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
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