Quaternion Wigner-Ville Distribution Associated with the Linear Canonical Transforms

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	Quaternion Wigner-Ville Distribution Associated with the Linear Canonical Transforms
	Fan, X.; Kou, K. I.; Liu, M.
	2016-06-24
Source Publication	Signal Processing
ISSN	0165-1684
Pages	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 (QLAF) associated with the QLCT. Next, the relation between these two novel concepts are derived. Moreover, the connection with analytic signal is also presented. Example with bandpass analytic signal illustrates the features of the proposed 4D distribution. Finally, the proposed distribution is applied to form the quaternion-valued linear frequency modulation.
Keyword	2d Quaternionwigner–ville Distribution Quaternion Ambiguity Function Quaternion Linear Canonical Transform Linear Frequency Modulation
Indexed By	SCIE
Language	英語English
The Source to Article	PB_Publication
Document Type	Journal article
Collection	DEPARTMENT OF MATHEMATICS
Corresponding Author	Kou, K. I.
Affiliation	University of Macau
Recommended Citation GB/T 7714	Fan, X.,Kou, K. I.,Liu, M.. Quaternion Wigner-Ville Distribution Associated with the Linear Canonical Transforms[J]. Signal Processing, 2016, 129-141.
APA	Fan, X.., Kou, K. I.., & Liu, M. (2016). Quaternion Wigner-Ville Distribution Associated with the Linear Canonical Transforms. Signal Processing, 129-141.
MLA	Fan, X.,et al."Quaternion Wigner-Ville Distribution Associated with the Linear Canonical Transforms".Signal Processing (2016):129-141.

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