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 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 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.

The linear canonical wavelet transform on some function spaces

2018 ◽  
Vol 16 (01) ◽  
pp. 1850010 ◽  
Author(s):  
Yong Guo ◽  
Bing-Zhao Li
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Operator ◽  
Function Spaces ◽  
Linear Continuous Operator ◽  
Convolution Theorem ◽  
Linear Canonical Transform ◽  
Equivalent Definition ◽  
New Space ◽  
Definition Of

It is well known that the domain of Fourier transform (FT) can be extended to the Schwartz space [Formula: see text] for convenience. As a generation of FT, it is necessary to detect the linear canonical transform (LCT) on a new space for obtaining the similar properties like FT on [Formula: see text]. Therefore, a space [Formula: see text] generalized from [Formula: see text] is introduced firstly, and further we prove that LCT is a homeomorphism from [Formula: see text] onto itself. The linear canonical wavelet transform (LCWT) is a newly proposed transform based on the convolution theorem in LCT domain. Moreover, we propose an equivalent definition of LCWT associated with LCT and further study some properties of LCWT on [Formula: see text]. Based on these properties, we finally prove that LCWT is a linear continuous operator on the spaces of [Formula: see text] and [Formula: see text].

The properties of generalized offset linear canonical Hilbert transform and its applications

2017 ◽  
Vol 15 (04) ◽  
pp. 1750031 ◽  
Author(s):  
Shuiqing Xu ◽  
Li Feng ◽  
Yi Chai ◽  
Youqiang Hu ◽  
Lei Huang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Hilbert Transform ◽  
Analytic Signal ◽  
Linear Canonical Transform ◽  
Single Sideband ◽  
Generalized Hilbert Transform ◽  
Offset Linear Canonical Transform ◽  
The Fourier Transform ◽  
The Hilbert Transform

The Hilbert transform is tightly associated with the Fourier transform. As the offset linear canonical transform (OLCT) has been shown to be useful and powerful in signal processing and optics, the concept of generalized Hilbert transform associated with the OLCT has been proposed in the literature. However, some basic results for the generalized Hilbert transform still remain unknown. Therefore, in this paper, theories and properties of the generalized Hilbert transform have been considered. First, we introduce some basic properties of the generalized Hilbert transform. Then, an important theorem for the generalized analytic signal is presented. Subsequently, the generalized Bedrosian theorem for the generalized Hilbert transform is formulated. In addition, a generalized secure single-sideband (SSB) modulation system is also presented. Finally, the simulations are carried out to verify the validity and correctness of the proposed results.

scholarly journals TEOREMA KONVOLUSI PADA TRANSFORMASI FOURIER FRAKSIONAL QUATERNION SISI KIRI DAN SIFAT-SIFATNYA

2019 ◽  
Vol 16 (1) ◽  
pp. 1-12
Author(s):  
N H Wibowo ◽  
S Musdalifah ◽  
Resnawati Resnawati
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Quaternion Algebra ◽  
Fractional Fourier Transform ◽  
Convolution Theorem ◽  
Quaternion Fourier Transform

Fourier transform (FT) is growing very rapidly and applying in various fields such as analyzing and decomposing signals in the frequency domain. FT has been extended to quaternion algebra known as the Quaternion Fourier Transform (QFT). The purpose of this paper are to formulate the definition and properties of the left sided Quaternion Fractional Fourier Transform (QFFT), to formulate the definition and convolution theorem for left sided QFFT. Firstly, the results showed the formulation of the left sided QFFT definition and some of the properties such as linearity, translation, modulation and scalar. Secondly, its showed the formulation of convolution theorem for left sided QFFT and also the left sided QFFT of conjugate and translation convolution.

scholarly journals Image Watermarking in the Linear Canonical Transform Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bing-Zhao Li ◽  
Yu-Pu Shi
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Image Watermarking ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Watermark Embedding ◽  
Simulation Results ◽  
The Fourier Transform ◽  
Signal Processing Methods

The linear canonical transform, which can be looked at the generalization of the fractional Fourier transform and the Fourier transform, has received much interest and proved to be one of the most powerful tools in fractional signal processing community. A novel watermarking method associated with the linear canonical transform is proposed in this paper. Firstly, the watermark embedding and detecting techniques are proposed and discussed based on the discrete linear canonical transform. Then the Lena image has been used to test this watermarking technique. The simulation results demonstrate that the proposed schemes are robust to several signal processing methods, including addition of Gaussian noise and resizing. Furthermore, the sensitivity of the single and double parameters of the linear canonical transform is also discussed, and the results show that the watermark cannot be detected when the parameters of the linear canonical transform used in the detection are not all the same as the parameters used in the embedding progress.

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