The system function of a discrete-time system is

(a) Assume that this discrete-time filter was designed by the impulse invariance method with T_d = 2; i.e., h[n] = 2h_c(2n), where h_c(t) is real. Find the system function H_c(s) of a continuous-time filter that could have been the basis for the design. Is your answer unique? If not, find another system function H_c(s).

(b) Assume that H(z) was obtained by the bilinear transform method with T_d = 2. Find the system function H_c(s) that could have been the basis for the design. Is your answer unique? If not, find another H_c(s).

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H(2) = 1-e-02;-1 1-e-04 -1