Abstract
In this paper, a new two-dimensional quaternion fractional Fourier transform is developed. The properties such as linearity, shifting and derivatives of the quaternion-valued function are studied. The convolution theorem and inversion formula are also established. An example with graphical representation is solved. An application related to two-dimensional quaternion Fourier transform is also demonstrated.
Highlights
In 1853, quaternions were developed by W
An application related to two-dimensional quaternion Fourier transform is demonstrated
The graphical representation of the quaternion fractional Fourier transform of the function (3.18) obtained using α = 1 and β = 1 in (3.19), is a particular case of (3.1) which is represented in the following figure: Figure 4
Summary
In 1853, quaternions were developed by W. In 2007 [9], author introduced right side quaternion Fourier transform. Authors in [1] developed quaternion domain Fourier transforms and its application in mathematical statistics. Quaternion fractional Fourier transform; convolution; operational calculus; graphical representation. The proposed two-dimensional quaternion fractional Fourier transform will transfer the signal to unified time-frequency domains. It has a wide range of applications in the field of optics and signal processing. Graphical interpretation of two-dimensional quaternion fractional Fourier transform is illustrated.
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