Precise expression relating the Fourier transform of a continuous signal to the fast Fourier transform of signal samples

Author

Cameron, William L.

Author_Institution

Defense & Space Group, Boeing Co., Seattle, WA, USA

Volume

43

Issue

12

fYear

1995

fDate

12/1/1995 12:00:00 AM

Firstpage

2811

Lastpage

2821

Abstract

The fast Fourier transform (FFT) signature of a finite duration, constant frequency, time signal displays sidebands which are a sampling artifact. An analytical expression is derived which precisely predicts artifact behavior. Using this expression, a precise spectral estimate (PSE) is derived. It is demonstrated that this method outperforms the FFT with and without Hamming weighting both in estimating the magnitudes and phases of the spectral components of a time series. Furthermore, PSE is capable of resolving frequency to a fraction of an FFT frequency resolution cell

Keywords

Fourier transforms; fast Fourier transforms; signal resolution; signal sampling; spectral analysis; time series; FFT frequency resolution cell; FFT signature; Fourier transform; Hamming weighting; analytical expression; constant frequency time signal; continuous signal; fast Fourier transform; finite duration time signal; precise spectral estimate; sampling artifact; sidebands; signal samples; spectral components; time series; Discrete Fourier transforms; Displays; Fast Fourier transforms; Fourier transforms; Frequency; Phase estimation; Sampling methods; Signal processing; Signal resolution; Signal sampling;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.476425

Filename

476425