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Quaternion Wigner–Ville distribution associated with the linear canonical transforms
Fan X.-L.2; Kou K.I.1; Liu M.-S.2
2017
Source PublicationSignal Processing
ISSN01651684
Volume130Pages:129-141
Abstract

The quaternion linear canonical transform (QLCT), a generalization of the classical 2D Fourier transform, has gained much popularity in recent years because of its applications in many areas, including color image and signal processing. There are relationship between Wigner distribution and ambiguity function. But, these relations are only suitable for complex-valued signals, and have not been investigated in quaternion linear canonical transforms. The purpose of this paper is to propose an equivalent relationship for the quaternion Wigner distribution and quaternion ambiguity function in the QLCT setting. First, we propose the 2D quaternion Wigner distribution (QLWD) and quaternion ambiguity function associated with the QLCT. Next, the relationship between these two novel concepts are derived. Moreover, the connection with the corresponding analytic signal are investigated. Examples with bandpass analytic signal illustrate the features of the proposed distributions. Finally a novel algorithm for the detection of quaternion-valued linear frequency-modulated signal is presented by using the proposed QLWD.

Keyword2d Quaternion Wigner–ville Distribution Linear Frequency Modulation Quaternion Ambiguity Function Quaternion Linear Canonical Transform
DOI10.1016/j.sigpro.2016.06.018
URLView the original
Indexed BySCI
Language英语
WOS Research AreaEngineering
WOS SubjectEngineering, Electrical & Electronic
WOS IDWOS:000386410200013
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Citation statistics
Cited Times [WOS]:11   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Universidade de Macau
2.South China Normal University
Recommended Citation
GB/T 7714
Fan X.-L.,Kou K.I.,Liu M.-S.. Quaternion Wigner–Ville distribution associated with the linear canonical transforms[J]. Signal Processing,2017,130:129-141.
APA Fan X.-L.,Kou K.I.,&Liu M.-S..(2017).Quaternion Wigner–Ville distribution associated with the linear canonical transforms.Signal Processing,130,129-141.
MLA Fan X.-L.,et al."Quaternion Wigner–Ville distribution associated with the linear canonical transforms".Signal Processing 130(2017):129-141.
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