If you look back at my earlier post on QAM, you will notice that in the modulator(transmitter side), you will notice that we are multiplying one signal by and the other by . These signals are generated by separating the original message signal into two signals, and then multiplying one by and the other by . Now, in the previous post I used a sinusoidal message signal for illustration. In reality, message signals are generally NOT perfect sinusoids.
Without further ado, here is the explanation of QAM (formulation heavily adapted from Telecommunication Breakdown by Johnson&Sethares)
Let the message be separated into two signals and . Then we modulate by multiplying one by and the other by . In other words, if is our modulated signal, is generated by the following:
. This is the signal transmitted. At the receiver, in the demodulater, we duplicated the signal received: call these and . =
. Putting this signal through a lowpass filter(filters high frequencies) gives , and we have recovered the message.
. With a lowpass filter, we get
We can look at some IT++ code in the future