Example: Leaky Integrator

$$\begin{eqnarray*} H_a(s) &=& \frac{1}{s+\epsilon } \;\longrightarrow\; H_d(z) \;=\;\frac{1}{\frac{1+\alpha}{T}\frac{1-z^{-1}}{1+\alpha\,z^{-1}}+\epsilon }\\ [5pt] &=& g \frac{1+\alpha z^{-1}}{1-pz^{-1}},\quad \zbox{p = \frac{1-\alpha\frac{\epsilon T}{1+\alpha}}{1+\frac{\epsilon T}{1+\alpha}}}, \quad g = \frac{T}{1+\alpha+\epsilon T} \end{eqnarray*}$$