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Proceedings of 2009 International Workshop on Information Security and Application (IWISA 2009)

Qingdao, China, November 21-22, 2009

Editors: Feng Gao and Xijun Zhu

AP Catalog Number: AP-PROC-CS-09CN004

ISBN: 978-952-5726-06-0

Page(s): 126-129

Sampling Theorems of Band-limited Signals in the Linear Canonical Transform Domain

Qiang Xiang, Kai-Yu Qin , and Chuan-Wu Zhang

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The linear canonical transform(LCT) has become a very active area in signal processing community in recent years, with many applications in optics, radar system analysis, filter design, phase retrieval, pattern recognition, etc. Many well-known transforms such as the Fourier transform,the fractional Fourier transform,and the Fresnel transform can be seen as special cases of the linear canonical transform. In this paper, the band-limited sampling theorems and reconstruction formulas for linear canonical transformed signals are derived . The previously developed sampling theorems in Fourier domain or fractional Fourier domain are shown to be special cases of the achieved results.Finally, an example of sampling a chirp signal is given, which demonstrate that a signal can be sampled without aliasing at a rate less than the Nyquist rate by using the sampling theorem for the LCT.

Index Terms

Linear canonical transform(LCT), Wigner distribution, Sampling theorem, Band-limited signal

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