scholarly journals Sampling in the Linear Canonical Transform Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Bing-Zhao Li ◽  
Tian-Zhou Xu
Keyword(s):  
Hilbert Transform ◽  
Sampling Rate ◽  
Sampling Theorem ◽  
Fourier Domain ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Generalized Hilbert Transform ◽  
Simulation Results ◽  
Bandpass Signals

This paper investigates the interpolation formulae and the sampling theorem for bandpass signals in the linear canonical transform (LCT) domain. Firstly, one of the important relationships between the bandpass signals in the Fourier domain and the bandpass signals in the LCT domain is derived. Secondly, two interpolation formulae from uniformly sampled points at half of the sampling rate associated with the bandpass signals and their generalized Hilbert transform or the derivatives in the LCT domain are obtained. Thirdly, the interpolation formulae from nonuniform samples are investigated. The simulation results are also proposed to verify the correctness of the derived results.

scholarly journals Spectral Analysis of Sampled Signals in the Linear Canonical Transform Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Bing-Zhao Li ◽  
Tian-Zhou Xu
Keyword(s):  
Spectral Analysis ◽  
Spectral Representation ◽  
Digital Signal ◽  
Sampling Theorem ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Two Dimensional ◽  
Research Papers ◽  
One Dimensional ◽  
Uniform Sampling

The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the linear canonical transform domain have been published. In this paper, we investigate the spectrum of sampled signals in the linear canonical transform domain. Firstly, based on the properties of the spectrum of uniformly sampled signals, the uniform sampling theorem of two dimensional signals has been derived. Secondly, the general spectral representation of periodic nonuniformly sampled one and two dimensional signals has been obtained. Thirdly, detailed analysis of periodic nonuniformly sampled chirp signals in the linear canonical transform domain has been performed.

scholarly journals Wigner-Ville Distribution Associated with the Linear Canonical Transform

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Rui-Feng Bai ◽  
Bing-Zhao Li ◽  
Qi-Yuan Cheng
Keyword(s):  
Signal Processing ◽  
Signal Detection ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Nonstationary Signal ◽  
Linear Frequency ◽  
Simulation Results ◽  
Definition Of ◽  
Linear Frequency Modulated Signal

The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates the Wigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of Wigner-Ville distribution associated with the linear canonical transform is given. Then, the main properties of the newly defined Wigner-Ville transform are investigated in detail. Finally, the applications of the newly defined Wigner-Ville transform in the linear-frequency-modulated signal detection are proposed, and the simulation results are also given to verify the derived theory.

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.

An Algorithm of the LMS Adaptive Filtering in Linear Canonical Transform Domain

2013 ◽  
Vol 385-386 ◽  
pp. 1407-1410 ◽  
Author(s):  
Yan Hong Zhang ◽  
Heng Zhao ◽  
Hui Hui Li
Keyword(s):  
Theoretical Analysis ◽  
Adaptive Filtering ◽  
Narrow Band ◽  
Lms Algorithm ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Nonstationary Signal ◽  
Filtering Algorithm ◽  
Wideband Signals ◽  
Simulation Results

In allusion to the non-stationary wideband signals, a LMS adaptive filtering algorithm based on linear canonical transform is proposed. In this method, the signal is first transformed to linear canonical transform domain. By using linear canonical transform and selecting appropriate transformation parameters, characteristics of the transformed signal appear to be stationary narrow-band in the corresponding linear canonical transform domain, and then, the transformed signal is filtered adaptively with LMS algorithm in this domain. Theoretical analysis and simulation results show that the algorithm is not only to solve the problem of extracting and filtering of nonstationary signal, and can obtain better filtering performance.

Sampling of bandlimited signals in the offset linear canonical transform domain based on reproducing kernel Hilbert space

2019 ◽  
Vol 18 (02) ◽  
pp. 1950054 ◽  
Author(s):  
Shuiqing Xu ◽  
Zhiwei Chen ◽  
Yi Chai ◽  
Yigang He ◽  
Xiang Li
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Sampling Theorem ◽  
Orthogonal Basis ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Uniform Sampling ◽  
Bandlimited Signals ◽  
Offset Linear Canonical Transform

The offset linear canonical transform (OLCT) has proven to be a novel and effective method in signal processing and optics. Many important properties and results of the OLCT have been well studied and published. In this work, the sampling theorem of the OLCT bandlimited signals based on reproducing kernel Hilbert space has been proposed. First, we show that the bandlimited signals in the OLCT domain form a reproducing kernel Hilbert space. Then, an orthogonal basis for the OLCT bandlimited signals has been obtained based on the reproducing kernel Hilbert space. By using the orthogonal basis, the uniform sampling theory for bandlimited signals associated with the OLCT has been obtained. Furthermore, the nonuniform sampling of the OLCT bandlimited signals also has been attained. Finally, the simulations are provided to prove the usefulness and correctness of the derived results.

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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