elis2tha, tha2elis (Frequency Domain Identification Toolbox)

Model conversion from/to the theta-format of the System Identification Toolbox

theta = elis2tha(pdat,cdat,varet)
theta = elis2tha(pdat,cdat,varet,numn,denomn)
[num,denom,delay,fs] = tha2elis(theta)
[num,denom,delay,fs,vary,ccovar] = tha2elis(theta,N,freqv)

Description

These are the two routines which convert models of the Frequency Domain System Identification Toolbox from/to the System Identification Toolbox. pdat is the parameter vector in ELiS (see exppar), or the name of a parameter file. cdat is the covariance matrix of the parameters if it is an array (the rows and columns of the fixed parameters should contain zeros), or the covariance vector (see expcov), or the name of the covariance file. cdat may be empty, if the covariances are not available.

varet is the variance of the time domain noise, reduced to the output of the system, without noise shaping.

If the input noise is zero, and the variances of the real and of the imaginary parts of the complex amplitudes are uniformly equal to vary in the N-point spectrum, varet should be calculated as: varet = 2/N*vary, and numn and denomn need not be given.

numn and denomn are the numerator and the denominator of the observation noise shaping filter (see "Model Conversions from/to the System Identification Toolbox" in the User's Guide). If the frequency domain noise shape is fitted by the noise shaping filter:

and C corresponds to numn, D to denomn, the value of varet should be 2/N. The sampling frequency for the noise shaping filters is the same as that of the parameter vector.

When transforming models from the theta-format of the System Identification Toolbox, theta is the array of the theta-format to be converted, and N is the number of FFT points (for the calculation of vary only). vary is a scalar if C(z)

D(z)

1, and a vector if the noise is not white. freqv is the vector of frequencies where the variances are to be calculated. If vary is not required, N and freqv are not necessary.

The output arguments of tha2elis are as follows: num is the numerator, denom is the denominator of the transfer function, delay is the additional delay in the model, fs is the sampling frequency, vary is the vector of frequency domain variances of the output complex amplitudes at the frequencies in freqv (or just the frequency domain variance if this is constant), and ccovar is the covariance matrix of the vector [num,denom,delay].

Default Argument Values

numn = 1, denomn = 1

Examples

theta = elis2tha('inpchanz.pbn','inpchanz.cbn',2/256*1e-9);
[num,denom,delay,fs] = tha2elis(theta);

Diagnostics

As it is discussed in "Model Conversions from/to the System Identification Toolbox" in the User's Guide, the covariances can usually be converted only by using linear approximation of a ratio. This is done automatically by the conversion routines, but if approximation was applied, a warning message is sent:

WARNING: variance of denom(1) is not zero in elis2tha

WARNING: ccovar will be approximated in tha2elis

If in elis2tha the variance of denom(1) is too large, that is, larger than 0.2*denom(1)^2, the calculated variances are useless. In this case an error message is sent:

var(denom(1)) is too large

It is checked in tha2elis whether the approximated covariances are plausible. If not, the warning message is:

WARNING: In tha2elis the approximated covariances are too large

elis2tha calls poly2th or mktheta, and tha2EliS calls th2poly or polyform, thus the System Identification Toolbox must be installed.