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快速傅里叶变换(FFT)算法在位场、电磁场和波场等地球物理场的高效数值模拟及其数据处理中发挥着重要作用.FFT算法本质上是一种实现离散傅里叶变换的计算方法,目前多种类型FFT算法组合,能够实现任意采样点数的离散傅里叶变换.离散频率计算是应用任意采样点数FFT算法求解地球物理场数值模拟和数据处理等问题的关键环节.本文从离散傅里叶变换作为傅里叶变换的一种数值逼近的观点出发,通过推导和分析任意采样点数离散傅里叶变换数学表达式,给出了离散频率的计算公式.以重力场向上延拓问题为例,通过理论模型数据实验,检验了本文给出的离散频率计算公式的正确性.
The Fast Fourier Transform (FFT) algorithm plays an important role in high-efficiency numerical simulation and data processing of geophysical fields such as field, electromagnetic field and wave field, etc. The FFT algorithm is essentially a calculation to realize the discrete Fourier transform Method, the current combination of multiple types of FFT algorithm, to achieve any discrete number of discrete Fourier transform discrete frequency calculation is the application of any sampling point FFT algorithm to solve the geophysical field numerical simulation and data processing issues such as the key link.This paper from discrete As a kind of numerical approximation of Fourier transform, Fourier transform is used to derive and analyze the mathematical expression of discrete Fourier transform of arbitrary sampling points, and the formula of discrete frequency is given.With the upward extension of gravity field As an example, the correctness of the discrete frequency formula given in this paper is verified through theoretical model data experiments.