Consider the cascade of two LTI systems, see Figure 3.21, where the input of the cascade is
Question:
(a) The input/output characterization of the first system is x(t) = dz(t)/dt. Find the corresponding output x(t)of the first system.
(b) It is known that for the second system when the input is δ(t)the corresponding output is e2tu(t), and that when the input is u(t)the output is 0.5(1 e 2t) u(t). Use this information to calculate the output y(t)of the second system when the input is x(t)found above.
(c) Determine the ordinary differential equation corresponding to the cascaded system with input z(t)and output y(t).
Figure 3.21:
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