Clifford Wavelet Transform and the Uncertainty Principle

Banouh, Hicham; Mabrouk, Anouar Ben; Kesri, Mohamed

doi:10.1007/s00006-019-1026-4

Cited by 9 publications

(3 citation statements)

References 56 publications

(16 reference statements)

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“…In [1,2,4] the authors showed that the copies ψ a,b,s constitute a dense set in L 2 (R n , R n , dV (x)). The Clifford-wavelet transform of an analyzed function…”

Section: Clifford Wavelets Toolkitmentioning

confidence: 99%

“…See [1,2,4]. As a result any analyzed function in L 2 (R n , dV (x)) may be reconstructed in the L 2 -sense by means of its Clifford-wavelet transform which constitutes the Clifford-wavelet Plancherel-Parseval formulas.…”

Section: Clifford Wavelets Toolkitmentioning

confidence: 99%

“…In [1,2,3,4], the authors have established the two following results on the uncertainty principle applied to the continuous Clifford wavelet transform.…”

Section: Logarithmic Uncertainty For Clifford Wavelet Transformmentioning

confidence: 99%

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A Quantum Wavelet Uncertainty Principle

2021

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In the present paper, an uncertainty principle is derived in the quantum wavelet framework. Precisely, a new uncertainty principle for the generalized q-Bessel wavelet transform, based on some q-quantum wavelet, is established. A two-parameters extension of the classical Bessel operator is applied to generate a wavelet function which is used for exploring a wavelet uncertainty principle in the q-calculus framework.

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“…In [1,2,4] the authors showed that the copies ψ a,b,s constitute a dense set in L 2 (R n , R n , dV (x)). The Clifford-wavelet transform of an analyzed function…”

Section: Clifford Wavelets Toolkitmentioning

confidence: 99%

Section: Clifford Wavelets Toolkitmentioning

confidence: 99%

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A Quantum Wavelet Uncertainty Principle

2021

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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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Clifford Valued Shearlet Transform

Sharma

Singh

2020

Adv. Appl. Clifford Algebras

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Clifford Wavelet Transform and the Uncertainty Principle

Cited by 9 publications

References 56 publications

A Quantum Wavelet Uncertainty Principle

A Quantum Wavelet Uncertainty Principle

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

Clifford Valued Shearlet Transform

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