Calculation of Fourier coefficients of a function given at a set of arbitrary points

Abstract

A numerical method is presented for the calculation of Fourier coefficients of a function which is given at a discrete set of arbitrary points. The function is approximated by a sum of Cheby̅shev polynomials. This is performed by Clenshaw's method of curve fitting, which is a least-squares method. The Cheby̅shev coefficients are then used to construct linear combinations of Bessel functions, which are very good approximations of the Fourier coefficients.