The Study of a Class of Multidimsion Stochastic System

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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-

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