椭圆球面波函数时频能量聚集性研究.pdf

第3期
Vol 10 No. 3
2015年6月
Journal of CAERT
Jun.2015
基础理论
dioi:10.3969/j.issn.1673-5692.2015.03.003
椭凤球面波函数时频能量聚集性硏究
刘晓',王红星2,刘传辉,张磊
(1.海军航空工程学院电子信息工程系,烟台264001;
2.山东省信号与信息处理重点实验室,烟台264001)
摘要:楠圆球面波喦数(PSWF)集是时烦域上能量聚集性最佳的信号形式,在提高系统频谱利用
率、降低频带间千扰方面具有天然优势。本文针对楠圆球面波函数最住时烦能量聚集性及其在工
程中应用的问题,重点研究了时限PSWF在频城的最佳能量聚集性,及其乘、加、卷积运算对PSWF
能量聚集性的影响,讨论了乘加卷积运算对PSWF工程应用的影响。理论分析和仿真结果表明,两
同频段同时间带宽积PSWF信号相加后带内能量聚集度介于两者之间;奇数阶FSWF与偶数阶
PSWF相乘后带内能量聚集度提高,奇數阶与奇数阶或偶数阶与偶數阶PSWF相氣后带内能量聚
集度大幅下降;两个同顿段同时间常宽积PSWF信号卷积后能量聚集度提高,且相卷枳的两个
PSWF阶数越低,运算后能量聚集度越高
关键词:椭圆球面波函数;时频能量聚集性;时间带宽枳;加卷积运算
中图分类号:TIN91.3文献标识码:A文章编号:1673-5692(2015)03-237-08
Study on Energy Concentration of PSWFS
LU Xiao, WA G Hong-xing", LIU CHUAN-HUI, ZHANG Lei
(1. Department of Electrical and In ormation Engimeering, Naval Aeronaulical and Astronautical University, Yanlai. China
2. Key Laboratory on Sigmal Information Processing of Shandong Provience, Yantai 264001, China)
Abstract: Prolate Spheroidal Wave Functions(PSWFS with the best energy concentration in time and
frequeney domain have natural advantages in improving spextral efficiency and reducing interference be
tween inter-frequency. On the issue of the best energy concentration in time and frequency domain ap-
plied to engineering, the energy concentration of single PSWF signal as well as the change of energy con
centration after adding, multiplying and convolution are analyzed. Theoretical analysis and simulation
sults show thal the energy concentration fall in between two PS WF signals after adding under the circum
stance of same frequency and time-bandwidth product; the energy concentration enhances a uer odd order
PSWF signal multiply by even order PSWF signal, and it reduces after odd order PSWF signal multiply by
odd order PSWF signal or even order PSWF signal multiply by even order PSWF signal; the energy con-
centration enhances after convolution, and
nd the lower the order of PSWF signals are, the more energy con
centration will be
Key words: PS WPS; energy concentration; time-bandwidth product; combination operation
收稿日期:2015-04-21修订日期:20150602
基金项目:画家自然科学基金资助项目(6077060:出山东省“泰山学者”建设工程专项经费基金资助项日(t2008130
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