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2. Consider the following interconnection of four LTI systems where each system is described by its...

Question:

2. Consider the following interconnection of four LTI systems where each system is described by its impulse response, denoted
2. Consider the following interconnection of four LTI systems where each system is described by its impulse response, denoted by h,(t) for i E (1,2,3,4): i (t) hi(t) r(t) z(t) (t)h) но hs(t) alt) h4(t) 2(t) It is not hard, but is tedious, to show that an interconnection of LTI systems is LTI. Assuming this result, consider the system a(t) b(t) where r(t) and b(t) are the same signals in the two block diagrams and h(t) is the impulse response of this LTI system. Questions: (a) Compute h(t) in terms of hi(t), 2)(t), and h4(t) (b) If h1(t) * h1(t) = δ(t), give a simplified formula for h(t).

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