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Abstract
In this paper, we use wavelet methods to analyse a class of multidimsionlinear stochastic system, we obtain its average power￠density degree￠wavelet expansion and relation of expansion coefficient.
Key words
Stochastic system; Density degree; Wavelet expansion; Average power; Relation
1.INTRODUCTION
The stochastic system is very importment in many aspacts.
Wavelet analysis is a remarkable tool for analyzing function of one or several variables that appear in mathematics or in signal and image processing. With hindsight the wavelet transform can be viewed as diverse as mathematics, physics and electrical engineering .The basic idea is to use a family of building blocksto representthe objectat handin an efficientand insightfulway, the buildingblockscome in different sizes, and are suitable for describing features with a resolution commensurate with their sizes.
There are two important aspects to wavelets, which we shall call“mathematical”and“algorithmic”. Numerical algorithms using wavelet bases are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in the new system of coordinates .As with all transformmethods such as approachhopes to achieve that the computationis faster in the new system of coordinates than in the original domain, wavelet based algorithms exhibit a number of new and important properties. Recently some personshave studiedwavelet problemsof stochastic processor stochastic system(see [1]-[17]). In this paper, we study the system (see [7])as follow to use wavelet methods.
We will take wavelet and use them in a series expansion of signal or function. Wavelet has its energy concentrated in time to give a tool for the analysis of transient,nonstationary,ortime-varying phenomena.It still has the oscillating wavelike characteristic but also has the ability to allow simultaneous time and frequencyanalysis withaflexiblemathematicalfoundation.Wetakewavelet andusethemin a series expansion of signals or functions much the same way a Fourier series the wave or sinusoid to represent a signal or function.In order to use the idea of multiresolution ,we will start by defining the scaling function and then define the wavelet in terms of it.
With the rapid development of computerized scientific instruments comes a wide variety of interesting problemsfordataanalysisandsignalprocessing.Infields rangingfromExtragalacticAstronomyto Molecu-
REFERENCES
[1]Cambanis S. (1994). Wavelet Approximation of Deterministic and Random Signals. IEEE Tran on Information Theory, 40(4), 1013-1029
[2]Flandrin P. (1992). Wavelet Analysis and Aynthesis of Fractional Brownian Motion. IEEE Tran on Information Theory, 38(2), 910-916.
[3]Krim H. (1995). Multiresolution Analysis of a Class of Nonstationary Processes. IEEE Tran on Information Theory, 41(4), 1010-1019.
[4]Priestley M B (1996). Wavelets and Time C Dependent Spectral Analysis. J of Time Series Analysis, 17(1), 85-103.
[5]Zhang J & Walter G G (1994). A Wavelet Based K-L-Like Expansion for Wide-Sense Stationary Processes. IEEE Trans Sig, Proc, 38(2), 814-823.
[6]Haobo R (2002). Wavelet Estimation for Jumps in a Heteroscedastic Regressian Model. Acta Mathematica Scientia, SerB, 22(2), 269-276.
[7]Arnold L (1974). Stochastic Differential Epuation. New York: John Wiley & Sons Inc.
[8]Wong E & Hajek B (1985). Stochastic Processes in Engineering Systeme. New York: Springs-Verlay.
[9]A. Hendi (2009). New Exact Travelling Wave Solutions for Some Nonlinear Evolution Equations. International Journal of Nonlinear Science, 7(3), 259-267.
[10] Xuewen Xia (2005). Wavelet Analysis of the Stochastic System with Coular Stationary Noise. Engineering Science, 3, 43-46.
[11] XuewenXia (2008).Wavelet DensityDegreeof ContinuousParameterAR Model.InternationalJournal Nonlinear Science, 7(4), 237-242.
[12] Xuewen Xia (2007). Wavelet Analysis of Browain Motion. World Journal of Modelling and Simulation, (3),106-112.
[13] Xuewen Xia & Ting Dai (2009).WaveletDensity Degreeof a Class of Wiener Processes. International Journal of Nonlinear Science, 7(3), 327-332.
[14] Xuewen Xia (2010). Haar Wavelet Density of the Linear Regress Processes with Rondom Coefficient. Proceedings of the Third International Conference on Modeling and Simulation, 2010(5).
[15] Xuewen Xia (2010). The Haar Wavelet Density of the Two Order Polynomial Stochastic Processes. Proceedings of the Third International Conference on Modeling and Simulation, 2010(3).
[16] Xuewen Xia (2011). The Study of Wiener Processes With N(0,1)-Random Trend Peocesses Based on Wavelet. Journal Information and Computing Science, (2).
[17] Xuewen Xia (2011).The Study of a Class of the Fractional Brownian Motion Based on Wavelet. Inter. J. of Nonlinear Science, (3).
