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Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform
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Motivated by the fact that the quaternion Fourier transform is a powerful tool in quaternion signal analysis, here, we study the quaternion quadratic-phase Fourier transform, which is a generalized version of the quaternion Fourier transform. We first give a definition of the quaternion quadratic-phase Fourier transform. We derive in detail some essential properties related to this generalized transformation. We explore how the quaternion quadratic-phase Fourier transform is related to the quaternion Fourier transform. It is shown that this relation allows us to obtain several versions of uncertainty principles concerning the quaternion quadratic-phase Fourier transform.
Title: Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform
Description:
Motivated by the fact that the quaternion Fourier transform is a powerful tool in quaternion signal analysis, here, we study the quaternion quadratic-phase Fourier transform, which is a generalized version of the quaternion Fourier transform.
We first give a definition of the quaternion quadratic-phase Fourier transform.
We derive in detail some essential properties related to this generalized transformation.
We explore how the quaternion quadratic-phase Fourier transform is related to the quaternion Fourier transform.
It is shown that this relation allows us to obtain several versions of uncertainty principles concerning the quaternion quadratic-phase Fourier transform.
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