THE ERRORS IN FFT ESTIMATION OF THE FOURIER-TRANSFORM

The problem of determining the error in approximating the Fourier tran sform by the discrete Fourier transform is studied. Exact formulas for the relative error are established for classes of functions, called c anonical-k (k greater than or equal to 0) here, and asymptotic error f ormulas are established for a much wider class of functions, called or der-k here. The formulas are dependent only on the class and not on th e function in the class whose Fourier transform is being approximated, and this facilitates the application of the results.