Frequency domain identification of linear time invariant systems under non-standard conditions

This paper presents a frequency domain identification method for parametric transfer function models of linear time invariant systems that takes into account the non-zero initial condition and/or the transient effects in the response of the system when excited by periodic or time limited signals. The method is useful for systems with large settling times where it takes too much time to wait measuring at the start of the experiment until the system reaches steady state. In the special case of free decay experiments the presented technique is a frequency domain version of fitting damped sinusoids embedded in noise. The theory is illustrated by simulations and a real measurement example.