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- Title
Convolution, Correlation and Uncertainty Principle in the One-Dimensional Quaternion Quadratic-Phase Fourier Transform Domain.
- Authors
Bhat, Mohammad Younus; Dar, Aamir H.; Zayed, Mohra; Bhat, Altaf A.
- Abstract
In this paper, we present a novel integral transform known as the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT). We first define the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT) of integrable (and square integrable) functions on R. Later on, we show that 1D-QQPFT satisfies all the respective properties such as inversion formula, linearity, Moyal's formula, convolution theorem, correlation theorem and uncertainty principle. Moreover, we use the proposed transform to obtain an inversion formula for two-dimensional quaternion quadratic-phase Fourier transform. Finally, we highlight our paper with some possible applications.
- Subjects
FOURIER transforms; HEISENBERG uncertainty principle; QUATERNIONS; INTEGRAL transforms; QUATERNION functions; MATHEMATICAL convolutions
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 13, p3002
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11133002