| 引力位的Walsh-Fourier级数展开及变换 |
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| 引用本文： | 孟嘉春,蔡喜楣,孟伟.引力位的Walsh-Fourier级数展开及变换[J].地球物理学报,1998,41(Z1):347-356. |
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| 作者姓名： | 孟嘉春 蔡喜楣 孟伟 |
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| 作者单位： | 1. 中国科学院测量与地球物理研究所, 武汉 430077;
2. 中国科学院武汉文献情报中心, 武汉 430071 |
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| 基金项目： | 国家自然科学基金,49384003;中国科学院院长基金,930156 |
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| 摘 要： | 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、数据压缩和位场谱表示方面好于Fourier变换
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| 关 键 词： | 引力位 球谐函数 Fourier变换 Walsh变换 快速Walsh－Hadanlard变换 |
| 收稿时间： | 1997-12-01 |
WALSH-FOURIER SERIES EXPANSION AND TRANSFORM FOR THE GRAVITATIONNAL POTENTIAL |
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| MENG JIA-CHUN,CAI XI-MEI,MENG WEI.WALSH-FOURIER SERIES EXPANSION AND TRANSFORM FOR THE GRAVITATIONNAL POTENTIAL[J].Chinese Journal of Geophysics,1998,41(Z1):347-356. |
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| Authors: | MENG JIA-CHUN CAI XI-MEI MENG WEI |
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| Institution: | 1. Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China;
2. Wuhan Documentation and Information Center, Chinese Academy of Sciences, Wuhan 430071, China |
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| Abstract: | 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. |
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| Keywords: | Gravitational potential Spherical harmonics Fourier transform Walsh transform Fast Walsh-Hadamard transform |
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