BURG METHOD PRESENTED BY :- Sarbjeet Singh NITTTR-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 spectrumdensity can be estimated.
BURG METHODAn order-recursive least-squares lattice method ,based on the minimization of the forward andbackward errors in linear predictors, with theconstraint that the AR parameters satisfy theLevinson – 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 METHODForward 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 ofreflection coefficients is given by :By substituting above equation into Levinson – DurbinRecursion and performing minimization w.r.t. reflectionCoefficient ,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 estimateof 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 :-
ADVANTAGESHigh frequency resolutionStable AR modelComputationally efficient method
DISADVANTAGES Spectral line splitting occurs at high SNR Spurious peaks Frequency bias
APPLICATIONSFlood forecastingGeographical data processingRadar and sonarImagingSpeechRadio astronomyBiomedicineoceanography
REFERENCESDIGITAL SIGNAL PROCESSING, 4TH EDITIONBY JOHN G. PROAKIS.