引力位的Walsh-Fourier级数展开及变换

WALSH-FOURIER SERIES EXPANSION AND TRANSFORM FOR THE GRAVITATIONNAL POTENTIAL

借助Walsh变换实现引力位球谐函数的快速Fourier变换导出了球谐函数的Walsh—Fourier变换、转换矩阵的快速Walsh—Hadamard变换算法及其数据压缩方法还讨论了Walsh—Fouriede换的特性及其在球谐分析中的应用研究表明：当序率和频率等同时．Walsh．Fourier变换和Fourier变换的结果完全一致，两者曲线形态相同;按双精度运算，两种方法的计算准确度均可达到±（10－15-10－14）；Walsh－Fourler变换可以用实数变换取代Fourier变换的复数变换；快速Walsh－Hadamard变换速度提高的幅度将随着阶数的增加而递增：Walsh—Fourier变换可以用于序率和频率等同或不等同的情形Walsh—Fourler变换可在计算精度。

In this paper the fast Fourier transform of spherical harmonics for the gravitational POtential is carried out by means of the Walsh transform. The Walsh-Fourier transform of spherical harmonics and the fast Walsh-Hadamard transform algorithm of transition matrix and itS data compaction method are derived, the characteristics of Walsh-Fourier transform and its applications in spherical harmonic analysis are discussed as well. The researches show that the results of Walsh-Fourier transform coincide fully with Foaurer transform when the sequency is equated to the frequency, the figures of curve for the tWo transformations are the same; According to the operation of double precision type, the computational accuracy of two different methods can come to±(10 - 15-10 -14);The Walsh-Fourier transform can replace the complex transformation of Fourier transform by the real transformation; The range of speeding up the fast Walsh-Hadamaxd transform will be increased with the increase of order;The Walsh-Fourier transform can be used for the case where the sequency and the frequency are equalled or unequalled. The Walsh-Fourier transform is better than the Fourier transform in the computational accuracy, data compaction and representation of potential field spectrum.