burg method

BURG METHOD

PRESENTED BY :-Sarbjeet SinghNITTTR-Chandigarh

CONTENTS

INTRODUCTION BURG METHOD ADVANTAGES OF BURG METHOD DISADVANTAGES OF BURG METHOD APPLICATIONS

INTRODUCTION

A parametric method for power spectrum density estimation.

A model for the signal generation can be constructed with a no. of parameters that can be estimated from observed data.

From the model and estimated parameters, power spectrum density can be estimated.

BURG METHOD

An order-recursive least-squares lattice method , based on the minimization of the forward and backward errors in linear predictors, with the constraint that the AR parameters satisfy the Levinson – Durbin recursion.

BURG METHOD

To derive the estimator, let the given data be x(n), n = 0, 1,………N-1 and let the forward and backward linear prediction estimates of order ‘m’ , be :-

BURG METHOD

Forward error,

Backward error,

The least squares error is :-

This error is to be minimized by selecting the prediction coefficients , subject to the constraint that they satisfy the Levinson- Durbin recursion given by :-

where is the mth reflection coefficient in the lattice filter realization.

The forward and backward prediction errors in terms of reflection coefficients is given by :

By substituting above equation into Levinson – Durbin Recursion and performing minimization w.r.t. reflection Coefficient ,we get :

is an estimate of the cross correlation between the forward and backward prediction errors.

As the denominator term is simply the least- squares estimate of the forward and backward errors, , so

is an estimate of the total squared error .

From the estimates of the AR parameters, the power spectrum estimate is given by :-

ADVANTAGES

High frequency resolutionStable AR modelComputationally efficient method

DISADVANTAGES

Spectral line splitting occurs at high SNRSpurious peaks Frequency bias

APPLICATIONS

Flood forecastingGeographical data processingRadar and sonarImagingSpeechRadio astronomyBiomedicineoceanography

REFERENCES

DIGITAL SIGNAL PROCESSING, 4TH EDITION BY JOHN G. PROAKIS.