Generalized distributions, sampling theorem revisited and an end to an impulse invariance error

2015 ◽  
Author(s):  
M.J. Corinthios
Keyword(s):  
Sampling Theorem ◽  
Generalized Distributions

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.

scholarly journals Experimental demonstration of a long-period grating based on the sampling theorem

2006 ◽  
Vol 88 (21) ◽  
pp. 211103 ◽  
Author(s):  
Min-Suk Kwon ◽  
Young-Bo Cho ◽  
Sang-Yung Shin
Keyword(s):  
Sampling Theorem ◽  
Experimental Demonstration ◽  
Long Period Grating ◽  
Long Period

CHARACTERIZATION OF IMAGE SPACE OF A WAVELET TRANSFORM

2006 ◽  
Vol 04 (03) ◽  
pp. 547-557 ◽  
Author(s):  
CAIXIA DENG ◽  
YULING QU ◽  
LIJUAN GU
Keyword(s):  
Wavelet Transform ◽  
Truncation Error ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Sampling Theorem ◽  
Image Space ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Scope Of Application

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.

scholarly journals On the analytic form of the discrete Kramer sampling theorem

2001 ◽  
Vol 25 (11) ◽  
pp. 709-715 ◽  
Author(s):  
Antonio G. García ◽  
Miguel A. Hernández-Medina ◽  
María J. Muñoz-Bouzo
Keyword(s):  
Orthogonal Polynomials ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Analytic Form ◽  
Sampling Theorem ◽  
Discrete Version ◽  
Moment Problems ◽  
Sturm Liouville ◽  
The Subject ◽  
Sampling Expansions

The classical Kramer sampling theorem is, in the subject of self-adjoint boundary value problems, one of the richest sources to obtain sampling expansions. It has become very fruitful in connection with discrete Sturm-Liouville problems. In this paper a discrete version of the analytic Kramer sampling theorem is proved. Orthogonal polynomials arising from indeterminate Hamburger moment problems as well as polynomials of the second kind associated with them provide examples of Kramer analytic kernels.

A New Weak Galerkin Finite Element Scheme for the Brinkman Model

2016 ◽  
Vol 19 (5) ◽  
pp. 1409-1434 ◽  
Author(s):  
Qilong Zhai ◽  
Ran Zhang ◽  
Lin Mu
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Optimal Order ◽  
Brinkman Model ◽  
Weak Galerkin ◽  
Order Error ◽  
Brinkman Equations ◽  
Generalized Distributions ◽  
Variational Form ◽  
Weak Derivatives

AbstractThe Brinkman model describes flow of fluid in complex porous media with a high-contrast permeability coefficient such that the flow is dominated by Darcy in some regions and by Stokes in others. A weak Galerkin (WG) finite element method for solving the Brinkman equations in two or three dimensional spaces by using polynomials is developed and analyzed. The WG method is designed by using the generalized functions and their weak derivatives which are defined as generalized distributions. The variational form we considered in this paper is based on two gradient operators which is different from the usual gradient-divergence operators for Brinkman equations. The WG method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. Optimal-order error estimates are established for the corresponding WG finite element solutions in various norms. Some computational results are presented to demonstrate the robustness, reliability, accuracy, and flexibility of the WG method for the Brinkman equations.

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