基于勒让德多项式的椭圆球面波脉冲设计方法

Design of prolate spheroidal wave function pulse based on legendre polynomials

针对椭圆球面波函数(PSWF)硬件实现困难的问题,从PSWF与勒让德多项式二者微分方程定义的相似性出发,提出一种基于归一化勒让德多项式的PSWF脉冲设计方法。该方法根据所设计脉冲的时宽和时间带宽积两个参数生成对称矩阵,计算该矩阵的特征向量,得到各阶归一化勒让德多项式的系数,通过归一化勒让德多项式加权求和的方法构建PSWF脉冲。该方法可以通过改变归一化勒让德多项式的系数快速设计不同的PSWF脉冲,具有实时性好、精度可控和硬件复杂度低的优点。

To simplify the hardware complexity of prolate spheroidal wave function（PSWF）implementation,a new design method prolate spheroidal wave function pulse based on normalized Legendre polynomial was proposed.We generated a symmetry matrix according to the pulse parameters,and got the Legendre polynomial coefficients by computing the eigenvectors of the matrix.On this basis,we constructed the required PSWF pulse by the normalized Legendre polynomial approximation method.In the PSWF pulse design procedure,the proposed method can design new PSWF pulses by changing Legendre polynomial coefficients,and it can generate PSWF fastly and accurately with low implementation complexity.