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

  1. derick007

    derick007 Member

    Feb 5, 2013

    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

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