Kernel-induced sampling theorem for bandpass signals with uniform sampling

2013 ◽  
Author(s):  
Akira Tanaka
Keyword(s):  
Sampling Theorem ◽  
Uniform Sampling ◽  
Bandpass Signals

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 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.

scholarly journals Bandpass Sampling – An Opportunity To Stress The Importance Of In-Depth Understanding

2010 ◽  
Vol 1 (1) ◽  
pp. 43-46
Author(s):  
Harold P. E. Stern
Keyword(s):  
Mathematical Models ◽  
Sampling Theorem ◽  
Physical Processes ◽  
Complete Understanding ◽  
Bandpass Sampling ◽  
Nyquist Rate ◽  
Shannon’S Sampling Theorem ◽  
Bandpass Signals

Many bandpass signals can be sampled at rates lower than the Nyquist rate, allowing significant practical advantages. Illustrating this phenomenon after discussing (and proving) Shannon’s sampling theorem provides a valuable opportunity for an instructor to reinforce the principle that innovation is possible when students strive to have a complete understanding of physical processes and mathematical models. 

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