scholarly journals A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Simple Proof ◽  
Linear Canonical Transform ◽  
Quaternion Fourier Transform ◽  
Inverse Transform ◽  
Fundamental Relationship ◽  
Quaternion Linear Canonical Transform

We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied.

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 Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Linear Canonical Transform ◽  
Two Dimensional ◽  
Quaternion Fourier Transform ◽  
Gaussian Functions ◽  
The Fourier Transform ◽  
Definition Of ◽  
Quaternion Linear Canonical Transform

A definition of the two-dimensional quaternion linear canonical transform (QLCT) is proposed. The transform is constructed by substituting the Fourier transform kernel with the quaternion Fourier transform (QFT) kernel in the definition of the classical linear canonical transform (LCT). Several useful properties of the QLCT are obtained from the properties of the QLCT kernel. Based on the convolutions and correlations of the LCT and QFT, convolution and correlation theorems associated with the QLCT are studied. An uncertainty principle for the QLCT is established. It is shown that the localization of a quaternion-valued function and the localization of the QLCT are inversely proportional and that only modulated and shifted two-dimensional Gaussian functions minimize the uncertainty.

scholarly journals Modifikasi Teorema Konvolusi Transformasi Kanonikal Linier Quaternion Sisi Kiri

2020 ◽  
Vol 16 (2) ◽  
pp. 116-125
Author(s):  
W Oktaviana ◽  
S Musdalifah ◽  
Resnawati
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Convolution Theorem ◽  
Linear Canonical Transform ◽  
Quaternion Fourier Transform ◽  
Fundamental Relationship ◽  
Quaternion Linear Canonical Transform

ABSTRACTQuaternion Linear Canonical Transform (QLCT) is a generalization of the Linear Canonical Transform (LCT) onquaternion algebra which plays an important role in optics and signal processing. QLCT can be seen asgeneralization of Quaternion Fourier Transform (QFT). Based on the fact, this paper propose the formulat ofmodification convolution theorem based on left-sided QLCT by considering the fundamental relationship betweenleft-sided QLCT and QFT. The results showed the modification convolution theorem for left-sided QLCT based onrelationship between left-sided QLCT and QFT as a sum of multiplication of left-sided QFT can be derived.Keywords : Convolution Theorem, Quaternion Fourier Transform, Quaternion Linear Canonical 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.

Some properties of windowed linear canonical transform and its logarithmic uncertainty principle

2016 ◽  
Vol 14 (03) ◽  
pp. 1650015 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Complex Function ◽  
Young Inequality ◽  
Orthogonality Relation ◽  
Linear Canonical Transform ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
The Fourier Transform

Based on the relationship between the Fourier transform (FT) and linear canonical transform (LCT), a logarithmic uncertainty principle and Hausdorff–Young inequality in the LCT domains are derived. In order to construct the windowed linear canonical transform (WLCT), Gabor filters associated with the LCT is introduced. Using the basic connection between the classical windowed Fourier transform (WFT) and the WLCT, a new proof of inversion formula for the WLCT is provided. This relation allows us to derive Lieb’s uncertainty principle associated with the WLCT. Some useful properties of the WLCT such as bounded, shift, modulation, switching, orthogonality relation, and characterization of range are also investigated in detail. By the Heisenberg uncertainty principle for the LCT and the orthogonality relation property for the WLCT, the Heisenberg uncertainty principle for the WLCT is established. This uncertainty principle gives information how a complex function and its WLCT relate. Lastly, the logarithmic uncertainty principle associated with the WLCT is obtained.

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