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Mathematical Problems in Engineering
Volume 2012, Article ID 504580, 13 pages
http://dx.doi.org/10.1155/2012/504580
Research Article

Sampling in the Linear Canonical Transform Domain

Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 28 March 2012; Accepted 20 May 2012

Academic Editor: Carlo Cattani

Copyright © 2012 Bing-Zhao Li and Tian-Zhou Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the interpolation formulae and the sampling theorem for bandpass signals in the linear canonical transform (LCT) domain. Firstly, one of the important relationships between the bandpass signals in the Fourier domain and the bandpass signals in the LCT domain is derived. Secondly, two interpolation formulae from uniformly sampled points at half of the sampling rate associated with the bandpass signals and their generalized Hilbert transform or the derivatives in the LCT domain are obtained. Thirdly, the interpolation formulae from nonuniform samples are investigated. The simulation results are also proposed to verify the correctness of the derived results.