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 tilde operation
• sfact discrete time spectral factorization
• fspecg stable factorization of continuous time dynamical systems