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P. Van gucht and A. Bultheel
Using orthogonal rational functions for system identification
We establish two different algorithms that return an approximation of
a system transfer function if input and ouput data are given.
The model we use, is written as a linear combination of
orthogonal rational functions (ORF),
with respect to a weight function which depends on the input data.
In the first algorithm a continous inner product leads to a least squares problem with a well conditioned matrix. Due to the fact that the data is finite we cannot solve the least squares problem recursively. This problem can be solved if we use a discrete inner product. For this approach however we need the z-transform of the input and output in some points.