Octonion quadratic-phase Fourier transform: inequalities, uncertainty principles, and examples

In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPF...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2024; no. 1; pp. 134 - 52
Main Authors: Kumar, Manish, Bhawna
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 16.10.2024
Springer Nature B.V
SpringerOpen
Subjects:
Algebra
Analysis
Applications of Mathematics
Data compression
Fourier transform
Fourier transforms
Inequalities
Inequality
Integral transforms
Investigations
Lie groups
Mathematics
Mathematics and Statistics
Octonion quadratic-phase Fourier transform
Principles
Quaternions
Sharp inequalities
Signal processing
Uncertainty principles
Wavelet transforms
26A42
Sharp inequalities
Uncertainty principles
42B10
Octonion quadratic-phase Fourier transform
Fourier transform
26D15
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this article, we define the octonion quadratic-phase Fourier transform (OQPFT) and derive its inversion formula, including its fundamental properties such as linearity, parity, modulation, and shifting. We also establish its relationship with the quaternion quadratic-phase Fourier transform (QQPFT). Further, we derive the Parseval formula and the Riemann–Lebesgue lemma using this transform. Furthermore, we formulate two important inequalities (sharp Pitt’s and sharp Hausdorff–Young’s inequalities) and three main uncertainty principles (logarithmic, Donoho–Stark’s, and Heisenberg’s uncertainty principles) for the OQPFT. To complete our investigation, we construct three elementary examples of signal theory with graphical interpretations to illustrate the use of OQPFT and discuss their particular cases.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03213-2