On Choosing Fourier Transforms for Practical Geoscience Applications

Abstract

The variety of definitions of Fourier transforms can create confusion for practical applications. This paper examines the choice of formulas for Fourier transforms and determines the appropriate choices for geoscience applications. One set of Discrete Fourier Transforms can be defined that approximate Fourier integrals and provide transforms between sampled continuous functions in both domains. For applications involving transforms between a continuous function and a discrete function a second set of Discrete Fourier Transforms is needed with different scaling factors. Two classes of application are presented: those where either form of transforms can be used and those where it is necessary to use a particular transform to obtain the correct results.