Consider the cascade of two continuous-time systems shown in Figure 6.24. The input-output characterization of system A is x(t) = dz(t)/dt. It is known that system B is linear and time-invariant, and that when x(t) = δ(t) its output is y(t)=e^ˆ’2tu(t), and that when the input is x(t) = u(t) the output is y(t) = 0.5(1ˆ’e^ˆ’2t) u(t). If z(t) is

(a) Use the given information about system B to calculate the output y(t) corresponding to x(t);

(b) Find the differential equation characterizing the overall system with input z(t) and output y(t).

Figure 6.24:

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1-t 0