Windowed Octonion Quadratic Phase Fourier Transform: Sharp Inequalities, Uncertainty Principles, and Examples in Signal Processing

In this paper, we define the Windowed Octonion Quadratic Phase Fourier Transform (WOQPFT) and derive its inversion formula, including its essential properties, such as linearity, anti-linearity, parity, scaling, modulation, shifting, and joint time-frequency shifting, as well as its link to Octonion...

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Bibliographic Details
Published in:IEEE access Vol. 12; pp. 146771 - 146794
Main Authors: Kumar, Manish, Bhawna
Format: Journal Article
Language:English
Published: IEEE 2024
Subjects:
Algebra
Donoho-Stark’s uncertainty principle
Fourier transforms
Heisenberg’s uncertainty principle
Linearity
logarithmic uncertainty principle
Quantum mechanics
Quaternions
sharp Hausdorff-young’s inequality
sharp Pitt’s inequality
Signal analysis
Signal resolution
Time-frequency analysis
Uncertainty
Vectors
Windowed octonion quadratic phase Fourier transform
ISSN:2169-3536, 2169-3536
Online Access:Get full text
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Summary:In this paper, we define the Windowed Octonion Quadratic Phase Fourier Transform (WOQPFT) and derive its inversion formula, including its essential properties, such as linearity, anti-linearity, parity, scaling, modulation, shifting, and joint time-frequency shifting, as well as its link to Octonion Quadratic Phase Fourier Transform (OQPFT). Additionally, we derive the Riemann-Lebesgue lemma using this transform. Following the present analysis, we formulated Sharp Pitt's and Sharp Hausdorff-Young's inequalities. Further, Logarithmic, Heisenberg's, and Donoho-Stark's uncertainty principles are also formulated. The practical application of WOQPFT and the five elementary examples of signal theory are discussed, and their particular cases are analyzed through graphical visualization, including interpretation.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2024.3473298