吉林大学学报(工学版) ›› 2013, Vol. 43 ›› Issue (06): 1675-1679.doi: 10.7964/jdxbgxb201306038

• 论文 • 上一篇    下一篇

椭圆球面波函数微分系统求解及仿真

钟佩琳, 王红星, 赵志勇, 陈昭男   

  1. 海军航空工程学院 电子信息工程系, 山东 烟台 264001
  • 收稿日期:2012-05-03 出版日期:2013-11-01 发布日期:2013-11-01
  • 作者简介:钟佩琳(1984-),女,博士研究生.研究方向:非正弦波通信理论及应用.E-mail:hellopeilin@126.com
  • 基金资助:

    国家自然科学基金项目(60772056);山东省"泰山学者"建设工程项目.

Resolution and simulation of differential system for prolate spherical wave functions

ZHONG Pei-lin, WANG Hong-xing, ZHAO Zhi-yong, CHEN Zhao-nan   

  1. Department of Electronic and Information Engineering, Naval Aeronautical and Astronautical University, Yantai 264001, China
  • Received:2012-05-03 Online:2013-11-01 Published:2013-11-01

RICH HTML

0   

PDF (PC)

331

摘要：

针对已有椭圆球面波函数求解算法计算量大、硬件实现复杂度高及产生困难的问题,从微分系统状态方程求解的角度,提出了一种计算精度高、时间及空间复杂度低的椭圆球面波函数求解算法,并在此基础上构建了易于硬件实现的产生椭圆球面波函数的系统仿真模型。将本文算法与Parr B提出的基于特征值分解的数值算法进行仿真比较,结果显示:两种算法求得的椭圆球面波函数具有一致的波形和频谱,而本文算法的复杂度要低于Parr B算法。同时,系统模型的仿真结果显示:系统输出波形与理论求解结果一致,验证了所构建系统模型的正确性和可行性。

关键词: 通信技术, 椭圆球面波函数, 微分系统求解, 系统模型

Abstract:

The existing algorithms for Prolate Spherical Wave Functions (PSWFs) demand large amount of computation and high complexity in hardware implementation. To overcome the above weaknesses, a new algorithm with high accuracy and low complexity in both time and space domains was proposed in terms of computing the state equation of differential system. Then a simulation model of the system is constructed to generate PSWFs. This simulation model is easy for hardware implementation. The proposed algorithm was compared with the one proposed by Parr B. Results show that, when both algorithms obtain identical waveform and spectrum, the one proposed in this paper has much lower complexity. Simulation results of the system model show that the output waveforms are the same as the theoretical solutions, which verify the correctness and feasibility of the constructed system model.

Key words: communication technology, prolate spheroidal wave functions, differential system resolving, system model

中图分类号: 

  • TN911.7

[1] Slepian D, Pollak H O. Prolate spheroidal wave functions, Fourier analysis, and uncertainty-I[J]. Bell System Tech Journal, 1961, 40(1): 43-63.

[2] Moore I C, Cada M. Prolate spheroidal wave functions, an introduction to the Slepian series and its properties[C]//Appl Comput Harmon Anal. San Diego:Academic Press, 2004: 208-230.

[3] Zhao Hui, Ran Qi-wen, Ma Jing, et al. Generalized prolate spheroidal wave functions associated with linear canonical transform[J]. IEEE Trans on Signal Processing, 2010, 58(6): 3032-3041.

[4] Wei Li-ying, Rodney A K, Tharaka A L. An optimal basis of band-limited functions for signal analysis and design[J]. IEEE Trans on Signal Processing, 2010, 58(11): 5744-5755.

[5] Dullaert W, Reichardt L, Rogier H. Improved detection scheme for chipless RFIDs using prolate spheroidal wave function-based noise filtering[J]. IEEE Antennas and Wireless Propagation Letters, 2011, 10: 472-475.

[6] Parr B, Cho B, Wallace K. A novel ultra-wideband pulse design algorithm[J]. IEEE Communication Letters, 2003, 7(5): 219-221.

[7] Xiao H, Rokhlin V, Yarvin N. Prolate spheroidal wavefunctions, quadrature and interpolation[J]. Inverse Problems, 2001, 17(4): 805-838.

[8] Khare K, George N. Sampling theory approach to prolate spheroidal wave functions[J]. Journal of Physics A: Mathematical and General, 2003, 36(39): 10011-10021.

[9] Khare K. Bandpass sampling and bandpass analogues of prolate spheroidal functions[J]. Signal Processing, 2006, 86(7): 1550-1558.

