Quaternionic Linear Canonical Wave Packet Transform

Bhat, Younis Ahmad; Sheikh, Neyaz Ahmad

doi:10.1007/s00006-022-01224-0

Cited by 6 publications

(2 citation statements)

References 34 publications

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“…For a more precise understanding of quaternion integral transforms, one can refer to [1,17,20,23,24,34].…”

Section: Existing Quaternion Transformsmentioning

confidence: 99%

“…[10][11][12][13][14][15][16]. Furthermore, QFT has been generalized to quaternion fractional Fourier and quaternion linear canonical domains [17][18][19][20][21][22], and their associated localized transforms have been investigated in [23][24][25]. The collective findings of these studies have contributed significantly to the elucidation of the underlying principles governing quaternion-valued FTs and their potential utility across a broad spectrum of disciplines.…”

Section: Introductionmentioning

confidence: 99%

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Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform

Urynbassarova

Teali

2023

Mathematics

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Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical transform (QOLCT), which is the most general form of QFT with additional free parameters. We explore the properties of 2D right-sided QOLCT, including inversion and Parseval formulas, besides its relationship with other transforms. We also examine the convolution and correlation theorems of 2D right-sided QOLCT, followed by several uncertainty principles. Additionally, we present an illustrative example of the proposed transform, demonstrating its graphical representation of a given signal and its transformed signal. Finally, we demonstrate an application of QOLCT, where it can be utilized to generalize the treatment of swept-frequency filters.

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“…For a more precise understanding of quaternion integral transforms, one can refer to [1,17,20,23,24,34].…”

Section: Existing Quaternion Transformsmentioning

confidence: 99%