Sharper uncertainty principles for the windowed Fourier transform

2014 ◽  
Vol 62 (1) ◽  
pp. 46-55 ◽  
Author(s):  
Ming-Sheng Liu ◽  
Kit Ian Kou ◽  
Joao Morais ◽  
Pei Dang
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principles ◽  
Windowed Fourier Transform

scholarly journals Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Mawardi Bahri
Keyword(s):  
Fourier Transform ◽  
Natural Extension ◽  
Orthogonality Relation ◽  
Current Work ◽  
Linear Canonical Transform ◽  
Uncertainty Principles ◽  
Complex Conjugation ◽  
Inversion Theorem ◽  
Windowed Fourier Transform

AbstractThe windowed linear canonical transform is a natural extension of the classical windowed Fourier transform using the linear canonical transform. In the current work, we first remind the reader about the relation between the windowed linear canonical transform and windowed Fourier transform. It is shown that useful relation enables us to provide different proofs of some properties of the windowed linear canonical transform, such as the orthogonality relation, inversion theorem, and complex conjugation. Lastly, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with this transformation.

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.

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