scholarly journals On the error in reconstructing a non-bandlimited function by means of the bandpass sampling theorem

1967 ◽  
Vol 18 (1) ◽  
pp. 75-84 ◽  
Author(s):  
J.L Brown
2010 ◽  
Vol 1 (1) ◽  
pp. 43-46
Author(s):  
Harold P. E. Stern

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. 


Author(s):  
A.V. Alekseev

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.


2006 ◽  
Vol 88 (21) ◽  
pp. 211103 ◽  
Author(s):  
Min-Suk Kwon ◽  
Young-Bo Cho ◽  
Sang-Yung Shin

Author(s):  
CAIXIA DENG ◽  
YULING QU ◽  
LIJUAN GU

In this paper, Journe wavelet function is introduced as a wavelet generating function. The expression of reproducing kernel function for the image space of this wavelet transform is obtained based on the fact that the image space of the wavelet transform is a reproducing kernel Hilbert space. Then the isometric identity of Journe wavelet transform is obtained. The connections between the image space of the wavelet transform and the image space of the known reproducing kernel space are established by the theories of reproducing kernel. The properties and the structures of the image space of the wavelet transform can be characterized by the properties and the structures of the image space of the known reproducing kernel space. Using the ideas of reproducing kernel, we consider there are relations between the wavelet transform and the sampling theorem. Meanwhile, the approximations in sampling theorems is shown and the truncation error is given. This provides a theoretical basis for us to study the image space of the general wavelet transform and broadens the scope of application of theories of the reproducing kernel space.


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