Frequency-domain identification of linear time-invariant systems under nonstandard conditions

This paper presents a frequency-domain identification method for parametric transfer function models of linear time invariant systems that takes into account the nonzero 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 for the system to reach a steady state so that measurements can begin. In the special case of free decay experiments the presented technique is a frequency-domain version of fitting exponentially damped sinusoids embedded in noise. The theory is illustrated by simulations and a real measurement example.