| 论组合法滤波的数学物理概念 |
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| 引用本文： | 黄洪泽.论组合法滤波的数学物理概念[J].地球物理学报,1984,27(5):471-482. |
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| 作者姓名： | 黄洪泽 |
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| 摘 要： | 本文以傅里叶变换为基础,用类似数学滤波中的数学分析方法,比较系统地研究了组合法滤波的数学物理概念及方法的内在规律。可以把方向特性函数P（ω）看作是一种周期“波动”函数,而组合的加权分布函数h（x）则是其离散“频谱”。因此可以引用符合于频谱分析的物理概念来研究反演问题。可以看出,组合滤波的加权分布函数及方向特性分别相当于数学滤波中的滤波因子及频率响应;而数字滤波的移门法等又可以引伸到构成组合法带通滤波中去。二者在数学上有其共性,可以互相引用,在物理上又有各自的特殊性。研究结果给组合法以比较全面的认识,扩大了组合法应用的功能。
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| 关 键 词： | 组合法 方向特性曲线 数学物理 离散分布 加权分布 连续分布 重复周期 奇数项 频谱 视波长 |
| 收稿时间： | 1983-05-07 |
ON THE MATHEMATICAL AND PHYSICAL CONCEPTIONS OF PATTERN FILTERING |
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| HUANG HONG-ZE.ON THE MATHEMATICAL AND PHYSICAL CONCEPTIONS OF PATTERN FILTERING[J].Chinese Journal of Geophysics,1984,27(5):471-482. |
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| Authors: | HUANG HONG-ZE |
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| Abstract: | This paper deals systematically with the mathematical and physical conceptions and the internal relations of pattern filtering by using an analysis method similar to that used in digital filtering. Differing from the usual consideration, directivity function could be considered as a periodical ' wave' function, whereas the weighted distribution function is the discrete ' spectrum' of it. Thus the physical conceptions of spectrum analysis can be applied to the study of problems of reverse solution.It is interesting to show that the weighted distribution function and the directivity function are correspondent to the filter operator and the frequency response of digital filter respectively, whereas the passband shift method can also be applied to bandpass filtering of pattern filtering. Hence, there are properties common to both of them and thus could be utilized by eachother. However, they differ from eachother in their own specialities.Results of the study give an overall understanding of the theory of pattern filtering, and thus enlarge the application of pattern filtering. |
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