Find the time function \(y(k T)\) corresponding to the following closed form \(\mathcal{Z}\)-transforms \(Y(z)\) :

(a) \(Y(z)=\frac{4 z}{z^{2}-1}\)

(b) \(Y(z)=\frac{2 z}{z^{2}-0.5 z-0.5}\)

(c) \(Y(z)=\frac{0.522 z^{2}+0.361 z-0.203}{z^{3}-2.347 z^{2}+1.797 z-0.449}\)

For each of these, use the following methods:

(i) Inverse transform method

(ii) Partial fraction expansion and use of \(\mathcal{Z}\)-transform table

(iii) Power series expansion