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.TH FREQ G "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
freq - frequency response
.SH CALLING SEQUENCE
.nf
[x]=freq(A,B,C [,D],f)
[x]=freq(NUM,DEN,f)
.fi
.SH PARAMETERS
.TP 15
A, B, C, D
: real matrices of respective dimensions \fVnxn, nxp, mxn, mxp\fR.
.TP
NUM,DEN
: polynomial matrices of dimension \fVmxp\fR
.TP
x
: real or complex matrix
.SH DESCRIPTION
\fVx=freq(A,B,C [,D],f)\fR returns a real or complex \fVmxp*t\fR matrix
such that:
.LP
\fVx(:,k*p:(k+1)*p)= C*inv(f(k)*eye-A)*B + D\fR.
.LP
Thus, for \fVf\fR taking values along the imaginary axis or
on the unit circle \fVx\fR is the continuous or discrete time
frequency response of \fV(A,B,C,D)\fR.
.LP
\fVx=freq(NUM,DEN,f)\fR returns a real or complex matrix \fVx\fR such
that columns \fVk*(p-1)+1\fR to \fVk*p\fR of \fVx\fR contain the matrix
\fVNUM(f(k))./DEN(f(k))\fR
.SH EXAMPLE
.nf
s=poly(0,'s');
sys=(s+1)/(s^3-5*s+4)
rep=freq(sys("num"),sys("den"),[0,0.9,1.1,2,3,10,20])
[horner(sys,0),horner(sys,20)]
//
Sys=tf2ss(sys);
[A,B,C,D]=abcd(Sys);
freq(A,B,C,[0,0.9,1.1,2,3,10,20])
.fi
.SH SEE ALSO
repfreq, horner
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