The application of the discrete Fourier transform in the estimation of power spectra, coherence, and bispectra of geophysical data

Abstract

The computation of power spectra, cross spectra, coherence, and bispectra of various types of geophysical random processes is part of the established routine. Since it is routine, some of the standard procedures need to be examined rather carefully to be certain that the assumptions behind the procedures are applicable to the data on hand. The basic criteria for a particular method are its resolution bandwidth, its variance, and its bias. In this paper several basic power‐spectrum estimation procedures are reviewed and their statistical and mathematical properties are discussed. The direct use of the discrete Fourier transform for various spectrum calculations is discussed in detail, and its properties are compared with the standard procedure that uses the cosine transform of the estimated correlation function.