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function [num,den]=frfit(w,fresp,order,weight)
//Calling sequence:
//[num,den]=frfit(w,fresp,r,weight)
//sys=frfit(w,fresp,r,weight)
//
// w: vector of frequencies in Hz
// fresp: vector of frequency responses at these frequencies.
// weight: vector of weights given to each point
//
// Fits frequency response data points by a bi-stable transfer
// function
// G(s) = num(s)/den(s)
// of order r.
// freq(num,den,%i*w) should be close to fresp
//
// changing frequencies to rad/s
// Copyright INRIA
w=2*%pi*w;
[LHS,RHS]=argn(0);
if RHS==3
weight=ones(w);
end
w=w(:);fresp=fresp(:);weight=weight(:);
Mean=sum(fresp)/size(fresp,'*');
if max(abs(fresp-Mean)) < .1*max(abs(fresp))
num=real(Mean); den=1; return
end
order1=order+1;npts=length(w);wmed=1;
if RHS < 4 then
weight=ones(npts,1);
end
M0=zeros(order+1,1); M1=M0;
M0(1)=1; M1(2)=1; M=[M0 M1];
for i=1:order-1,
Mt=2*[0;M1(1:order)]-M0;
M=[M Mt];
M0=M1; M1=Mt;
end
k=2;km=1;
sl0=round((log10(abs(fresp(k)))-log10(abs(fresp(km))))/(log10(w(k))-log10(w(km))));
k=npts;km=k-1;
slinf=round((log10(abs(fresp(k)))-log10(abs(fresp(km))))/(log10(w(k))-log10(w(km))));
if slinf>0&slinf<20
w=[w;[10;15]*w(npts)];
fresp=[fresp;[1;1]*10^slinf*abs(fresp(npts))];
weight=[weight;1;1];
npts=npts+2;
slinf=0;
end
if sl0>0
mindeg=max(abs(sl0),-slinf+abs(sl0));
else
mindeg=max(abs(sl0),-slinf);
end
if mindeg > order
warning('Filter order too small');
sl0=sign(sl0)*min(order,sl0);
if sl0>0 then
slinf=-(order-abs(sl0));
else
end
slinf=-order;
end
jw=%i*w;mag=abs(fresp);t0=ones(npts,1); t1=jw;A=[ones(npts,1),jw];
for i=1:order-1,
t=2*jw.*t1-t0;
A=[A,t];
t0=t1; t1=t;
end
Aom=A;
//A=[A -diag(fresp)*A];AA=A;om0=w;
A=[A, -fresp*ones(1,size(A,2)).*A];AA=A;om0=w;
Acons=[]; ycons=[];
if sl0<=0
Acons=[Acons; zeros(-sl0,order1) M(1:-sl0,:);...
M(1,:) -(mag(1)*w(1)^(-sl0))*M(1-sl0,:)];
ycons=[ycons; zeros(-sl0+1,1)];
elseif sl0>0
Acons=[Acons; M(1:sl0,:) zeros(sl0,order1);...
M(1+sl0,:)*w(1)^sl0 -mag(1)*M(1,:)];
ycons=[ycons; zeros(sl0+1,1)];
end
Acons=[Acons;zeros(1,order1) M(order1,:)];ycons=[ycons;1];
if slinf<=0
Acons=[Acons; M(order1+slinf:order1,:) zeros(-slinf+1,order1)];
ycons=[ycons; mag(npts)*w(npts)^(-slinf); zeros(-slinf,1)];
end
[nc,nv]=size(Acons);
if nc >= nv
x=Acons\ycons;
else
indin=1:nv; indout=[];
for i=1:nc,
if i<nc,
[m,ix]=max(abs(Acons(i:nc,i:nv)));ix=ix(2);
else
[m,ix]=max(abs(Acons(i:nc,i:nv)));
end
Acons(:,i:nv)=[Acons(:,i+ix-1) Acons(:,[i:i+ix-2,i+ix:nv])];
indout=[indout,indin(ix)];indin=indin([1:ix-1,ix+1:nv-i+1]);
x=Acons(i:nc,i); Atmp=Acons(i:nc,i+1:nv); ytmp=ycons(i:nc);
if x(1)>=0
sgn=1;
else
sgn=-1;
end
aux=sgn*sqrt(x'*x);x(1)=x(1)+aux;nx2=.5*x'*x;
Atmp=[[-aux;zeros(nc-i,1)] Atmp-x*((x'*Atmp)/nx2)];
ytmp=ytmp-x*((x'*ytmp)/nx2);
Acons(i:nc,i:nv)=Atmp;ycons(i:nc)=ytmp;
end
perm=[indout indin];
Ac1=Acons(:,1:nc); Ac2=Acons(:,nc+1:nv);
A=A(1:npts,:);
A=[real(A);imag(A)];
A=A(:,perm);
A1=A(:,1:nc); A2=A(:,nc+1:nv);
A=A2-A1*(Ac1\Ac2);
y=-A1*(Ac1\ycons);
fweight=ones(npts,1);
ind=find(w > 10);
fweight(ind)=((1) ./(w(ind)^order));
ind=find(w < .01);
fweight(ind)=(1./(w(ind)^min(0,sl0)))';
fweight=weight.*fweight;
//Wt=diag([fweight;fweight]);
//x=pinv(Wt*A)*(Wt*y);
//x=pinv([fweight;fweight]*ones(1,size(A,2)).*A)*(vvv.*y);
vvv=[fweight;fweight];
x=(vvv*ones(1,size(A,2)).*A)\(vvv.*y);
x=[Ac1\(ycons-Ac2*x);x];
[s,perm]=sort(-perm);s=-s;
x=x(perm);
nresp=Aom*x(1:order1); dresp=Aom*x(order1+1:2*order1);
relerr=abs(abs(nresp./dresp)./mag-1)';
for kk=1:prod(size(relerr));relerr(kk)=min(1,relerr(kk));end
relerr=relerr(:);
ind=find(mag < .01); relerr(ind)=relerr(ind)*.3;
ind=find(relerr>.5);
if ind<>[]
fweight(ind)=( exp(relerr(ind)*log(10)) ).*fweight(ind);
end
//Wt=diag([fweight;fweight]);
//x=pinv(Wt*A)*(Wt*y);
//x=pinv([fweight;fweight]*ones(1,size(A,2)).*A)*(vvv.*y);
x=([fweight;fweight]*ones(1,size(A,2)).*A)\(vvv.*y);
x=[Ac1\(ycons-Ac2*x);x];x=x(perm);
end
a=x(1:order1); b=x(order1+1:2*order1);
num=fliplr((M*a)');den=fliplr((M*b)');
err=abs(AA*x);
num=num(-slinf+1:order1);
junk=poly(fliplr(num),'s','c')
rn=roots(junk); rn=-abs(real(rn))+%i*imag(rn);
l=length(rn);
for k=1:l
if real(rn(k))>-1e-3
rn(k)=-1.e-3+%i*imag(rn(k))
end
end
junk=poly(fliplr(den),'s','c');
dn=roots(junk); dn=-abs(real(dn))+%i*imag(dn);
l=length(dn);
for k=1:l
if real(dn(k))>-1e-3
dn(k)=-1.e-3+%i*imag(dn(k))
end
end
polyrn=poly(fliplr(rn),'s');
polydn=poly(fliplr(dn),'s');
num=real(num(1)*polyrn);
den=real(den(1)*polydn);
if LHS==1
num=syslin('c',num/den)
end
function m=fliplr(m)
//Utility fct
[p,q]=size(m);
m=m(:,q:-1:1);
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