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.TH specfact 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
specfact - spectral factor
.SH CALLING SEQUENCE
.nf
[W0,L]=specfact(A,B,C,D)
.fi
.SH DESCRIPTION
Given a spectral density matrix \fVphi(s)\fR:
.nf
-1 -1
R + C*(s*I-A) * B + B'*(-s*I-A') * C' with R=D+D' > 0
.fi
\fVspecfact\fR computes \fVW0\fR and \fVL\fR such
that \fVW(s)=W0+L*(s*I-A)^-1*B\fR is a
spectral factor of of \fVPHI(s)\fR, i.e.
.LP
\fVphi(s)=W'(-s)*W(s)\fR
.SH EXAMPLE
.nf
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
.fi
.SH SEE ALSO
gtild, sfact, fspecg
.SH AUTHOR
F. D.
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