The errors in FFT estimation of the Fourier transform

Author

Becker, Ronald I. ; Morrison, Norman

Author_Institution

Dept. of Math., Cape Town Univ., Rondebosch, South Africa

Volume

44

Issue

8

fYear

1996

fDate

8/1/1996 12:00:00 AM

Firstpage

2073

Lastpage

2077

Abstract

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⩾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

Keywords

Fourier transforms; approximation theory; discrete Fourier transforms; error analysis; estimation theory; fast Fourier transforms; functional analysis; DFT; FFT estimation errors; approximation; asymptotic error formulas; canonical-k functions; continuous Fourier transform; discrete Fourier transform; order-k functions; relative error; Band pass filters; Chebyshev approximation; Circuit noise; Delay; Digital filters; Estimation error; Finite impulse response filter; Fourier transforms; Signal processing algorithms; Speech processing;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.533728

Filename

533728