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arburg() - Signal Processing

```a = arburg(x,p) returns
the normalized autoregressive (AR) parameters corresponding to a model
of order p for the input array, x.
If x is a vector, then the output array, a,
is a row vector. If x is a matrix, then the parameters
along the nth row of a model
the nth column of x. a has p + 1 columns. p must
be less than the number of elements (or rows) of x.[a,e] = arburg(x,p) returns
the estimated variance, e, of the white noise input.[a,e,rc] = arburg(x,p) returns
the reflection coefficients in rc.```

Syntax

`a = arburg(x,p)[a,e] = arburg(x,p)[a,e,rc] = arburg(x,p)`

Example

```Parameter Estimation Using Burg's MethodOpen This ExampleUse a vector of polynomial coefficients to generate an AR(4) process by filtering 1024 samples of white noise. Reset the random number generator for reproducible results. Use Burg's method to estimate the coefficients.rng default

A = [1 -2.7607 3.8106 -2.6535 0.9238];

y = filter(1,A,0.2*randn(1024,1));

arcoeffs = arburg(y,4)

arcoeffs =

1.0000   -2.7743    3.8408   -2.6843    0.9360

Generate 50 realizations of the process, changing each time the variance of the input noise. Compare the Burg-estimated variances to the actual values.nrealiz = 50;

noisestdz = rand(1,nrealiz)+0.5;

randnoise = randn(1024,nrealiz);

for k = 1:nrealiz
y = filter(1,A,noisestdz(k) * randnoise(:,k));
[arcoeffs,noisevar(k)] = arburg(y,4);
end

plot(noisestdz.^2,noisevar,'*')
title('Noise Variance')
xlabel('Input')
ylabel('Estimated')

Repeat the procedure using arburg's multichannel syntax.realiz = bsxfun(@times,noisestdz,randnoise);

Y = filter(1,A,realiz);

[coeffs,variances] = arburg(Y,4);

hold on
plot(noisestdz.^2,variances,'o')

q = legend('Single channel loop','Multichannel');
q.Location = 'best';```