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# lattn

recursive solution of normal equations

### Syntax

`[la,lb]=lattn(n,p,cov)`

### Arguments

n

maximum order of the filter

p

fixed dimension of the MA part. If `p= -1`, the algorithm reduces to the classical Levinson recursions.

cov

matrix containing the `Rk`'s (`d*d` matrices for a d-dimensional process).It must be given the following way

la

list-type variable, giving the successively calculated polynomials (degree 1 to degree n),with coefficients Ak

### Description

solves recursively on `n` (`p` being fixed) the following system (normal equations), i.e. identifies the AR part (poles) of a vector ARMA(n,p) process,

where {`Rk;k=1,nlag`} is the sequence of empirical covariances.

### Example

```//Generate the process
t1=0:0.1:100;
y1=sin(2*%pi*t1)+sin(2*%pi*2*t1);
y1=y1+rand(y1,"normal");

//Covariance of y1
nlag=128;
c1=corr(y1,nlag);
c1=c1';

//Compute the filter with maximum order=15 and p=1
n=15;
[la1,sig1]=lattn(n,1,c1);

//Compare result of poles with p=-1 and with levin function
[la2,sig2]=lattn(n,-1,c1);
for i=1:n
s2=roots(la2(i));
s2=log(s2)/2/%pi/.1; //estimated poles
s2=gsort(imag(s2));
s2=s2(1:i/2);
end;
[la3,sig3]=levin(n,c1);
for i=1:n
s3=roots(la3(i));
s3=log(s3)/2/%pi/.1; //estimated poles
s3=gsort(imag(s3));
s3=s3(1:i/2);
end;```

### See also

• levin — Toeplitz system solver by Levinson algorithm (multidimensional)
• lattp — Identification of MA part of a vector ARMA process

### Comments

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