A new kind of convolution, correlation and product theorems related to quaternion linear canonical transform

Zhen Wei Li; Wen Biao Gao; Bing Zhao Li

doi:10.1007/s11760-020-01728-x

A new kind of convolution, correlation and product theorems related to quaternion linear canonical transform

Zhen Wei Li, Wen Biao Gao, Bing Zhao Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

The quaternion linear canonical transform (QLCT) has been investigated and used for many years by various research communities; it has been shown to be a powerful tool for signal processing. In this paper, a novel canonical convolution operator and a related correlation operator for QLCT are proposed. Moreover, based on the proposed operators, the corresponding generalized convolution, correlation and product theorems are studied.

Original language	English
Pages (from-to)	103-110
Number of pages	8
Journal	Signal, Image and Video Processing
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s11760-020-01728-x
Publication status	Published - Feb 2021

Keywords

Convolution operator
Correlation operator
Linear canonical transform
Product theorem
Quaternion linear canonical transform

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10.1007/s11760-020-01728-x

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abstract = "The quaternion linear canonical transform (QLCT) has been investigated and used for many years by various research communities; it has been shown to be a powerful tool for signal processing. In this paper, a novel canonical convolution operator and a related correlation operator for QLCT are proposed. Moreover, based on the proposed operators, the corresponding generalized convolution, correlation and product theorems are studied.",

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AB - The quaternion linear canonical transform (QLCT) has been investigated and used for many years by various research communities; it has been shown to be a powerful tool for signal processing. In this paper, a novel canonical convolution operator and a related correlation operator for QLCT are proposed. Moreover, based on the proposed operators, the corresponding generalized convolution, correlation and product theorems are studied.

KW - Convolution operator

KW - Correlation operator

KW - Linear canonical transform

KW - Product theorem

KW - Quaternion linear canonical transform

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A new kind of convolution, correlation and product theorems related to quaternion linear canonical transform

Abstract

Keywords

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