基于Karhunen-Loeve变换的正交椭圆球面波脉冲波形设计  

The Design of Orthogonal Prolate Spheroidal Wave Function Pulse Waveform Based on Karhunen-Loeve Transform

作　　者：王红星[1] 陈昭男[1] 刘传辉[1] 赵志勇[1] 

机构地区：[1]海军航空工程学院电子信息工程系,烟台264001

出　　处：《电子与信息学报》2012年第10期2415-2420,共6页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(60772056);山东省"泰山学者"建设工程专项经费资助课题

摘　　要：针对正交椭圆球面波函数(PSWF)脉冲硬件实现复杂度高和难以实时产生的问题,通过对PSWF脉冲求解和正交化两个过程的优化整合,该文提出了一种基于Karhunen-Loeve变换的正交PSWF脉冲波形设计方法。该方法首先将PSWF脉冲表示为Legendre多项式加权求和的形式,通过对原脉冲互相关矩阵进行Karhunen-Loeve变换,得到正交系数矩阵,从而实现PSWF脉冲的正交化。以此为基础,设计了一种高效快捷的正交PSWF脉冲实现方案,建立了正交PSWF脉冲与Legendre多项式系数向量的对应关系,能够通过改变特征多项式的系数来快速设计正交PSWF脉冲,同时具有实时性好和实现复杂度低的优点,为正交PSWF脉冲的工程化实现提供了一种高效快捷的新方案。The orthogonal pulse design based on Prolate Spheroidal Wave Function （PSWF） is hard for hardware design. By the optimization and integration of the pulse solution and orthogonalizaiton procedure, a novel orthogonal PSWF pulse waveform design based on Karhunen-Loeve transform is proposed. The method represents firstly PSWF into a series of Legendre functions, and the factor matrix for orthogonality is achieved by Karhunen-Loeve transform of the cross correlation matrix. On this basis, an efficient hardware implementation of orthogonal PSWF pulse is put forward. The proposed method builds a mapping between orthogonal PSWF pulse and coefficient vector of Legendre polynomial, and the method can be used to design orthogonal PSWF pulses by changing eigenpolynomial coefficients effectively. Meanwhile, the method has good real-time performance and low hardware complexity and provides a fast and efficient scheme pulse. for the engineering realization of orthogonal PSWF pulse.

关 键 词：信号处理 非正弦波 正交脉冲 椭圆球面波函数 Karhunen—Loeve变换 

分 类 号：TN911.7[电子电信—通信与信息系统]