Lattice-based Multi-channel Sampling Theorem for Linear Canonical Transform

2021 ◽  
pp. 103168
Author(s):  
Firdous A. Shah ◽  
Azhar Y. Tantary
Keyword(s):  
Sampling Theorem ◽  
Linear Canonical Transform

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 Solving Generalized Wave and Heat Equations Using Linear Canonical Transform and Sampling Formulae

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Real Line ◽  
Sampling Theorem ◽  
Heat Equations ◽  
Linear Canonical Transform ◽  
The Real ◽  
Essential Properties

Several essential properties of the linear canonical transform (LCT) are provided. Some results related to the sampling theorem in the LCT domain are investigated. Generalized wave and heat equations on the real line are introduced, and their solutions are constructed using the sampling formulae. Some examples are presented to illustrate our results.

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.

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.

Aliased polyphase sampling theorem for the offset linear canonical transform

Optik ◽  
2020 ◽  
Vol 200 ◽  
pp. 163410
Author(s):  
Shuiqing Xu ◽  
Zhiwei Chen ◽  
Ke Zhang ◽  
Yigang He
Keyword(s):  
Sampling Theorem ◽  
Linear Canonical Transform ◽  
Offset Linear Canonical Transform

Beyond The Sampling Theorem- Compressive Sensing and its Applications

2013 ◽  
Vol 7 (4) ◽  
pp. 18-22
Author(s):  
M.D. Aisha Sulthana ◽  
R. Balamurali
Keyword(s):  
Compressive Sensing ◽  
Sampling Theorem

FORMULATION AND SOLUTION OF OPTIMIZATION PROBLEM REDUNDANCY SYSTEM COMPRISING SITUATION CENTER

2019 ◽  
pp. 44-50
Author(s):  
A.V. Alekseev
Keyword(s):  
Analytical Model ◽  
Quality Indicators ◽  
Significant Influence ◽  
Optimization Problem ◽  
Sampling Theorem ◽  
Sampling Frequency ◽  
Generalized Sampling ◽  
Optimal Value ◽  
Situation Center ◽  
Situation Centers

The analysis of the concept, properties and features of heterogeneous redundancy in modern complex ergatic systems, including those included in the situation centers (SC). On the basis of the qualimetric paradigm, the generalized analytical model of quality and optimization of quality by private, group, summary and aggregated quality indicators is justified. Practical ways of realization of the model and methods of optimization of the objects which are a part of SC and them as a whole at the expense of reduction of structural, functional and other types of redundancy under the obligatory condition of non-reduction of the required value of quality are given. On the example of the generalized sampling theorem when choosing the optimal value of the sampling frequency of the real bandpass signal, the criticality and significant influence on the redundancy of data in their further processing in the SC is shown.

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