PROPERTIES OF THE FSF MODEL WITH FAST SAMPLING

The properties of the FSF model with respect to choice of the sampling interval are summarized in the theorem below. 

Proof Taking the Fourier transform of h t) gives the continuous-time frequency response of the process as 

If we choose to evaluate the frequency response up to the Nyquist frequency, radians/time, in increments of then we can write for wi = radians/time, I = 0, 1, 2. 

Example 4.1. This example compares a discrete-time, rational transfer function model with the FSF model in terms of the effect of sampling rate on the model parameters. Consider a third order system with time delay given by 

The FSF model parameters correspond to the frequency rraponse of the discrete-time transfer function models presented in Equations (4.12)-(4.14) at three sets of frequencies  

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