Spectral information from fourier analysis of digitized quartz grain profiles

Abstract

Fourier analysis of closed curves defining two-dimensional images has emerged as a promising new tool for the quantification of projected shape in detrital quartz grains. The Fourier method has received added impetus with the introduction of microprocessor-controlled video imaging systems that permit automated acquisition and processing of digital information for hundreds of grains in a few hours. Although new methods and technology have removed much of the tedium and subjectivity associated with older representations of particle shape, other problems are introduced during the acquisition and interpretation of Fourier shape spectra that find their analog in conventional time series analysis. These include the aliasing problem and the treatment of quantization errors which attend the digitization process, along with decisional problems regarding the selection of harmonics and the smoothing of spectral power estimates from individual grain shapes. Our work with quartz grain shapes suggests that bandwidth averaging of power estimates over four adjacent harmonics is an effective smoothing procedure and that harmonics 18 through 21 may constitute a suitable standard band for multiple study comparisons.