scholarly journals Erratum To: The Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform

2021 ◽  
Author(s):  
Y. El Haoui
Keyword(s):  
Linear Canonical Transform ◽  
Offset Linear Canonical Transform

The extrapolation of bandlimited signals in the offset linear canonical transform domain

Optik ◽  
2019 ◽  
Vol 180 ◽  
pp. 626-634 ◽  
Author(s):  
Shuiqing Xu ◽  
Songbing Tao ◽  
Yi Chai ◽  
Xi Yang ◽  
Yigang He
Keyword(s):  
Transform Domain ◽  
Linear Canonical Transform ◽  
Bandlimited Signals ◽  
Offset Linear Canonical Transform

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.

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