Convolution, correlation, and sampling theorems for the offset linear canonical transform

被引：0
|
作者：
Qiang Xiang
KaiYu Qin
机构：
[1] University of Electronic Science and Technology of China,College of Automation
[2] Southwest University for Nationalities,College of Electrical and Information
[3] University of Electronic Science and Technology of China,Institute of Astronautics and Aeronautics
来源：
Signal, Image and Video Processing | 2014年 / 8卷
关键词：
Offset linear canonical transform; Convolution theorem; Correlation theorem; Linear canonical transform; Sampling theorem; Multiplicative filtering;
D O I：
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中图分类号：
学科分类号：
摘要：
The offset linear canonical transform (OLCT), which is a time-shifted and frequency-modulated version of the linear canonical transform, has been shown to be a powerful tool for signal processing and optics. However, some basic results for this transform, such as convolution and correlation theorems, remain unknown. In this paper, based on a new convolution operation, we formulate convolution and correlation theorems for the OLCT. Moreover, we use the convolution theorem to investigate the sampling theorem for the band-limited signal in the OLCT domain. The formulas of uniform sampling and low-pass reconstruction related to the OLCT are obtained. We also discuss the design method of the multiplicative filter in the OLCT domain. Based on the model of the multiplicative filter in the OLCT domain, a practical method to achieve multiplicative filtering through convolution in the time domain is proposed.
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页码：433 / 442
页数：9
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