# QAM

Discussion in 'Mathematics and Physics' started by derick007, Sep 8, 2014.

1. ### derick007Member

Joined:
Feb 5, 2013
Messages:
89
Likes:
1
Location:
NORTHERN IRELAND, UK
Hi

I am trying to write an equation using Fourier Analyses to describe the frequency spectrum of a 64 QAM signal.

I believe the time equation for a QAM signal can be written as :

Si(t) = Ai cos(wct+Θi) where i=
one of many symbols i.e. for 64 QAM one of 64 (6 bit) symbols.

OR another form would be

A(t) cos (2πfct + φ) = A(t) cos (2πfct) cos (φ) - A(t) sin (2πfct) sin (φ)

Using Fourier Series

Ci =Si(t) e-jWnt
dt for t = T/2 to t=-T/2, we can choose values for Ai and theta i.e. Ai=7.07 and theta = 0.142 rads.

I have done the integration by parts and come up with the following equation

Ci = 7.07 [ e-jWnt { wc sin(wct+0.142) - jwn cos(wct+0.142) } ]
{
wc2 - wn2
}

within the same time limits. I can choose a value for wc but I am not sure about the value for wn ? What about the imaginery parts of the equation ? Presumably to get the complete spectrum, there are 64 values for Ci ? Does this make any sense ?

Regards, Derek