[10] 舒根春,王红星,赵志勇,等. 基于带通采样的椭圆球面波函数数值解法[J].电路与系统学报,2011,16(5):132-136. Shu Gen-chun, Wang Hong-xing, Zhao Zhi-yong,et al. Numerical solution of prolate spheroidal wave functions based on bandpass sampling[J]. Journal of Circuits and Systems, 2011, 16(5): 132-136.

[11] 刘锡国,王红星,刘传辉,等.基于重构滤波的非正弦时域正交调制实现方法[J].吉林大学学报:工学版,2012,42(2):505-509. Liu Xi-guo,Wang Hong-xing,Liu Chuan-hui,et al.Realization method of non-sinusoidal orthogonal modulation in time domain based on reconstruction filtering[J].Journal of Jilin University(Engineering and Technology Edition),2012,42(2):505-509.

[12] Rokhlin V, Xiao H. Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit[J]. Applied and Computational Harmonic Analysis, 2007, 22(1): 105-123.

[13] Flammer C. Spheroidal Wave Functions[M]. California: Stanford University Press, 1957: 16-21, 29.
[1] 周彦果,张海林,陈瑞瑞,周韬. 协作网络中采用双层博弈的资源分配方案[J]. 吉林大学学报(工学版), 2018, 48(6): 1879-1886.
[2] 孙晓颖, 扈泽正, 杨锦鹏. 基于分层贝叶斯网络的车辆发动机系统电磁脉冲敏感度评估[J]. 吉林大学学报(工学版), 2018, 48(4): 1254-1264.
[3] 董颖, 崔梦瑶, 吴昊, 王雨后. 基于能量预测的分簇可充电无线传感器网络充电调度[J]. 吉林大学学报(工学版), 2018, 48(4): 1265-1273.
[4] 牟宗磊, 宋萍, 翟亚宇, 陈晓笑. 分布式测试系统同步触发脉冲传输时延的高精度测量方法[J]. 吉林大学学报(工学版), 2018, 48(4): 1274-1281.
[5] 丁宁, 常玉春, 赵健博, 王超, 杨小天. 基于USB 3.0的高速CMOS图像传感器数据采集系统[J]. 吉林大学学报(工学版), 2018, 48(4): 1298-1304.
[6] 陈瑞瑞, 张海林. 三维毫米波通信系统的性能分析[J]. 吉林大学学报(工学版), 2018, 48(2): 605-609.
[7] 张超逸, 李金海, 阎跃鹏. 双门限唐检测改进算法[J]. 吉林大学学报(工学版), 2018, 48(2): 610-617.
[8] 关济实, 石要武, 邱建文, 单泽彪, 史红伟. α稳定分布特征指数估计算法[J]. 吉林大学学报(工学版), 2018, 48(2): 618-624.
[9] 李炜, 李亚洁. 基于离散事件触发通信机制的非均匀传输网络化控制系统故障调节与通信满意协同设计[J]. 吉林大学学报(工学版), 2018, 48(1): 245-258.
[10] 孙晓颖, 王震, 杨锦鹏, 扈泽正, 陈建. 基于贝叶斯网络的电子节气门电磁敏感度评估[J]. 吉林大学学报(工学版), 2018, 48(1): 281-289.
[11] 武伟, 王世刚, 赵岩, 韦健, 钟诚. 蜂窝式立体元图像阵列的生成[J]. 吉林大学学报(工学版), 2018, 48(1): 290-294.
[12] 袁建国, 张锡若, 邱飘玉, 王永, 庞宇, 林金朝. OFDM系统中利用循环前缀的非迭代相位噪声抑制算法[J]. 吉林大学学报(工学版), 2018, 48(1): 295-300.
[13] 王金鹏, 曹帆, 贺晓阳, 邹念育. 基于多址干扰和蜂窝间互扰分布的多载波系统联合接收方法[J]. 吉林大学学报(工学版), 2018, 48(1): 301-305.
[14] 石文孝, 孙浩然, 王少博. 无线Mesh网络信道分配与路由度量联合优化算法[J]. 吉林大学学报(工学版), 2017, 47(6): 1918-1925.
[15] 姜来为, 沙学军, 吴宣利, 张乃通. LTE-A异构网络中新的用户选择接入和资源分配联合方法[J]. 吉林大学学报(工学版), 2017, 47(6): 1926-1932.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 《吉林大学学报(工学版)》编辑部
地址：长春市人民大街5988号　电话：+86-431-85095297　传真：+86-431-85094074　E-mail: xbgxb@jlu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发