Problem-2: The transfer function of an LTI system is $H(s) = \frac{s}{(s+2)(s^2+s+1)}$. Find the impulse-response $h(t)$ of the system. (Points: 20) Problem-3: An LTI system is described by the differential equation,
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We need to find the impulse response $h(t)$, which is the inverse Laplace transform of $H(s)$. Show more…
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Problem 1: (50 points) Consider a continuous LTI system, y(t), with impulse response h(t): 1. For 1 < t < 2, h(t) = 1 For 2 < t < 3, h(t) = 3 - t Otherwise, h(t) = 0 2. For 0 < t < 1, x(t) = 1 Otherwise, x(t) = 0 A) Find the response y(t) to the input x(t). B) Find the response y(t) to the input x(t) = { 2, -1 <= t < 0 1, 0 <= t < 1 0, Otherwise } Hint: A little thought can save you a lot of time. C) Determine if the system is: i) Causal ii) Stable Please explain your answers.
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