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.