Wigner-Ville distribution and ambiguity function associated with the quaternion offset linear canonical transform

Bhat, Mohammad Younus; Almanjahie, Ibrahim M.; Dar, Aamir H.; Dar, Javid Gani

doi:10.1515/dema-2022-0175

Cited by 9 publications

(8 citation statements)

References 29 publications

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“…Moreover they also studied the convolution and correlation theorems associated WVD-QPFT. More results in this direction can be found in [30]- [33].…”

Section: Introductionmentioning

confidence: 82%

Wigner-Ville distribution and ambiguity function of QPFT signals

Mohammad,

Aamir Hamid

2023

AUCMCS

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The quadratic phase Fourier transform(QPFT) has received my attention in recent years because of its applications in signal processing. At the same time the applications of Wigner-Ville distribution (WVD) and ambiguity function (AF) in signal analysis and image processing can not be excluded. In this paper we investigated the Wigner-Ville Distribution (WVD) and ambiguity function (AF) associated with quadratic phase Fourier transform (WVD-QPFT/AF-QPFT). Firstly, we propose the definition of the WVD-QPFT, and then several important properties of newly defined WVD-QPFT, such as nonlinearity, boundedness, reconstruction formula, orthogonality relation and Plancherel formula are derived. Secondly, we propose the definition of the AF-QPFT, and its with classical AF, then several important properties of newly defined AF-QPFT, such as non-linearity, the reconstruction formula, the time-delay marginal property, the quadratic-phase marginal property and orthogonal relation are studied. Further, a novel quadratic convolution operator and a related correlation operator for WVD-QPFT are proposed. Based on the proposed operators, the corresponding generalized convolution, correlation theorems are studied. Finally, a novel algorithm for the detection of linear frequency-modulated(LFM) signal is presented by using the proposed WVD-QPFT and AF-QPFT.

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“…Moreover they also studied the convolution and correlation theorems associated WVD-QPFT. More results in this direction can be found in [30]- [33].…”

Section: Introductionmentioning

confidence: 82%

Wigner-Ville distribution and ambiguity function of QPFT signals

Mohammad,

Aamir Hamid

2023

AUCMCS

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“…In recent years, the research on generalization of various kinds of transformations using the linear canonical transform has developed rapidly. In [2,4,5,13,17,21], the authors presented Wigner-Ville distribution associated with the linear canonical transforms. Some inequalities related to this transformation were demonstrated in detail.…”

Section: Introductionmentioning

confidence: 99%

Various generalizations of uncertainty principles related to the linear canonical ambiguity function

Bahri,

Bachtiar,

Amir

et al. 2024

J. Math. Computer Sci.

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The uncertainty principle is a fundamental result of the Fourier transform and is currently one of the most rapidly developing areas of mathematics due to its application in various transformations. This paper deals with the linear canonical ambiguity function. It combines the classical ambiguity function and the linear canonical transform. We derive in detail various uncertainty principles related to the proposed transformation.

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“…In recent years, with the continuous progress of mathematical theory, researchers have begun to extend the concept of integral transforms to the field of quaternion algebra. This extension has led to new theoretical frameworks, such as the quaternion Fourier transform (QFT) [27,28], the quaternion fractional Fourier transform (QFRFT) [29,30], the quaternion linear canonical transform (QLCT) [31][32][33][34], and the quaternion offset linear canonical transform (QOLCT) [7,35,36]. These theoretical frameworks provide new methods and tools for processing and analyzing quaternion signals.…”

Section: Introductionmentioning

confidence: 99%

Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application

Wang,

Feng

2024

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Convolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter analysis. Firstly, we propose QLCcT by combining quaternion algebra with linear canonical cosine transform (LCcT), which extends LCcT to Hamiltonian quaternion algebra. Secondly, we introduce weighted convolution and correlation operations for QLCcT, accompanied by their corresponding theorems. We also explore the properties of QLCcT. Thirdly, we utilize these proposed convolution structures to analyze multiplicative filter models that offer lower computational complexity compared to existing methods based on quaternion linear canonical transform (QLCT). Additionally, we discuss the rationale behind studying such transforms using quaternion functions as an illustrative example.

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Wigner-Ville distribution and ambiguity function associated with the quaternion offset linear canonical transform

Cited by 9 publications

References 29 publications

Wigner-Ville distribution and ambiguity function of QPFT signals

Wigner-Ville distribution and ambiguity function of QPFT signals

Various generalizations of uncertainty principles related to the linear canonical ambiguity function

Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application

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