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Quadrature amplitude modulation

  1. Jan 12, 2008 #1
    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

    [​IMG]

    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.
     
  2. jcsd
  3. Jan 12, 2008 #2

    mda

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    No, I don't think that's correct... what do the X elements do?
    What does the Sigma element do?
     
  4. Jan 13, 2008 #3
    X: multiplication
    Sigma: addition

    I think of that :
    x_qam(t)=m1(t)*cos(wp*t)+m2(t)*sin(wp*t)

    But what about the -Pi/2 ?
     
    Last edited: Jan 13, 2008
  5. Jan 13, 2008 #4

    mda

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    correct. -pi/2 is a phase shift from cos to sin.
     
  6. Feb 21, 2008 #5
    xqam= m1(t)*cos(wp*t) + m2(t)*cos(wp*t)*sin(wp*t)

    The -Pi/2 block converts the cos into a sine.

    At the top before the LP filter you have m1(t)*cos^2(wp*t) + m2(t)*cos^2(wp*t)*sin(wp*t)

    The LP filter drops the high frequency components using trig identities. See http://en.wikipedia.org/wiki/Quadrature_amplitude_modulation
     
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