G(s)= $\frac{1}{s^{2} + \sqrt{2}s + 1}$ |$\ S - \rightarrow A\frac{1 - z^{- 1}}{1 + z^{- 1}}$ = A$\frac{1 - \frac{1}{z}}{1 + \frac{1}{z}} = \ \ $A$\frac{\frac{z - 1}{z}}{\frac{z + 1}{z}}\ $= A$\frac{z - 1}{z + 1}$
G(s) =$\frac{1}{\left( A\frac{1 - z^{- 1}}{1 + z^{- 1}} \right)^{2} + \sqrt{2\ }A\frac{1 - z^{- 1}}{1 + z^{- 1}} + 1}$ = $\frac{1}{A^{2}\frac{z^{2} - 2z + 1}{z^{2} + 2z + 1} + \sqrt{2\ }A\frac{z - 1}{z + 1} + 1}$ / * $\frac{z^{2} + 2z + 1}{z^{2} + 2z + 1}$
G(s) = $\frac{z^{2} + 2z + 1}{A^{2}\left( z^{2} - 2z + 1 \right) + \sqrt{2\ }A(\left( z - 1 \right)*(z + 1)) + z^{2} + 2z + 1}$
G(s) = $\frac{z^{2} + 2z + 1}{A^{2}\left( z^{2} - 2z + 1 \right) + \sqrt{2\ }A*\left( z^{2} - 1 \right) + z^{2} + 2z + 1}$