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Amplitude modulation with pulse-train carrier

y(t)=x(t)c(t) with c(t) be a pulse train

$ C(t)= \sum^{\infty}_{k = -\infty} a_k e^{jk\frac{2\pi}{T}t} $

Thus Y(W)= $ \frac{1}{2\pi}X(W)*C(W) $ where $ C(W)= \sum^{\infty}_{k = -\infty} a_k 2\pi\delta(\omega-\frac{2\pi}{T}) $

For k=0,$ a_0 $ is the average of signal over 1 period.

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