Strictly Proper Transfer Functions

An even stricter criterion than Proper Transfer Function

We can decompose the proper transfer function as:

$$G(s)=G_{sp}(s)+G_{\infty }$$

Where $G_{\infty }={\lim }_{\omega \to \infty }|G(jw)|$ For a strictly proper transfer function this will always be $0$.

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Meaning that the following function is proper:

$$h(s)=\frac{s+1}{s^2-2s+1}$$