Quaternion Quadratic Phase Dunkl Transform: Its Properties and Uncertainty Principle
Abstract
Motivated by the wide applications of the quadratic phase integral transform in signal processing, optics, and time frequency analysis, in this paper we develop a new integral transform called the quaternion quadratic phase Dunkl transform (QQPDT). We present a detailed study of its fundamental properties. In particular, we establish continuity, linearity, scaling, modulation, Riemann Lebesgue result, inversion formula, and Parsevals identity. In addition, we estab lish Heisenberg and Donoho-Stark-type uncertainty principles for the QQPDT. Finally, we develop a signal recovery algorithm in the QQPDT domain. The proposed method enables the reconstruction of missing signal information from partial observations under suitable localization conditions.
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BibTeX
@misc{prasad2026quaternion,
title = {{Quaternion Quadratic Phase Dunkl Transform: Its Properties and Uncertainty Principle}},
author = {Akhilesh Prasad and Debabrata Biswal and Manab Kundu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12516},
eprint = {2609.12516},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12516},
}
RIS
TY - UNPB
TI - Quaternion Quadratic Phase Dunkl Transform: Its Properties and Uncertainty Principle
AU - Akhilesh Prasad
AU - Debabrata Biswal
AU - Manab Kundu
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.12516
UR - https://arxiv.org/abs/2609.12516
AB - Motivated by the wide applications of the quadratic phase integral transform in signal processing, optics, and time frequency analysis, in this paper we develop a new integral transform called the quaternion quadratic phase Dunkl transform (QQPDT). We present a detailed study of its fundamental properties. In particular, we establish continuity, linearity, scaling, modulation, Riemann Lebesgue result, inversion formula, and Parsevals identity. In addition, we estab lish Heisenberg and Donoho-Stark-type uncertainty principles for the QQPDT. Finally, we develop a signal recovery algorithm in the QQPDT domain. The proposed method enables the reconstruction of missing signal information from partial observations under suitable localization conditions.
ER -