Fast method for computing the Fourier integral transform via Simpson's numerical integration.

A new algorithm for computing the Fourier transform is described. The method is based on the calculation of the Fourier integral transform (FIT) with the aid of the numerical Simpson's integration technique. Compared to the conventional fast Fourier transform (FFT), the new SFIT algorithm, gives results which are much closer to the analytic Fourier transform for discrete signals. Especially in the calculation of the phase spectra considerable improvement is obtained. The N-point SFIT can effectively be computed by using two N/2-point FFTs.