3) Determine the differential equation corresponding to a system with transfer function as follows in the Laplace (complex-frequency) domain: 1 H(s) 0.15 +1 4) 5) Then, find its response to the unit step input signal with zero initial conditions. Using sampling rate of 40 samples per second find a discrete-time transfer function in the Z-Transform domain and the corresponding difference equation using the backward difference method. 6) Using sampling rate of 40 samples per second find a discrete-time transfer function in the Z-Transform domain and the corresponding difference equation using the forward difference method. 7) Find the approximate unit step response of the discrete-time systems in problems 5 and 6 and compare with the one from problem 4 at the sampling instants.

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