specfact

Scilab Function
Last update : April 1993

specfact - spectral factor

### Calling Sequence

  `[W0,L]=specfact(A,B,C,D)`

### Description

Given a spectral density matrix `phi(s)` :

                     -1                   -1
         R + C*(s*I-A) * B  +  B'*(-s*I-A') * C'  with R=D+D' > 0

`specfact` computes `W0` and `L` such that `W(s)=W0+L*(s*I-A)^-1*B` is a spectral factor of of `PHI(s)` , i.e.

`phi(s)=W'(-s)*W(s)`

### Examples

    A=diag([-1,-2]);B=[1;1];C=[1,1];D=1;s=poly(0,'s');
    W1=syslin('c',A,B,C,D);
    phi=gtild(W1,'c')+W1;
    phis=clean(ss2tf(phi))
    clean(phis-horner(phis,-s)');   //check this is 0...
    [A,B,C,D]=abcd(W1);
    [W0,L]=specfact(A,B,C,D);
    W=syslin('c',A,B,L,W0)
    Ws=ss2tf(W);
    horner(Ws,-s)*Ws

### See Also

`gtild` , `sfact` , `fspecg` ,

### Author

F. D.