Cosine for synchronous demodulation

[ƒ(x)]

Homework Statement

Synchronous demodulate x(t).

Homework Equations

xc(t) = cos(2pi*fc*t), fc is the carrier frequency
xm(t) = cos(2pi*fm*t), fm is the modulation frequency

x(t) = xc(t)*(1+m*xm(t)), m is the modulation index
m = .8
fc = 2000 hz
fm = 200 hz

The Attempt at a Solution

I really don't even know where to start. I know synchronous demodulation means I multiply x(t) by a function, but how do I come up with that function? I realize that I could divide x(t) by (1+m*xm(t)), but that doesn't seem to be what the problem is asking.

 

[NascentOxygen]

xc(t) = cos(2pi*fc*t), fc is the carrier frequency
xm(t) = cos(2pi*fm*t), fm is the modulation frequency

x(t) = xc(t)*(1+m*xm(t)), m is the modulation index
m = .8
fc = 2000 hz
fm = 200 hz

The Attempt at a Solution

I really don't even know where to start. I know synchronous demodulation means I multiply x(t) by a function, but how do I come up with that function? I realize that I could divide x(t) by (1+m*xm(t)), but that doesn't seem to be what the problem is asking.

No, that would involve the receiver being able to predict the modulation perfectly, so there would be little point in sending it in the first place.

I don't know where to start, either. But isn't synchronous something about multiplying by the carrier? So why not try multiplying x(t) by x_c(t) and see what you can get from that? The whole idea is to recover x_m(t), presumably?

 

[ƒ(x)]

No, that would involve the receiver being able to predict the modulation perfectly, so there would be little point in sending it in the first place.

I don't know where to start, either. But isn't synchronous something about multiplying by the carrier? So why not try multiplying x(t) by x_c(t) and see what you can get from that? The whole idea is to recover x_m(t), presumably?

I think I'm supposed to do x(t) * xc(t) and then the next step is to use a step function of sorts. The point is to recover xc(t) since that's the original signal.

Edit: My mistake, I was misreading the problem. You're correct. I'm supposed to recover xm(t).