Consider a system whose input and output are related by the first-order differential equation (P2.33-1). Assume that the system satisfies the condition of final rest [i.e., if x(t) = 0 for t > t0, then y(t) = 0 for t > t0]. Show that this system is not casual. [Hint: Consider two inputs to the system, x1 (t) = 0 and x2(t) = et (u (t) — u (t – 1)), which result in outputs y1 (t) and y2 (t), respectively. Then show that y1 (t) ≠ y2 (t) for t < O.]
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