The errors in FFT estimation of the Fourier transform

摘要

The problem of determining the error in approximating the Fourier transform by the discrete Fourier transform is studied. Exact formulas for the relative error are established for classes of functions, called canonical-k (k/spl ges/0), and asymptotic error formulas are established for a much wider class of functions, called order-k. The formulas are dependent only on the class and not on the function in the class whose Fourier transform is being approximated, and this facilitates the application of the results.