Convolution, Correlation and Uncertainty Principle in the One-Dimensional Quaternion Quadratic-Phase Fourier Transform Domain

In this paper, we present a novel integral transform known as the one-dimensional quaternion quadratic-phase Fourier (1D-QQPFT). We first define (1D-QQPFT) of integrable (and square integrable) functions on R. Later on, show that 1D-QQPFT satisfies all respective properties such inversion formula, linearity, Moyal’s convolution theorem, correlation theorem and uncertainty principle. Moreover, use proposed to obtain an formula for two-dimensional transform. Finally, highlight our paper with some possible applications.