Amplitude Modulation
The signal is transmitted to receiver by communication channel.
In this process, information bearing signal, x(t), is embeded by carrier signal, c(t) which has its amplitude.
So the modulated signal is the product of these two signals:
$ y(t) = x(t)c(t) $
Here are two types of carriers.
(1) complex exponential type
Suppoese $ c(t) $ is $ e^{jw_{c}t}. $
$ y(t) = e^{jw_{c}t} $
$ Y(w) = F(e^{jw_{c}t}x(t)) = \frac{1}{2\pi}F(e^{jw_{c}t})X(w) $
$ = \frac{1}{2\pi}2\pi\delta(w-w_{c}) * X(w) = X(w-w_{c}) $ , where * is convolution
Thus, X(w) was delayed by $ w_{c} $
To demodulate, multiply $ y(t) $ by $ e^{jw_{c}t} $.
(2) Sinusidal type
