burg method

15
BURG METHOD PRESENTED BY :- Sarbjeet Singh NITTTR-Chandigarh

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Page 1: Burg method

BURG METHOD

PRESENTED BY :-Sarbjeet SinghNITTTR-Chandigarh

Page 2: Burg method

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 spectrum density can be estimated.

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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.

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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 METHOD

Forward 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 of reflection coefficients is given by :

By substituting above equation into Levinson – Durbin Recursion and performing minimization w.r.t. reflection Coefficient ,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 estimate of 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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ADVANTAGES

High frequency resolutionStable AR modelComputationally efficient method

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DISADVANTAGES

Spectral line splitting occurs at high SNRSpurious peaks Frequency bias

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APPLICATIONS

Flood forecastingGeographical data processingRadar and sonarImagingSpeechRadio astronomyBiomedicineoceanography

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REFERENCES

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

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