Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 536464, 19 pages
Research Article

Spectral Analysis of Sampled Signals in the Linear Canonical Transform Domain

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

Received 11 September 2011; Revised 11 December 2011; Accepted 13 December 2011

Academic Editor: Zhan Shu

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.


The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the linear canonical transform domain have been published. In this paper, we investigate the spectrum of sampled signals in the linear canonical transform domain. Firstly, based on the properties of the spectrum of uniformly sampled signals, the uniform sampling theorem of two dimensional signals has been derived. Secondly, the general spectral representation of periodic nonuniformly sampled one and two dimensional signals has been obtained. Thirdly, detailed analysis of periodic nonuniformly sampled chirp signals in the linear canonical transform domain has been performed.