Fast fourier integration of piecewise polynomial functions

The fast Fourier transform (FFT) is a high-speed technique for computing the discrete Fourier transform of a function. The FFT is exact only for discrete (sampled) functions. A technique is presented which utilizes the FFT and its associated computational speed, and computes the Fourier transform of "smooth" functions with better accuracy than the FFT alone. In particular, algorithms using the FFT for transformation of piecewise polynomial functions are presented.