Improved method for the discrete fast Fourier transform

A new algorithm is proposed here for the discrete fast Fourier transform with greatly reduced aliasing which is known to be inherent in the conventional algorithm of Cooley and Tukey, unless the function is band limited and the sampling frequency satisfies the Nyquist condition. Like the algorithm recently proposed by Schütte and extended by Mäkinen in this journal, this is also based on the polynomial expansion of the function to be transformed but more general in formulation and less restrictive than theirs. Its power is demonstrated with a few non-band-limited functions that can be exactly transformed with chosen limits as usually met in different experimental situations. In all cases tried, this yields, in general, much improved accuracy in comparison to others at little or no corresponding increase of computation time.