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BURG METHOD PRESENTED BY :- Sarbjeet Singh NITTTR-Chandigarh
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CONTENTS INTRODUCTION BURG METHOD ADVANTAGES OF BURG METHOD DISADVANTAGES OF BURG METHOD APPLICATIONS
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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.
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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.
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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 :-
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BURG METHODForward error,Backward error,The least squares error is :-
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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.
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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 :
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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 .
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From the estimates of the AR parameters, the power spectrum estimate is given by :-
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ADVANTAGESHigh frequency resolutionStable AR modelComputationally efficient method
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DISADVANTAGES Spectral line splitting occurs at high SNR Spurious peaks Frequency bias
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APPLICATIONSFlood forecastingGeographical data processingRadar and sonarImagingSpeechRadio astronomyBiomedicineoceanography
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REFERENCESDIGITAL SIGNAL PROCESSING, 4TH EDITIONBY JOHN G. PROAKIS.
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