Reconstruction of a compactly supported function from the discrete sampling of its Fourier transform

Author

Yin, Jiahong ; De Pierro, Alvaro R. ; Wei, Musheng

Author_Institution

Dept. of Appl. Math., State Univ. of Campinas, Brazil

Volume

47

Issue

12

fYear

1999

fDate

12/1/1999 12:00:00 AM

Firstpage

3356

Lastpage

3364

Abstract

We derive a new relation between the discrete Fourier transform of a discrete sampling set of a compactly supported function and its Fourier transform. From this relation, we obtain a new window function. We then propose a new efficient algorithm to reconstruct the original function from the discrete sampling of its Fourier transform, which can adopt the fast Fourier transform and has much better accuracy than those in the literature. Several numerical experiments are also provided, illustrating the results

Keywords

discrete Fourier transforms; filtering theory; signal reconstruction; signal sampling; Fourier transform; compactly supported function reconstruction; discrete Fourier transform; discrete sampling; efficient algorithm; fast Fourier transform; filtering approach; numerical experiments; signal processing; window function; Discrete Fourier transforms; Fast Fourier transforms; Filters; Fourier series; Fourier transforms; Helium; Interpolation; Mathematics; Sampling methods; Signal processing algorithms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.806079

Filename

806079