经典功率谱估计

Classical Power Spectrum Estimation

Abstract With the increasing need of spectrum, various computational methods and algorithms have been proposed in the literature. Keeping these views and facts of spectrum shaping capability by FRFT based windows we have proposed a closed form solution for Bartlett window in fractional domain. This may be useful for analysis of different upcoming generations of mobile communication in a better way which are based on OFDM technique. Moreover, it is useful for real-time processing of non-stationary signals. As per our best knowledge the closed form solution mentioned in this paper have not been reported in the literature till date.This paper focuses on classical period spectral estimation and moderu spectral estimation based on Burg algorithm. By comparing various algorithms in computational complexity and resolution, Burg algorithm was used to signal processing finally. Experimental and simulation results indicated that digital signal processing system would meet system requirements for measurement accuracy.

Keywords periodogram spectral estimation ; Burg algorithm

I. INTRODUCTION

When we expand the frequency response of any digital filter by means of Fourier series, we get impulse response of the digital filter in the form of coefficients of the Fourier series. But the resultant filter is unrealizable and also its impulse response in infinite in duration. If we directly truncate this series to a finite number of points we have to face with well known Gibbs phenomenon, so we modify the Fourier coefficients by

multiplying it with some finite weighing sequence called window functions, w(n). One desirable characteristics of the Fourier transform of most of the window functions comprises of a central or main lobe of small width containing most of its energy.. Also its side lobes should decay rapidly as the frequency tends to π.

1. PERIODOGRAM SPECTRAL ESTIMATION

IF signal by A/u conversion obtain a group of sample data x(1), x(2) ... , through the power spectrum estimates, give the energy of analyzed signal with the frequency distribution and analyze the signal frequency components. Classical power spectrum estimation has two main methods, namely, direct method and auto-correlation method. They are kind of non-parametric methods whose features have nothing to do with any model parameters. Non-parametric spectrum estimation signal extends with N points for the cycle, so it is also known as periodogram. Direct method is regard the N-point observation data X N (n )of the random signal x(n) as an energy limited signal, having direct access to Fourier transform X N (e jw) of X N (n ), and then make the square o f amplitude divided by N as the real power spectrum estimation Of X N (n ).

Spectral estimation methods include the following assumptions and steps.

The stationary random signal X(n) is regarded as the state traversal , using a sample x(n) instead of X(n), and then use N observations xN(n) to estimate the power spectrum p(w) of x(n). Using the record of a