基于Walsh函数系的椭圆球面波脉冲波形重构方法

A Reconstructing Method of PSWF Pulse Waveform using Walsh Functions

目前PSWF的脉冲产生方法在硬件实现方面有着编程复杂,计算量大,资源消耗多等制约因素,因此亟需一种适合实时产生PSWF脉冲信号的方法。通过分析Walsh函数系的特点和产生原理,提出了一种基于Walsh函数系的PSWF脉冲波形重构方法。其中,Walsh系数可以通过已有的PSWF数值点与P编号的Walsh矩阵求解得出,再截取所需精度的Walsh系数参与重构PSWF脉冲波形,从而达到降低存储量的目的。由于Walsh码型中的±1与数字电路中的01有着天然对应的关系,重构时只需将Walsh系数相加减,从而降低计算量。仿真结果表明,利用Walsh函数系可以较好地重构PSWF脉冲波形,且算法简单,避免了乘法运算,降低了计算量和存储量,有利于工程实现。

The current realization methods of PSWF pulse in the hardware is constrained by complexity of programming,heavy large calculation,resource consumption,therefore a suitable real-time pulse signal generating method of PSWF is necessary.By analyzing the characteristics and principle of Walsh functions,this paper proposed a reconstruction method of PSWF pulse waveform based on Walsh functions,which can be solved by the existing PSWF data points and P-numbered Walsh matrix.Interception of the required accuracy of Walsh functions involved in the reconstruction of PSWF pulse waveform achieves the goal of reducing memory size.The Walsh codes ±1 have a natural corresponding relationship to 0,1 codes of digital circuits,thus the amount of computation could be reduced by addition and subtraction of the Walsh coefficients.The simulation results show that,according to the engineering requirements of accuracy,the use of Walsh functions could better reconstruct the PSWF pulse waveform.The algorithm,simplified by avoiding the multiplication,can reduce the amount of computation and storage requirement,and provides a easy way of engineering realization.