APPLICATION OF FAST FOURIER TRANSFORMATION ALGORITHM FOR TERRAIN-PROFILE CHARACTERIZATION

摘要

This paper first reviews the Blackman-Tukey method as it is applied for the determination of the Power Spectral Density (PSD) of terrain profiles. Detrending is discussed briefly and a modified exponential filter is introduced which is better suited for terrain profile analysis than those used in the past. The Discrete Fast Fourier Transformation algorithm is explained by means of a numerical example. This algorithm was first published by Cooley and Tukey. It requires considerably less computer time for the direct computation of the PSD than the Indirect Blackman-Tukey scheme. A flow chart is provided which can service as the basis for a computer program for the determination of the Fourier Transform of discrete data. The inaccuracies and distortions caused by the presence of short (high frequency) component-waves and non-Fourier waves are examined and an evaluation is provided for a number of methods which are recommended in the literature for the reduction of these distortions.