Double Side-band (DSB) Modulation

Using DSB amplitude modulation, we would transmit the product of f and a "carrier signal"

, where is relatively large (ideally, we would want this so large that

the Fourier transform of f was zero outside [ ]).

Note: This is very close to zero for | | > 30, so we will take that as our carrier frequency.

After modulation:

> g := x -> cos(30*x)*f(x);

Note that the outline of the signal f is visible in the "envelope" of the modulated signal g:

> gp:=plot(g(x),x=0..5,color=red):

> fp:=plot(f(x),x=0..5,color=black):

> with(plots): display({fp,gp});

>

Fourier Transform of the Modulated Signal

Synchronous Demodulation

Question: How can we recover f(x) from this information?