Generalized Sampling Expansion for Bandlimited Signals Associated With the Fractional Fourier Transform

Author

Wei, Deyun ; Ran, Qiwen ; Li, Yuanmin

Author_Institution

Nat. Key Lab. of Tunable Laser Technol., Harbin Inst. of Technol., Harbin, China

Volume

17

Issue

6

fYear

2010

fDate

6/1/2010 12:00:00 AM

Firstpage

595

Lastpage

598

Abstract

The aim of the generalized sampling expansion (GSE) is the reconstruction of an unknown continuously defined function f(t), from the samples of the responses of M linear time invariant (LTI) systems, each sampled by the 1/M th Nyquist rate. In this letter, we investigate the GSE in the fractional Fourier transform (FRFT) domain. Firstly, the GSE for fractional bandlimited signals with FRFT is proposed based on new linear fractional systems, which is the generalization of classical generalized Papoulis sampling expansion. Then, by designing fractional Fourier filters, we obtain reconstruction method for sampling from the signal and its derivative based on the derived GSE and the property of FRFT. Last, the potential application of the GSE is presented to show the advantage of the theory.

Keywords

Fourier transforms; bandlimited signals; signal sampling; bandlimited signals; fractional Fourier transform; generalized Papoulis sampling expansion; generalized sampling expansion; linear time invariant systems; Fractional bandlimited signal; fractional Fourier filter; fractional Fourier transform; generalized sampling expansion;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2010.2048642

Filename

5451122