Quadrature amplitude modulation

[assortim]

Homework Statement

The problem is about the http://en.wikipedia.org/wiki/Quadrature_amplitude_modulation" . This is a work from my course Analog signal processing.
Here is the scheme

http://img99.imageshack.us/img99/9449/zrgwj2.jpg

Two things to do :
1. Find the expression of x_qam(t)
2. Show that each of the signals m1(t) and m2(t) can be extract thanks to the synchronous detection using two local oscillators in quadrature (cf. scheme)2. The attempt at a solution
For the first question, I say :
m1(t)=cos(wp*t)
m2(t)=cos(wp*t-Pi/2)*sin(wp*t-Pi/2)
But I really doubt that is correct.

For the second question, I have no idea :(

As it is an work from my course "Analog signal processing", it should deal with transform Fourier and this kind of stuff but I really don't know how to start. It would be really great to have some help.

 

[mda]

No, I don't think that's correct... what do the X elements do?
What does the Sigma element do?

 

[assortim]

No, I don't think that's correct... what do the X elements do?
What does the Sigma element do?

X: multiplication
Sigma: addition

I think of that :
x_qam(t)=m1(t)*cos(wp*t)+m2(t)*sin(wp*t)

But what about the -Pi/2 ?

 

[mda]

correct. -pi/2 is a phase shift from cos to sin.

 

[unplebeian]

xqam= m1(t)*cos(wp*t) + m2(t)*cos(wp*t)*sin(wp*t)

The -Pi/2 block converts the cos into a sine.

At the top before the LP filter you have m1(t)*cos^2(wp*t) + m2(t)*cos^2(wp*t)*sin(wp*t)

The LP filter drops the high frequency components using trig identities. See http://en.wikipedia.org/wiki/Quadrature_amplitude_modulation