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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。
Based on the Fourier transform, this paper researches the mathematical laws and concepts of the method of combinatorial filtering and the inherent laws of the method by using mathematical analysis methods similar to mathematical filtering. The directional characteristic P (ω) can be thought of as a periodic “wave” function, whereas the combined weighted distribution h (x) is its discrete “spectrum.” Therefore, we can use the physical concept of spectral analysis to study the inversion problem. It can be seen that the combined filtering of the weighted distribution function and direction characteristics are equivalent to the mathematical filter of the filter factor and frequency response; and digital filtering shift gate method can be extended to constitute a combination of band-pass filter to go. The two have commonalities in mathematics, they can refer to each other and have their own particularities in physics. The research results give the combination method a more comprehensive understanding and expand the function of the combination method.