(a) Find \(e(0), e(1)\), and \(e(10)\) for

\[E(z)=\frac{0.8}{z(z-0.6)} \]

using the inversion formula.

(b) Check the value of \(e(0)\) using the initial-value property.

(c) Check the values calculated in part (a) using partial fractions.

(d) Find \(e(k)\) for \(k=0,1,2,3\), and 4 if \(z[e(k)]\) is given by

\[E(z)=\frac{1.98 z}{\left(z^{2}-0.9 z+0.9ight)(z-0.8)\left(z^{2}-1.2 z+0.27ight)}\]

(e) Find a function \(e(t)\) which, when sampled at a rate of \(10 \mathrm{~Hz}(T=0.1 \mathrm{~s})\), results in the transform \(E(z)=2 z /(z-0.6)\).

(f) Repeat part (e) for \(E(z)=2 z /(z+0.6)\).

(g) From parts (e) and (f), what is the effect on the inverse \(z\)-transform of changing the sign on a real pole?