Accurate Fourier Analysis of Arbitrary Functions Defined by Discrete Data Values.

A computerized analysis has been developed to determine the Fourier coefficients of arbitrary functions defined by discrete point values. The method described in this report is more accurate than the trapezoidal integration technique commonly used. Basically, the technique is a summation of exact integrals defined in small regions by a Taylor Series expansion of the data. Derivatives necessary for the expansion are determined by a parametric spline curve function, fitting the original data. The parametric spline is described briefly. Examples of the use and accuracy of a coefficient computation program are presented. The described method is shown to have twice the accuracy of the previous method for equal computation times. The ultimate accuracy of the method is shown to be an order of magnitude better than that of the older method.