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

被引：53
|
作者：
Xiang, Qiang [1 ,2 ]
Qin, KaiYu [3 ]
机构：
[1] Univ Elect Sci & Technol China, Coll Automat, Chengdu 610054, Peoples R China
[2] Southwest Univ Nationalities, Coll Elect & Informat, Chengdu 610041, Peoples R China
[3] Univ Elect Sci & Technol China, Inst Aeronaut & Astronaut, Chengdu 610054, Peoples R China
来源：
SIGNAL IMAGE AND VIDEO PROCESSING | 2014年 / 8卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Offset linear canonical transform; Convolution theorem; Correlation theorem; Linear canonical transform; Sampling theorem; Multiplicative filtering; FRACTIONAL FOURIER-TRANSFORM; PRODUCT THEOREM; REPRESENTATIONS; EIGENFUNCTIONS; OPERATIONS; SIGNALS;
D O I：
10.1007/s11760-012-0342-0
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
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：10
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