Tighter Uncertainty Principles Based on Quaternion Fourier Transform

2015 ◽  
Vol 26 (1) ◽  
pp. 479-497 ◽  
Author(s):  
Yan Yang ◽  
Pei Dang ◽  
Tao Qian
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principles ◽  
Quaternion Fourier Transform

Uncertainty principles related to quaternionic windowed Fourier transform

2020 ◽  
Vol 18 (03) ◽  
pp. 2050015
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principles ◽  
Quaternion Fourier Transform ◽  
Windowed Fourier Transform ◽  
The Relationship

In this paper, we first introduce uncertainty principles for the quaternion Fourier transform (QFT). We then provide a different proof of the well-known properties of the quaternionic windowed Fourier transform (QWFT) using properties of the QFT which is a little bit simpler than usual. Based on uncertainty principles for the QFT and the relationship between the QFT and QWFT, we establish uncertainty principles related to the QWFT.

scholarly journals A Version of Uncertainty Principle for Quaternion Linear Canonical Transform

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Mawardi Bahri ◽  
Resnawati ◽  
Selvy Musdalifah
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Young Inequality ◽  
Linear Canonical Transform ◽  
Two Dimensional ◽  
Research Papers ◽  
Quaternion Fourier Transform ◽  
Quaternion Linear Canonical Transform ◽  
The Relationship

In recent years, the two-dimensional (2D) quaternion Fourier and quaternion linear canonical transforms have been the focus of many research papers. In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT. We also discuss the generalization of the Hausdorff-Young inequality in the QLCT domain.

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