Documentation of trf

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Function Synopsis

[G,PV]=trf(th,nnu,w,nny)

Help text

TRF    Computes a model's frequency function.

   G = trf(TH)  or  [G,NSP] = trf(TH)

   TH: A matrix defining a model, as described in HELP THETA
   G is returned as the transfer function estimate, and NSP (if specified)
   as the noise spectrum, corresponding to the model TH. These matrices
   contain also estimated standard deviations, calculated from the
   covariance matrix in TH, and are  of the standard frequency function
   format (see HELP FREQFUNC).If TH describes a time series, G is returned
   as its spectrum.

   If the model TH has several inputs, G will be returned as the transfer
   functions of selected inputs # j1 j2 .. jk by
   G = trf(TH,[j1 j2 ... jk])  [default is all inputs]. The functions
   are computed at 128 equally spaced frequency-values between 0(excluded)
   and pi/T, where T is the sampling interval specified by TH. The func-
   tions can be computed at arbitrary frequencies w RAD/S, (a row vector,
   generated e.g. by LOGSPACE) by G = trf(TH,ku,w). The transfer function
   can be plotted by BODEPLOT. bodeplot(trf(TH)) is a possible
   construction. If the model TH has several outputs, G will be returned
   as the frequency function at selected outputs ky (a row vector) by
   G=trf(TH,ku,w,ky); (Default is all outputs). See also TH2FF.

Cross-Reference Information

Listing of function trf

function [G,PV]=trf(th,nnu,w,nny)

%   L. Ljung 7-7-87, 1-25-92
%   Copyright (c) 1986-98 by The MathWorks, Inc.
%   $Revision: 2.3 $  $Date: 1997/12/02 03:40:22 $

T=gett(th);

% *** Set up default values ***
if nargin<4, nny=[];end
if nargin<3, w=[];end
if nargin<2 , nnu=[];end
if T>0,wdef=pi*[1:128]/128/T;
else wdef=logspace(log10(pi/abs(T)/100),log10(10*pi/abs(T)),128);
end
if isempty(w),w=wdef;end
if length(w)==1, if w<0, w=wdef;end,end
[nrw,ncw]=size(w);if nrw>ncw, w=w.';end
if T>0 & any(w>pi/T),disp('WARNING: Frequencies in w exceed the Nyquist frequency!'),end

if isempty(nnu), nnu=1:th(1,3);end
if length(nnu)==1,if nnu==0,nnu=[];end,if nnu<0,nnu=1:th(1,3);end,end
if isthss(th), if nargout==1, eval('G=trfss(th,nnu,nny,w);')
             else eval('[G,PV]=trfss(th,nnu,nny,w);'),end,return,end
% *** Compute the model polynomials and form the basic
%      matrix of frequencies ***
nu=th(1,3);
[a,b,c,d,f]=th2poly(th);
na=th(1,4);nb=th(1,5:4+nu);nc=th(1,5+nu);nd=th(1,6+nu);
nf=th(1,7+nu:6+2*nu);nk=th(1,7+2*nu:6+3*nu);nnd=na+sum(nb)+nc+nd+sum(nf);
nm=max([length(a)+length(f)-1 length(b) length(c) length(d)+length(a)-1]);
   i=sqrt(-1);
if T>0,OM=exp(-i*[0:nm-1]'*w*T);end
if T<=0,
OM=ones(1,length(w));
for kom=1:nm-1
OM=[OM;(i*w).^kom];
end
[nrth,ncth]=size(th);
if nrth>3+nnd,delays=th(nrth,1:length(nk));else delays=zeros(1,length(nk));end
end

% *** Compute the transfer function(s) GC=B/AF ***

sc=1;kf=0;ks=0;nrc=length(w)+1;
for k=nnu
    G(1,sc:sc+2)=[100+k,k,k+20];
    G(2:nrc,sc)=w';
     gn=conv(a,f(k,:));
if T>0,indb=1:length(b(k,:));indg=1:length(gn);
else indb=length(b(k,:)):-1:1; indg=length(gn):-1:1;end
     GC=(b(k,:)*OM(indb,:))./(gn*OM(indg,:));
    G(2:nrc,sc+1)=abs(GC');
    G(2:nrc,sc+2)=phase(GC)'*180/pi;
    if T<0, G(2:nrc,sc+2)=G(2:nrc,sc+2)-w'*delays(k)*180/pi;end
sc=sc+3;
end
if nargout==1 & nu>0, return, end

% *** Compute the transfer function H=C/AD ***

hn=conv(a,d);
if T>0,indc=1:length(c);indh=1:length(hn);
else indc=length(c):-1:1; indh=length(hn):-1:1;end
H=(c*OM(indc,:))./(hn*OM(indh,:));
PV(1,1:3)=[100,0,50];
PV(2:nrc,1)=w';
PV(2:nrc,2)=abs(T)*(abs(H).^2)'*th(1,1);

if isempty(nnu) G=PV;end