A tabular method for performing Fourier analysis of complex biological shape

Abstract

Whilst linear dimensions are easily measured and analysed numerically, curvilinear forms are difficult both to define and to compare and are frequently left unexplored. A method of describing curved or non-uniform shapes, which has become popular among a number of biological workers, is Fourier analysis — a numerical analytical technique with an established mathematical background. Of the three stages followed when using this technique to describe biological shape - the construction of a wave-like curve from the shape being studied, the numerical (Fourier) analysis and the use of the Fourier coefficients to perform statistical analyses - that of how the Fourier analysis is performed is largely unreported. This leaves many unclear about how to perform a technique which they may otherwise find useful. A tabular method, which allows the computational steps of Fourier analysis to be monitored throughout, is described. This procedure can be readily performed, using a computer spreadsheet or on paper. The original curve may also be reconstructed from the Fourier coefficients, allowing one to check the success and accuracy of the method and to determine the number of coefficients necessary to define the shape to the required precision.