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.TH frep2tf 4 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
frep2tf - transfer function realization from frequency response
.SH CALLING SEQUENCE
.nf
[h [,err]]=frep2tf(frq,repf,dg [,dom,tols,weight])
.fi
.SH PARAMETERS
.TP 10
frq
: vector of frequencies in Hz.
.TP
repf
: vector of frequency response
.TP
dg
: degree of linear system
.TP
dom
: time domain (\fV'c'\fR or \fV'd'\fR or \fVdt\fR)
.TP
tols
: a vector of size 3 giving the relative and absolute tolerance
and the maximum number of iterations (default values are \fVrtol=1.e-2; atol=1.e-4, N=10\fR).
.TP
weight
: vector of weights on frequencies
.TP
h
: SISO transfer function
.TP
err
: error (for example if \fVdom='c'\fR \fVsum(abs(h(2i*pi*frq) - rep)^2)/size(frq,*)\fR)
.SH DESCRIPTION
Frequency response to transfer function conversion. The order of \fVh\fR
is a priori given in \fVdg\fR which must be provided.
The following linear system is solved in the least square sense.
.nf
weight(k)*(n( phi_k) - d(phi_k)*rep_k)=0, k=1,..,n
.fi
where \fVphi_k= 2*%i*%pi*frq\fR when \fVdom='c'\fR and \fVphi_k=exp(2*%i*%pi*dom*frq\fR if not. If the \fVweight\fR vector is not given a default
penalization is used (when \fVdom='c'\fR).
A stable and minimum phase system can be obtained by using function \fVfactors\fR.
.SH EXAMPLE
.nf
s=poly(0,'s');
h=syslin('c',(s-1)/(s^3+5*s+20))
frq=0:0.05:3;repf=repfreq(h,frq);
clean(frep2tf(frq,repf,3))
Sys=ssrand(1,1,10);
frq=logspace(-3,2,200);
[frq,rep]=repfreq(Sys,frq); //Frequency response of Sys
[Sys2,err]=frep2tf(frq,rep,10);Sys2=clean(Sys2)//Sys2 obtained from freq. resp of Sys
[frq,rep2]=repfreq(Sys2,frq); //Frequency response of Sys2
xbasc();bode(frq,[rep;rep2]) //Responses of Sys and Sys2
[sort(trzeros(Sys)),sort(roots(Sys2('num')))] //zeros
[sort(spec(Sys('A'))),sort(roots(Sys2('den')))] //poles
dom=1/1000; // Sampling time
z=poly(0,'z');
h=syslin(dom,(z^2+0.5)/(z^3+0.1*z^2-0.5*z+0.08))
frq=(0:0.01:0.5)/dom;repf=repfreq(h,frq);
[Sys2,err]=frep2tf(frq,repf,3,dom);
[frq,rep2]=repfreq(Sys2,frq); //Frequency response of Sys2
xbasc();plot2d1("onn",frq',abs([repf;rep2])');
.fi
.SH SEE ALSO
imrep2ss, arl2, time_id, armax, frfit
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