An analog averager is characterized by the following relationship where x(t) is the input and y(t) the

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An analog averager is characterized by the following relationship

dy(t) dt —D 0.5[x(t) — х(t — 2)]

where x(t) is the input and y(t) the output. If x(t) = u(t) ˆ’ 2u(t ˆ’ 1) + u(t ˆ’ 2),

(a) find the Fourier transform of the output Y(Ω);

(b) find y(t) from Y(Ω).

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