1. The problem statement, all variables and given/known data The problem is about the quadrature amplitude modulation. This is a work from my course Analog signal processing. Here is the scheme 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.