Determine the original analog transfer function corresponding to [H(z)=frac{2 z^{2}-left(mathrm{e}^{-0.2}+mathrm{e}^{-0.4} ight) z}{left(z-mathrm{e}^{-0.2} ight)left(z-mathrm{e}^{0.4} ight)}] assuming that the

Determine the original analog transfer function corresponding to

\[H(z)=\frac{2 z^{2}-\left(\mathrm{e}^{-0.2}+\mathrm{e}^{-0.4}\right) z}{\left(z-\mathrm{e}^{-0.2}\right)\left(z-\mathrm{e}^{0.4}\right)}\]

assuming that the following method was employed in the analog to discrete-time mapping, with \(T=2\) :

(a) Impulse invariance method.

(b) Bilinear transformation method.