椭圆球面波函数时频能量聚集性研究  

Study on Energy Concentration of PSWFs

作　　者：刘晓[1] 王红星[1,2] 刘传辉[1] 张磊[1] 

机构地区：[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

出　　处：《中国电子科学研究院学报》2015年第3期237-244,共8页Journal of China Academy of Electronics and Information Technology

基　　金：国家自然科学基金资助项目(60772056);山东省"泰山学者"建设工程专项经费基金资助项目(ts20081130)

摘　　要：椭圆球面波函数(PSWF)集是时频域上能量聚集性最佳的信号形式,在提高系统频谱利用率、降低频带间干扰方面具有天然优势。本文针对椭圆球面波函数最佳时频能量聚集性及其在工程中应用的问题,重点研究了时限PSWF在频域的最佳能量聚集性,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,两个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PSWF与偶数阶PSWF相乘后带内能量聚集度提高,奇数阶与奇数阶或偶数阶与偶数阶PSWF相乘后带内能量聚集度大幅下降;两个同频段同时间带宽积PSWF信号卷积后能量聚集度提高,且相卷积的两个PSWF阶数越低,运算后能量聚集度越高。Prolate Spheroidal Wave Functions（ PSWFs） with the best energy concentration in time and frequency domain have natural advantages in improving spextral efficiency and reducing interference between inter-frequency. On the issue of the best energy concentration in time and frequency domain applied to engineering,the energy concentration of single PSWF signal as well as the change of energy concentration after adding,multiplying and convolution are analyzed. Theoretical analysis and simulation results show that the energy concentration fall in between two PSWF signals after adding under the circumstance of same frequency and time-bandwidth product; the energy concentration enhances after 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 concentration enhances after convolution,and the lower the order of PSWF signals are,the more energy concentration will be.

关 键 词：椭圆球面波函数 时频能量聚集性 时间带宽积 乘加卷积运算 

分 类 号：TN911.3[电子电信—通信与信息系统]