The input-output equation for an analog averager is

let x(t) = e^jΩ0t. Since the system is LTI then the output should be y(t) = e^jΩ0t H(jΩ₀).

(a) Find the integral for the given input and then compare it with the above equation to find H(jΩ₀), the response of the averager at frequency ­0.

(b) Find the impulse response h(t), from the input-output equation, and its Laplace transform H(s) to verify that H(jΩ₀) obtained above is correct.

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