应用任意采样点数FFT算法时离散频率计算

Computation of discrete frequency when using FFT algorithm with random sampling points

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.

Fast Fourier Transform（ FFT） algorithm plays an important role in efficient numerical simulation and data processing of geophysical fields, such as gravity, magnetic field and electromagnetic field. FFT is intrinsically a numerical computational method for discrete Fourier transform. Now there are many kinds of FFT algorithms that can carry out discrete Fourier transform with random sampling points. Computation of discrete frequency is a key part in correctly using FFT algorithms to resolve numerical simulation and data processing of geophysical fields. In this study,treating discrete Fourier transform as a numerical approximation of Fourier transform, we give the formula for computing discrete frequency by analyzing the process of deriving discrete Fourier transform expression. We use spectral method to resolve the problem of continuation of gravity field by theoretical model data.Experimental results further verify the correctness of the presented formula for computing discrete frequency.