1.1.3    Model order selection

The main problem in all signal processing techniques is an automatic selection of the model order. To this end, a modified version of the Akaike Information Criterion (AIC) and the Minimum Description Length (MDL) traditionally used in parametric modelling of data [4, 9] are used by the QProny module. These criteria calculate the error between the model and the data samples, using all damped sinusoids produced as a result of parametric modelling. A model order, which corresponds to a minimum of some measure (e.g. AIC or MDL), is regarded as the best one.

Such an approach may lead to contradicting results and also often yields too high model orders. In order to overcome this problem the criteria have been modified in the following way. All the terms whose amplitudes are below 10^-3 are set to zero. Similar operation is carried out for all sinusoidal terms corresponding to the frequencies outside the band of interest. The first operation is called thresholding and the other is band-limiting. Both operations greatly improve the efficiency and consistency of model order selection.