Modelling the Spectrum of Potency a Stationary Random Process in the Form of Spline First Order at the Random Number of Data in Instant of Time

Irina Ustinova ,A D Kozlova

doi:10.1088/1757-899x/142/1/012027

Abstract

The spectrum of potency as same the function of correlation is one of the most important characteristic of the second process random order. The spectrum of potency allows to judge about, that structure of process gives opportunity to take estimation of spectrum composition of useful signals and hindrances, allows to produce synthesis (reconstruction) the signals and to build filters and to obtain the estimates filtration. The purpose of this presenting work is modeling of process random stationary potency spectrum by random dates number in measurement moments. Using by probability theory methods and mathematical statistics was derived unbiased estimator of the potency spectrum in the form of spline first order, and were researched statistic characteristics estimation.

Highlights

One of the modern methods digital processing of signals is digital the spectrum analysis
The aim of this work is modeling the spectrum of potency a random fixed process in the form of spline first order at random number data at the time of determined as follows [16,17,18]
Found of values ( ), we find the consistently S0, S1, which we join by straight line segments, that gives on estimate S( ) in the form of spline first order

Summary

Introduction

One of the modern methods digital processing of signals is digital the spectrum analysis. Density function the spectrum of potency defines the distribution of the dispersion a random process the frequency [2]. 2. Estimation the density of the spectrum with the help of procedure using fast Fourier transforms. Estimation the density of the spectrum with the help of procedure using fast Fourier transforms Such approach for at the spectrum analysis virtual and, as rule, to provide deriving acceptable results. 4. In the works [9,10,11] set, that there is a relation the spectrum of potency with a fractal characteristics a random process. The aim of this work is modeling the spectrum of potency a random fixed process in the form of spline first order at random number data at the time of determined as follows [16,17,18]. S(t) there is an algebraic polynomial of power m

Solution of the problem

The estimate of the dispersion obtained estimates the spectrum of potency

The simulation modeling obtained estimated

Conclusion