摘要
针对当前求解大时间带宽积椭圆球面波函数(PSWF)无统一表达式的问题,通过对基于Hermite函数和Legendre多项式的显式渐近表达式求解误差的理论和数值分析,提出一种大时间带宽积PSWF及其微分算子特征值的显式渐近表达式,明确了大时间带宽积(c>10π)PSWF及其微分算子特征值基于Hermite函数和Legendre多项式的精确高效求解的适用条件和计算方法.性能对比分析结果表明,本文提出的表达式可保证各阶PSWF及其微分算子特征值始终满足误差要求,且正交性与能量聚集性具有显著优势.
To address the problems that currently solve large time-bandwidth product prolate spheroidal wave functions(PSWF)with no uniform expression,an explicit asymptotic expression of the large time-bandwidth product PSWF and its differential operator eigenvalues is proposed.The expression is proposed using the theoretical and numerical analyses of the solution errors of the explicit asymptotic expressions based on the Hermite function and Legendre polynomial.The applicable conditions and calculation methods of the large time-bandwidth product(c>10π)PSWF and its differential operator eigenvalues are accurately and efficiently solved using the Hermite function and Legendre polynomial.Results of the performance comparison analysis indicate that the proposed expression can ensure PSWF and its differential operator eigenvalues of all orders always meet the error requirements.Moreover,the orthogonality and energy concentration of PSWF signals have significant advantages.
作者
赛雷
王红星
陆发平
刘传辉
Lei SAI;Hongxing WANG;Faping LU;Chuanhui LIU(Teaching and Research Office of Aviation Communication,Naval Aviation University,Yantai 264001,China;Key Laboratory on Signal&Information Processing of Shandong Province,Naval Aviation University,Yantai 264001,China)
出处
《中国科学：信息科学》
CSCD
北大核心
2020年第10期1574-1587,共14页
Scientia Sinica(Informationis)
基金
国家自然科学基金(批准号:61701518)
山东省“泰山学者”建设工程专项经费基金(批准号:20081130)项目资助。
