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RobustFrfEstimate.m
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RobustFrfEstimate.m
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function varargout=RobustFrfEstimate(U,Y)
%
%Robust method for estimating a frequency response. Input data are periodic
%measured over several periods and repeated over several realisations
%(experiments).
%
%Input arguments
%
% U = FFT of input signals, size F x P x R. Rows are the frequencies at which
% the frf is estimated. Columns are the periods. Finial dimension for
% realisations.
% Y = FFT of output signal, size F x P x R similar to U
%
%Output arguments
% Gfrf=RobustFrfEstimate(U,Y)
% [Gfrf,stdG]=RobustFrfEstimate(U,Y)
% [Gfrf,stdG,stdGn]=RobustFrfEstimate(U,Y)
% [Gfrf,stdG,stdGn,stdGs]=RobustFrfEstimate(U,Y)
%
% Gfrf = Estimated frf, best linear approximation, size F x 1
% stdG = Standard deviation of the frf, total variance, size F x 1
% stdGn = noise standard deviation on the frf, size F x 1
% stdGs = stocahstic nonlinear distortion variance, size F x1%
%
%W.D.Widanage (01/05/2010) (@home)
[F,P,R]=size(U);
G_EveryPeriod=Y./U; %frf for each period and each realisation
Gfrf=mean(mean(G_EveryPeriod,2),3); %best linear approximate
varG=var(mean(G_EveryPeriod,2),0,3)/R; %variance over averaged periods scaled by R to give
%variance of Gfrf which is a statistic
%averaged over realisations
stdG=sqrt(varG);
varGn=mean(var(G_EveryPeriod,0,2),3)/(P*R); %variance over periods and the mean over realisations,
%scaled by P and R to make it
%relative to the statistic Gfrf
stdGn=sqrt(varGn);
varGs=R*(varG-varGn); % variance of stocastic nonlinear contributions
stdGs=sqrt(varGs);
switch nargout
case 1
varargout={Gfrf};
case 2
varargout={Gfrf,stdG};
case 3
varargout={Gfrf,stdG,stdGn};
case 4
varargout={Gfrf,stdG,stdGn,stdGs};
end
end