Frequency weighted subspace based system identification in the frequency domain

Frequency weighting capabilities are introduced in a subspace based frequency domain identification algorithm. Weighting matrices constructed from the impulse response of weighting filters are used to weight a Hankel matrix prior of deriving the signal subspace by the singular value decomposition. The resulting algorithm is shown to asymptotically produce models which are the frequency weighted balanced truncation of the identified system. An illustrative example shows the applicability of the method for finite data.