Question: An analog system has the following input-output relation, and zero otherwise. The input is x(t) and y(t) is the output. (a) Is this system LTI?

An analog system has the following input-output relation,

rl+T/2 y(t) I-T/2 ip(1)x

and zero otherwise. The input is x(t) and y(t) is the output.

(a) Is this system LTI? If so, can you determine without any computation the impulse response of the system? Explain.

(b) Is this system causal? Explain.

(c) Find the unit-step response s(t) of the given system and from it find the impulse response h(t). Is this a BIBO stable system? Explain.

(d) Find the response due to a pulse x(t) = u(t) ˆ’ u(t ˆ’ 1).

rl+T/2 y(t) I-T/2 ip(1)x

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