Clifford-Valued Stockwell Transform and the Associated Uncertainty Principles

Shah, Firdous A.; Teali, Aajaz A.; Bahri, Mawardi

doi:10.1007/s00006-022-01204-4

Cited by 3 publications

(1 citation statement)

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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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