Suppose that a causal lti discrete-time system has the impulse response h1(n) = 0.5 nu(n) (10) and that an anti-causal lti discrete-time system has the impulse response h2(n) = 3nu(−n − 1). (11)

(a) if these two systems are connected in cascade, what is the transfer function h(z) and roc of the total system?
(b) find the impulse response h(n) of the total system, show your derivation, and make a stem plot of h(n) using matlab.
(c) consider the stable inverse g(z) = 1/h(z). find the roc of g(z) and g(n). make a stem plot g(n) using matlab. verify in matlab that it is an inverse by convolving g(n) and h(n) to get δ(n). (you will need to truncate h and g first as they are infinite in length.)