NDLI: A Convolution and Correlation Theorem for the Linear Canonical Transform and Its Application

Content Provider	Springer Nature Link
Author	Wei, Deyun Ran, Qiwen Li, Yuanmin
Copyright Year	2011
Abstract	As a generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) plays an important role in many fields of optics and signal processing. Many properties for this transform are already known, but the correlation theorem, similar to the version of the Fourier transform (FT), is still to be determined. In this paper, firstly, we introduce a new convolution structure for the LCT, which is expressed by a one dimensional integral and easy to implement in filter design. The convolution theorem in FT domain is shown to be a special case of our achieved results. Then, based on the new convolution structure, the correlation theorem is derived, which is also a one dimensional integral expression. Last, as an application, utilizing the new convolution theorem, we investigate the sampling theorem for the band limited signal in the LCT domain. In particular, the formulas of uniform sampling and low pass reconstruction are obtained.
Starting Page	301
Ending Page	312
Page Count	12
File Format	PDF
ISSN	0278081X
Journal	Circuits, Systems, and Signal Processing
Volume Number	31
Issue Number	1
e-ISSN	15315878
Language	English
Publisher	SP Birkhäuser Verlag Boston
Publisher Date	2011-05-25
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Convolution theorem Correlation theorem Linear canonical transform Sampling Electronics and Microelectronics, Instrumentation Circuits and Systems Signal, Image and Speech Processing Electrical Engineering
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Signal Processing

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