Clifford-valued linear canonical transform: Convolution and uncertainty principles

Shah, Firdous A.; Teali, Aajaz A.

doi:10.1016/j.ijleo.2022.169436

Cited by 7 publications

(1 citation statement)

References 10 publications

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“…As a result, the theory of Cli ord algebras has attained an overwhelming response and gained a respectable status in higher-dimensional signal and image processing mainly due to the reason that such algebras encompass all dimensions at once unlike the multidimensional tensorial approach with tensor products of one-dimensional phenomena. is true multidimensional nature allows speci c constructions of higher dimensional signal and image processing tools including the Cli ord Fourier transforms [7,8], Cli ord Gabor transforms, Cli ord wavelet transforms, and other integral transforms in general [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Clifford‐Valued Shearlet Transforms on Cl_(P,_Q)‐Algebras

Shah

Teali

Bahri

2022

Journal of Mathematics

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The shearlet transform is a promising and powerful time-frequency tool for analyzing nonstationary signals. In this article, we introduce a novel integral transform coined as the Clifford-valued shearlet transform on Cl(p,q) algebras which is designed to represent Clifford-valued signals at different scales, locations, and orientations. We investigated the fundamental properties of the Clifford-valued shearlet transform including Parseval’s formula, isometry, inversion formula, and characterization of range using the machinery of Clifford Fourier transforms. Moreover, we derived the pointwise convergence and homogeneous approximation properties for the proposed transform. We culminated our investigation by deriving several uncertainty principles such as the Heisenberg–Pauli–Weyl uncertainty inequality, Pitt’s inequality, and logarithmic and local-type uncertainty inequalities for the Clifford-valued shearlet transform.

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Section: Introductionmentioning

confidence: 99%

Clifford‐Valued Shearlet Transforms on Cl_(P,_Q)‐Algebras

Shah

Teali

Bahri

2022

Journal of Mathematics

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Clifford‐valued linear canonical wavelet transform and the corresponding uncertainty principles

Rafiq,

Bhat

2024

Math Methods in App Sciences

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The present article establishes a novel transform known as Clifford‐valued linear canonical wavelet transform which is intended to represent ‐dimensional Clifford‐valued signals at various scales, locations, and orientations. The suggested transform is capable of representing signals in the Clifford domain in addition to inheriting the characteristics of the Clifford wavelet transform. In the beginning, we demonstrate the proposed transform by the help of ‐dimensional difference of Gaussian wavelets. We then establish the fundamental properties of the proposed transform like Parseval's formula, inversion formula, and characterization of its range using Clifford linear canonical transform and its convolution. To conclude our work, we derive an analog of Heisenberg's and local uncertainty inequalities for the proposed transform.

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Two-sided Clifford-valued Linear Canonical Transform: Properties and Mustard Convolution

Teali

Shah

2023

Adv. Appl. Clifford Algebras

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Clifford-valued linear canonical transform: Convolution and uncertainty principles

Cited by 7 publications

References 10 publications

Clifford‐Valued Shearlet Transforms on Cl_(P,_Q)‐Algebras

Clifford‐Valued Shearlet Transforms on Cl_(P,_Q)‐Algebras

Clifford‐valued linear canonical wavelet transform and the corresponding uncertainty principles

Two-sided Clifford-valued Linear Canonical Transform: Properties and Mustard Convolution

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Clifford-valued linear canonical transform: Convolution and uncertainty principles

Cited by 7 publications

References 10 publications

Clifford‐Valued Shearlet Transforms on Cl(P,Q)‐Algebras

Clifford‐Valued Shearlet Transforms on Cl(P,Q)‐Algebras

Clifford‐valued linear canonical wavelet transform and the corresponding uncertainty principles

Two-sided Clifford-valued Linear Canonical Transform: Properties and Mustard Convolution

Contact Info

Product

Resources

About

Clifford‐Valued Shearlet Transforms on Cl_(P,_Q)‐Algebras

Clifford‐Valued Shearlet Transforms on Cl_(P,_Q)‐Algebras