The poles of the Laplace transform X(s) of an analog signal x(t) are p_1,2 =−1 ± j1, p₃ = 0, p_4,5 = ±j1, and there are no zeros. If we use the transformation z = e^sTs with T_s = 1,

(a) Determine where the given poles are mapped into the z-plane. Carefully plot the poles and zeros of the analog and the discrete-time signals in the Laplace and the z-planes.

(b) How would you determine if these poles are mapped inside, on or outside the unit disk in the z-plane? Explain.