In this paper, we use wavelet methods to analyse a class of multidimsionlinear stochastic system, we obtain its average power￠density degree￠wavelet expansion and relation of expansion coefficient.
Key words
Stochastic system; Density degree; Wavelet expansion; Average power; Relation
1.INTRODUCTION
The stochastic system is very importment in many aspacts.
Wavelet analysis is a remarkable tool for analyzing function of one or several variables that appear in mathematics or in signal and image processing. With hindsight the wavelet transform can be viewed as diverse as mathematics, physics and electrical engineering .The basic idea is to use a family of building blocksto representthe objectat handin an efficientand insightfulway, the buildingblockscome in different sizes, and are suitable for describing features with a resolution commensurate with their sizes.
There are two important aspects to wavelets, which we shall call“mathematical”and“algorithmic”. Numerical algorithms using wavelet bases are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in the new system of coordinates .As with all transformmethods such as approachhopes to achieve that the computationis faster in the new system of coordinates than in the original domain, wavelet based algorithms exhibit a number of new and important properties. Recently some personshave studiedwavelet problemsof stochastic processor stochastic system(see [1]-[17]). In this paper, we study the system (see [7])as follow to use wavelet methods.
We will take wavelet and use them in a series expansion of signal or function. Wavelet has its energy concentrated in time to give a tool for the analysis of transient,nonstationary,ortime-varying phenomena.It still has the oscillating wavelike characteristic but also has the ability to allow simultaneous time and frequencyanalysis withaflexiblemathematicalfoundation.Wetakewavelet andusethemin a series expansion of signals or functions much the same way a Fourier series the wave or sinusoid to represent a signal or function.In order to use the idea of multiresolution ,we will start by defining the scaling function and then define the wavelet in terms of it.
With the rapid development of computerized scientific instruments comes a wide variety of interesting problemsfordataanalysisandsignalprocessing.Infields rangingfromExtragalacticAstronomyto Molecu-
REFERENCES
[1]Cambanis S. (1994). Wavelet Approximation of Deterministic and Random Signals. IEEE Tran on Information Theory, 40(4), 1013-1029
[2]Flandrin P. (1992). Wavelet Analysis and Aynthesis of Fractional Brownian Motion. IEEE Tran on Information Theory, 38(2), 910-916.
[3]Krim H. (1995). Multiresolution Analysis of a Class of Nonstationary Processes. IEEE Tran on Information Theory, 41(4), 1010-1019.
[4]Priestley M B (1996). Wavelets and Time C Dependent Spectral Analysis. J of Time Series Analysis, 17(1), 85-103.
[5]Zhang J & Walter G G (1994). A Wavelet Based K-L-Like Expansion for Wide-Sense Stationary Processes. IEEE Trans Sig, Proc, 38(2), 814-823.
[6]Haobo R (2002). Wavelet Estimation for Jumps in a Heteroscedastic Regressian Model. Acta Mathematica Scientia, SerB, 22(2), 269-276.
[7]Arnold L (1974). Stochastic Differential Epuation. New York: John Wiley & Sons Inc.
[8]Wong E & Hajek B (1985). Stochastic Processes in Engineering Systeme. New York: Springs-Verlay.
[9]A. Hendi (2009). New Exact Travelling Wave Solutions for Some Nonlinear Evolution Equations. International Journal of Nonlinear Science, 7(3), 259-267.
[10] Xuewen Xia (2005). Wavelet Analysis of the Stochastic System with Coular Stationary Noise. Engineering Science, 3, 43-46.
[11] XuewenXia (2008).Wavelet DensityDegreeof ContinuousParameterAR Model.InternationalJournal Nonlinear Science, 7(4), 237-242.
[12] Xuewen Xia (2007). Wavelet Analysis of Browain Motion. World Journal of Modelling and Simulation, (3),106-112.
[13] Xuewen Xia & Ting Dai (2009).WaveletDensity Degreeof a Class of Wiener Processes. International Journal of Nonlinear Science, 7(3), 327-332.
[14] Xuewen Xia (2010). Haar Wavelet Density of the Linear Regress Processes with Rondom Coefficient. Proceedings of the Third International Conference on Modeling and Simulation, 2010(5).
[15] Xuewen Xia (2010). The Haar Wavelet Density of the Two Order Polynomial Stochastic Processes. Proceedings of the Third International Conference on Modeling and Simulation, 2010(3).
[16] Xuewen Xia (2011). The Study of Wiener Processes With N(0,1)-Random Trend Peocesses Based on Wavelet. Journal Information and Computing Science, (2).
[17] Xuewen Xia (2011).The Study of a Class of the Fractional Brownian Motion Based on Wavelet. Inter. J. of Nonlinear Science, (3).