基于Householder变换的正交PSWF脉冲设计

传统的Schmidt方法对椭圆球面波函数（PSWF）脉冲组进行正交化时，脉冲组的最大互相关值受脉冲个数的影响，同时还存在计算复杂度高的问题。针对上述问题，提出了基于Householder变换的正交化方法，通过将PSWF脉冲离散化，再依次对各离散的PSWF脉冲进行Householder变换，实现了对PSWF脉冲组进行QR分解，并得到新的正交PSWF脉冲组。仿真结果表明，与传统Schmidt方法相比，基于Householder变换的正交化方法使得脉冲组的最大互相关值从10-4降低到10-11，改善了脉冲组的正交性能，突破了脉冲组在脉冲个数的限制，并降低了计算复杂度，同时能够保持PSWF脉冲带内能量集中度高的优势。

Design of orthogonal pulse for prolate spheroidal wave function based on Householder transformation

In using traditional Schmidt method in the orthogonalization of the Prolate Spheroidal Wave Function (PSWF) pulses set, the maximum cross-correlation value of the pulses set is under the influence of pulse number, and this method has a high computational complexity. To solve the problems above, an orthogonalization method based on Householder transformation is presented. The QR decomposition is realized through discretizing the pulses set and Householder transformation for the discrete pulse, then the new PSWF orthogonalization pulses set is obtained. Simulation results show that comparing with Schmidt method, the orthogonalization method based on Householder transformation makes the max correlation value reduced from 10-4 to 10-11 and is not restricted to the pulse number, reduces the computational complexity, while maintaining the advantage of high energy concentration.