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Homework Help: Amplitude modulated

  1. Sep 12, 2005 #1
    An AM cosine wave is represented by x(t)=12+7*sin(pi*t-(1/3)*pi)]*cos(13*pi*t). Use phasors to show that x(t) can be expressed in form of:

    A1cos(w1*t+phi1) + A2cos(w2*t+phi2)+A3cos(w3*t+phi3) where w1<w2<w3.

    I am really stuck with this. dont know where to start. can someone please help me out???
     
  2. jcsd
  3. Sep 12, 2005 #2

    ehild

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    Homework Helper

    Use that

    [tex] cos(\omega t +\phi)= \frac{e^{i(\omega t + \phi)}+e^{-i(\omega t + \phi)}}{2} [/tex]

    and

    [tex] sin(\omega t +\phi)= \frac{e^{i(\omega t + \phi)}-e^{-i(\omega t + \phi)}}{2i} [/tex]

    Replace the sin and cos functions in x(t) with the exponential expressions, do all the multiplications, collect the terms with the same angular frequency and see what you get.

    ehild
     
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