Accurate Frequency Domain Identification of ODEs with Arbitrary Signals

The difficulty in frequency domain identification is that frequency components of arbitrary inputs and outputs are not related by the system's transfer function if signals are windowed. When rectangular windows are used, it is well known that this difference is related to transient effects that can be estimated alongside the systems' parameters windows. In this work, we generalize the approach for arbitrary windows, showing that signal windowing introduces additional terms in the system's equations. The formalism is useful for frequency-domain input-output analysis of a system, and also for system identification. For the latter application, the approach considerably reduces aliasing effects and allows the computation of the associated correction terms, reducing the number of parameters that need to be estimated. The system identification approach has features of the modulating-function technique, filtering out the effects of initial conditions while retaining the spectral interpretation of frequency-domain methods.