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.

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.

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 Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Mawardi Bahri ◽  
Muh. Saleh Arif Fatimah
Keyword(s):  
Fourier Transform ◽  
Inversion Formula ◽  
Ambiguity Function ◽  
Alternative Proof ◽  
Basic Relation ◽  
Linear Canonical Transform ◽  
Quaternion Fourier Transform ◽  
Fundamental Relationship ◽  
The Relationship

The quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT). Based on this fact, we provide alternative proof of the well-known properties of the QWVD-LCT such as inversion formula and Moyal formula. We also discuss in detail the relationship among the QWVD-LCT and other generalized transforms. Finally, based on the basic relation between the quaternion ambiguity function associated with the linear canonical transform (QAF-LCT) and the QFT, we present some important properties of the QAF-LCT.

scholarly journals Two-sided fractional quaternion Fourier transform and its application

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zunfeng Li ◽  
Haipan Shi ◽  
Yuying Qiao
Keyword(s):  
Fourier Transform ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Quaternion Fourier Transform ◽  
Inverse Transform ◽  
Definition Of ◽  
Differential Properties ◽  
The Relationship

AbstractIn this paper, we introduce the two-sided fractional quaternion Fourier transform (FrQFT) and give some properties of it. The main results of this paper are divided into three parts. Firstly we give a definition of the FrQFT. Secondly based on properties of the two-sided QFT, we study the relationship between the two-sided QFT and the two-sided FrQFT, and give some differential properties of the two-sided FrQFT and the Parseval identity. Finally, we give an example to illustrate the application of the two-sided FrQFT and its inverse transform in solving partial differential equations.

Sign in / Sign up

Export Citation Format

Share Document