System Identification Toolbox

Initial States for Frequency Domain Data

The calculations using frequency-domain data essentially assume that the underlying time-domain data is periodic. Otherwise treating convolutions as multiplications in the frequency domain creates end-effect errors. Therefore initial conditions are as important for frequency-domain data as for time-domain data. The proper initial conditions in the frequency domain are those that make up for deviations in periodicity of the original data.

From a formal point of view, these initial conditions can be handled quite analogously to the time-domain case. They can be taken as zero, which is the correct choice if indeed the original data was periodic. They can also be estimated and backcast. Therefore the values of the property InitialState can assume the same values, 'zero', 'estimate', 'backcast', and 'auto', as in the time-domain case.

Note, again, that the estimated value, x0, is tied to the data set for which it was estimated. In particular, you should not make any time-domain interpretation of it in case it was estimated using frequency-domain data.

Initial State

The Estimated Parameter Covariance Matrix