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Sketching the spectrum of a cosine wave

  1. Sep 28, 2008 #1
    1. The problem statement, all variables and given/known data

    An amplitude-modulated cosine wave is represented by the formula

    x(t) = [ 10 + cos(2*pi*(2000)*t) ] * cos(2*pi*10^4*t)

    Sketch the two-sided spectrum of the signal. Be sure to label important features of the plot.

    3. The attempt at a solution

    x(t) = 10 * cos(2*pi*(2000)*t) + cos(2*pi*(2000)*t) * cos(2*pi*10^4*t)

    = 10 * cos(2*pi*(2000)*t) + [ cos(2*pi*(2000+10^4)*t) * cos(2*pi*(2000-10^4)*t) ] / 2

    = 10 * cos(2*pi*(2000)*t) + 0.5 cos(2*pi*(2000+10^4)*t) +0.5 cos(2*pi*(2000-10^4)*t)

    I think up to this point works out mathematically, but I am not sure where to go from here. If anybody can provide any suggestions then it would be greatly appreciated.
    Last edited: Sep 28, 2008
  2. jcsd
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