018,11(03):1005-1015.
[12] YOSHIKAWA G,MATSUZAWA S,HIRATA K,et al.Meshless method based on weighted least square method for electrohydro dynamic problems[J/OL]IEEE Transactions on Magnetics,2015,51(03):61-66.
[13] ZHANG L,LI K,BAI E W,et al.Two stage orthogonal least squares methods for neural network construction[J/OL]IEEE Transactions on Neural Networks and Learning Systems,2015,26(08):1608-1621.
[14] WANG Wei,DAVID C,JODIE A,et al.Assessment of gait characteristics in total knee arthroplasty patients using a hierarchical partial least squares method[J/OL]IEEE Journal of Biomedical and Health Informatics,2018,22(01):205-214.
[15] LONG TENG FEI,JIAO WEI LI,HE GUO JIN.RPC estimation via e1-norm-regularized least squares (L1LS)[J/OL]IEEE Transactions on Geoscience and Remote Sensing,2015,53(08):4554-4567.
[16] Ndoye M,Anderson J M M,Greene D J.An MM-based algorithm for e1-norm-regularized least-squares estimation with an application to ground penetrating radar image reconstruction[J]IEEE Transactions on Image Processing,2016,25(5):2206-2221.
[17] Han Yubing,Wan Chuan.Scalable alternating projection and proximal splitting for array pattern synthesis[J/OL]International Journal of Antennas and Propagation,2015,(10):1-13.
[18] Han Y,Wan C,Sheng W,et al.Array synthesis using weighted alternating projection and proximal splitting[J/OL]IEEE Antennas Wireless Propagation Letter,2015,14:1006-1009.