(d)
An LTI system with input $x(n)$ and output $y(n)$ is described by the
difference equation:
$\frac{5}{2}y[n-1] + y[n-2] = x[n] - x[n-1]$
(i) Derive the z-transfer function, $H(z)$ of the LTI system in partial
fraction form.
(4 marks)
(ii) State all possible ROCs for $H(z)$.
(3 marks)
(iii) For each possible ROC, state whether it corresponds to a
causal, anti-causal, or non-causal impulse response $h(n)$.
(3 marks)
(iv) Determine (write an algebraic expression for) the impulse
response $h(n)$ of the only stable system having the z-transfer
function, $H(z)$ derived in (i).
(3 marks)
