Signal Processing Help: 3rd + 1st Order Nonlinear Device Multiplier

[Miscing]

Homework Statement

http://i.imgur.com/01AUp.png

Homework Equations

The Attempt at a Solution

Having some problems with this question, using a third + first order nonlinear device to make a multiplier. I'm fine with using a second order, but this one is stumping me. So, I take x(t) = m(t) + cos(wt) and plug it into x(t) + (x(t))^3 , and I get (expanding cos(wt)2 and cos(wt)3 terms:

5/2* m + cos(wt) + m^3 + 3* m^2* cos(wt) +3/2m cos(2wt) + 3/4* cos(wt) + 1/4* cos(3wt).

Problem: None of the terms contain m(t)cos(wt)! Then what am I supposed to filter out?

 

[NascentOxygen]

I might be wrong here, but ... looking for clues, I notice they speak of f_o and f_c ...

I wonder can f_c = 2·f_o?

 

[Miscing]

Thanks, after emailing the TA he confirmed that indeed fo is arbitrary here, and so fo = 2fc is the way to start answering this.