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# Burg method

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### Burg method

1. 1. BURG METHOD PRESENTED BY :- Sarbjeet Singh NITTTR-Chandigarh
2. 2. CONTENTS INTRODUCTION BURG METHOD ADVANTAGES OF BURG METHOD DISADVANTAGES OF BURG METHOD APPLICATIONS
3. 3. 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.
4. 4. BURG METHODAn 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.
5. 5. 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 :-
6. 6. BURG METHODForward error,Backward error,The least squares error is :-
7. 7. 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.
8. 8. 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 :
9. 9.  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 .
10. 10.  From the estimates of the AR parameters, the power spectrum estimate is given by :-
11. 11. ADVANTAGESHigh frequency resolutionStable AR modelComputationally efficient method
12. 12. DISADVANTAGES Spectral line splitting occurs at high SNR Spurious peaks Frequency bias
13. 13. APPLICATIONSFlood forecastingGeographical data processingRadar and sonarImagingSpeechRadio astronomyBiomedicineoceanography
14. 14. REFERENCESDIGITAL SIGNAL PROCESSING, 4TH EDITIONBY JOHN G. PROAKIS.