Question

signals and systems

Question 1 (30%): Consider a LTI systern which is comprised of four subsystems whose impulse responses are hi(t), h2(t). ha(t), and ha(t). u(t) f(t) hi(t) h2(t) 13 ha(1) Where: hi (t) = δ(t + 1) h2(t) = 2(u(t)-u(t-1)] hs(t) = 201t-2) h1(t) = u(t + 2)-u(t) a) (8%) Compute the overall impulse response htotal(t) of the system comprised of hi(t), h2(t), hs(t), and h4(t). Sketch and write the expression for htotai(t) b) (4%) Is the total system causal or non-causal? Fully justify your answer. Hint: If you have not done part a) take htotal(t) = et(u(t + 1) _ u(t-1)] c) (4%) Is the total system BIBO stable? Fully justify your answer. Hint: If you have not done part a) take htotal(t) = e'[a(t + 1)-u(t-1)] d) (7%) Compute the zero state unit step response of the total system. Hint: If you have not done part a) take htota(t) = etlu(t + 1)-u(t-1)] /(t) = e-2t(u(t-4) _ u(1-5)]. htotal(t) = efti(t + 1)-u(t-1)] e) (7%) Compute the zero state response of the total system to the input Hint: If you have not done part a) take