How well does the finite Fourier transform approximate the Fourier transform?
How well does the finite Fourier transform approximate the Fourier transform?
Abstract We show that the answer to the question in the title is “very well indeed.” In particular, we prove that, throughout the maximum possible range, the finite Fourier coefficients provide a good approximation to the Fourier coefficients of a piecewise continuous function. For a continuous periodic function, the size …