Generalized Frequency Response Function

Considering a NARX model, we can write the model as:

To obtain the of a NARX model, the function modelLags and then the function findCCoefficients are used.

After having the , the GFRF of degree n of this model can be obtained recursively using the expression below found by Peyton-Jones, J. C and Billings, S. A. (1989).

where:

This recursive function was implemented using the Symbolic Math Toolbox of Matlab in the function buildHn, which returns each H_n.

As for the GFRF computation just the dynamic components of the model are considered, if the NARX model has a constant term, it must be removed before the GFRF evaluation. This is done with the function removeConstant.