Question Three: The system function of a discrete-time system is 2 H(z) = 1-e-0.22-1 1 1-e-0.12-1 a) Assume that this discrete-time filter was designed by the impulse invariance method with T = 2, i.e. h[n] = 2hc(2n), where h(t) is a real-valued impulse response of a continuous-time filter. Find the system function He(s) of a continuous-time filter hc(t) that could have been used for this design. (8 marks) b) Assume that H(z) was obtained by the bilinear transformation method with T = 2. Find the system function Ho(s) of a continuous-time filter that could have been used for this design. (8 marks) c) Suppose that H₁(2), H2(2), and H(2) are transformed versions of continuous-time systems Ha(s), H2(s), and He(s), respectively. Which one of the two methods, i.e. impulse invariance, bilinear transformation, both, or neither, will guarantee that = H(2) H₁(2)H2(2) whenever He(s) = He1(s)H2(s)? Justify your answer. (9 marks) (Total: 25 marks)