求解椭圆球面波函数以及改进措施研究
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摘要
目的:优化设计椭圆球面波函数的求解算法,提供全新的改进措施。方法:通过重构椭圆球面波函数的求解方法,以求解精度为出发点,设计收敛速度较快的BPSWF函数重构求解算法。依据采样理论模型,通过信号重构与带通滤波选择性基础,优化椭圆球面波函数重构求解流程。在分析了重构求解算法的误区之后,总结其改进措施。在设计频域结构的基础上优化PSWF函数的收敛速度,以便为求解椭圆球面波函数提供可行性较高的理论参考。结果:全新的椭圆球面波函数求解算法较sinc基函数求解方法精准度更高,能够提升PSWF函数正交性,并促进其能量聚集性。结论:BPSWF函数重构求解算法的收敛性能较强,其仿真及理论分析结果能够证明其求解精准度,可以作为全新的改进措施。
Objectives: to optimize the algorithm of designing elliptical spherical wave function,and to provide new improvement measures. Methods: by reconstructing the method of solving the elliptic spherical wave function and solving the problem,a BPSWF function reconstruction algorithm with fast convergence speed is designed. Based on the sampling theory model,the reconstruction of elliptic spherical wave function is optimized by signal reconstruction and selective basis of bandpass filter. After analyzing the error of the reconstruction algorithm,the improvement measures are summarized. The convergence rate of the PSWF function is optimized on the basis of the design frequency domain structure so as to provide a theoretical reference for solving the elliptic spherical wave function. Results: the new elliptic spherical wave function algorithm is more accurate than sinc based method,which can improve the orthogonality of PSWF function and promote its energy aggregation.Conclusion: BPSWF function reconstruction algorithm has a strong convergence performance,and its simulation and theoretical analysis can prove its accuracy,which can be used as a new improvement measure.
Objectives: to optimize the algorithm of designing elliptical spherical wave function,and to provide new improvement measures. Methods: by reconstructing the method of solving the elliptic spherical wave function and solving the problem,a BPSWF function reconstruction algorithm with fast convergence speed is designed. Based on the sampling theory model,the reconstruction of elliptic spherical wave function is optimized by signal reconstruction and selective basis of bandpass filter. After analyzing the error of the reconstruction algorithm,the improvement measures are summarized. The convergence rate of the PSWF function is optimized on the basis of the design frequency domain structure so as to provide a theoretical reference for solving the elliptic spherical wave function. Results: the new elliptic spherical wave function algorithm is more accurate than sinc based method,which can improve the orthogonality of PSWF function and promote its energy aggregation.Conclusion: BPSWF function reconstruction algorithm has a strong convergence performance,and its simulation and theoretical analysis can prove its accuracy,which can be used as a new improvement measure.
引文
[1]刘晓,王红星,刘传辉,张磊.椭圆球面波函数时频能量聚集性研究[J].中国电子科学研究院学报,2015,10(03):237-244.
[2]康家方,王红星,刘传辉,赵志勇,刘锡国.基于IDFT的椭圆球面波函数重构产生方法[J].上海交通大学学报,2014,48(03):357-362.
[3]钟佩琳,王红星,赵志勇,陈昭男.椭圆球面波函数微分系统求解及仿真[J].吉林大学学报(工学版),2013,43(06):1675-1679.
[4]潘耀宗,孙小东,钟佩琳,刘传辉,王红星.一种新的基于椭圆球面波函数的非正弦短波通信的均衡方案[J].电子与信息学报,2012,34(12):2862-2868.
[5]钟佩琳,王红星,赵志勇,刘锡国,刘传辉.基于状态转移矩阵逼近的椭圆球面波函数求解方法[J].电子与信息学报,2012,34(10):2427-2431.
[2]康家方,王红星,刘传辉,赵志勇,刘锡国.基于IDFT的椭圆球面波函数重构产生方法[J].上海交通大学学报,2014,48(03):357-362.
[3]钟佩琳,王红星,赵志勇,陈昭男.椭圆球面波函数微分系统求解及仿真[J].吉林大学学报(工学版),2013,43(06):1675-1679.
[4]潘耀宗,孙小东,钟佩琳,刘传辉,王红星.一种新的基于椭圆球面波函数的非正弦短波通信的均衡方案[J].电子与信息学报,2012,34(12):2862-2868.
[5]钟佩琳,王红星,赵志勇,刘锡国,刘传辉.基于状态转移矩阵逼近的椭圆球面波函数求解方法[J].电子与信息学报,2012,34(10):2427-2431.