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A Novel Pulse Design Based on hermite functions for UWB Communications

The Journal of China Universities of Posts and Telecommunications 2006年第1期13卷 49-52页

作者： JIANG Guang-xing ZHU Hong-bo CAO Wei Wireless Communication and Electromagnetic Compatibility Laboratory Nanjing University of Posts and Telecommunications Nanjing 210003 P.R. China

This paper presents the design of a class of pulses that are based on hermite functions for ultra-wideband communication systems. The presented class of pulses can not only meet the power spectral emission constraints of federal communications commission, but also have a short duration for multiple accesses. This paper gives closed form expressions of auto-and cross-correlation functions of the proposed pulses, which can be used to evaluate the performance of the correlator receiver. Furthermore, the paper investigates, under various channel conditions, the spectrum characteristic and the bit error rate of the pulses＇ wave forms. The investigation conditions include additive white Gaussian noise channels, multipleaccess interference channels, and fading multipath channels. Our results indicate that our systematic algorithm is flexible for designing ultra-wideband pulses that conform to spectral emission constraints and offer good bit error rate performance.

关键词： pulse design UWB hermite functions multiple access multipath

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GENERALIZED EXPANSIONS IN HILBERT SPACE

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Acta Mathematica Scientia 1999年第3期19卷 241-250页

作者：丁夏畦罗佩珠 Institute of Applied Mathematics Academia Sinica Beijing 100080 China

In this paper the authors give a definite meaning to any formal trigonometrical series and generalize it to all abstract Hilbert space. Then in the case L-2(-infinity + infinity) they discussed extensively the general... 详细信息

关键词： generalized expansion Hilbert space hermite functions hyperbolic system

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Efficient hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains

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Numerical Mathematics(Theory,Methods and Applications) 2022年第4期15卷 1009-1040页

作者： Huiyuan Li Ruiqing Liu Li-Lian Wang State Key Laboratory of Computer Science/Laboratory of Parallel Computing Institute of SoftwareChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100190China Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological University637371Singapore

In this paper,we develop an efficient hermite spectral-Galerkin method for nonlocal diffusion equations in unbounded *** show that the use of the hermite basis can de-convolute the troublesome convolutional operations involved in the nonlocal *** a result,the“stiffness”matrix can be fast computed and assembled via the four-point stable recursive algorithm with O(N^(2))arithmetic ***,the singular factor in a typical kernel function can be fully absorbed by the *** the aid of Fourier analysis,we can prove the convergence of the *** demonstrate that the recursive computation of the entries of the stiffness matrix can be extended to the two-dimensional nonlocal Laplacian using the isotropic hermite functions as basis *** provide ample numerical results to illustrate the accuracy and efficiency of the proposed algorithms.

关键词： Nonlocal diffusion equation spectral-Galerkin hermite functions correlation/convolution recurrence algorithm

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A Sylvester-Based IMEXMethod via Differentiation Matrices for Solving Nonlinear Parabolic Equations

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Communications in Computational Physics 2013年第9期14卷 1001-1026页

作者： Francisco de la Hoz Fernando Vadillo Department of Applied Mathematics Statistics and Operations ResearchFaculty of Science and TechnologyUniversity of the Basque Country UPV/EHUBarrio Sarriena S/N48940 LeioaSpain

In this paper we describe a new pseudo-spectral method to solve numerically two and three-dimensional nonlinear diffusion equations over unbounded domains,taking hermite functions,sinc functions,and rational Chebyshev polynomials as basis *** idea is to discretize the equations by means of differentiation matrices and to relate them to Sylvester-type equations by means of a fourth-order implicit-explicit scheme,being of particular interest the treatment of three-dimensional Sylvester equations that we *** resulting method is easy to understand and express,and can be implemented in a transparent way by means of a few lines of *** test numerically the three choices of basis functions,showing the convenience of this new approach,especially when rational Chebyshev polynomials are considered.

关键词： Semi-linear diffusion equations pseudo-spectral methods differentiation matrices hermite functions sinc functions rational Chebyshev polynomials IMEX methods Sylvester equations blow-up

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Some Recent Advances on SpectralMethods for Unbounded Domains

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Communications in Computational Physics 2009年第2期5卷 195-241页

作者： Jie Shen Li-Lian Wang Department of Mathematics Purdue UniversityWest LafayetteIN47907USA Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological University637616Singapore

We present in this paper a unified framework for analyzing the spectral methods in unbounded domains using mapped Jacobi,Laguerre and hermite functions.A detailed comparison of the convergence rates of these spectral methods for solutions with typical decay behaviors is carried out,both theoretically and computationally.A brief review on some of the recent advances in the spectral methods for unbounded domains is also presented.

关键词： Spectral method unbounded domain orthogonal polynomials rational functions hermite functions Laguerre functions

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