simfou (Frequency Domain Identification Toolbox)

Generate simulated Fourier amplitudes from parameters and variances.

[x,y] = simfou(pdat,freqv,x0,vdat)
[x,y] = simfou(pdat,freqv,x0,vdat,expno)

Description

simfou generates simulated Fourier amplitudes (and perhaps also a Fourier file) for elis. The parameters of the transfer function are given in the vector pdat (see exppar), or in a file if pdat is a string. The frequencies are given in the vector freqv. The input amplitudes are given in the vector x0.

The variances are defined by vdat: if this is an 1-by-2 or 1-by-3 vector, its elements are taken as constant input and output variances (and perhaps the input-output covariance). If this is an N-by-2 or N-by-3 array, the variance vectors (and perhaps the covariance vector) are formed from the two (or three) columns. If this is a vector, the variance and covariance vectors are obtained using impvar. If it is a string, the variance file is looked for.

expno is the number of experiments to be generated.

Default Argument Values

expno = 1

Examples

The convergence properties of elis can be checked by running it several times on data simulated using a known transfer function:

freqv = [100:50:1000]';
num = 1; denom = [1e-6,1e-3,1];
pdat = exppar('s',num,denom);
vdat = [0.01,0.001];
[x,y] = simfou(pdat,freqv,[],vdat);
ploteltf(pdat,'',[freqv,x,y])
for k = 1:5
   [x,y] = simfou(pdat,freqv,[],vdat);
    Fdat = [freqv,x,y];
    [pvect,fit,Cp] = elis(Fdat,vdat,['s',0,2],[],'',100);
    pause
end

Diagnostics

The routine checks the validity of the variance values and their compatibility with the frequency vector, and sends an error message when incompatibility is found.

When the system is unstable (the real part of a root is

0 in the s-domain or the absolute value of a root is

1 in the z-domain), a warning message is sent:

WARNING! The given system is unstable in simfou

but the simulated values will be calculated in the frequency domain.

Algorithm

simfou calculates the input and output amplitude vectors, and adds zero-mean complex Gaussian noise with the given variances and properly set covariance to them.