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Homework Help: Fourier representation of CT peridic signals

  1. Feb 24, 2007 #1
    I want to find the Fourier coefficients for the following signal:

    [tex] \cos(2 \pi t)^2 [/tex]

    Can I simply use the identity?:

    [tex] \frac{1}{2} + \frac{\cos(2 \pi t)}{2} [/tex]

    And then use the complex definition:

    [tex] \frac{1}{2} + \frac{1}{4} (\exp{j2 \pi t} + \exp{-j2 \pi t}) [/tex]


    From the synthesis equation I can get:
    [tex] a_0 = \frac{1}{2} [/tex], [tex] a_1 = \frac{3}{4} [/tex]

    Thanks
     
    Last edited: Feb 24, 2007
  2. jcsd
  3. Feb 25, 2007 #2

    AlephZero

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    [tex] \cos(2 \pi t)^2 [/tex] is a strange (non-standard) notation.

    If you mean [tex] \cos^2(2 \pi t)[/tex] then your method is almost correct - it equals [tex] \frac{1}{2} + \frac{\cos(4 \pi t)}{2} [/tex]


    If you mean [tex] \cos(4 \pi^2 t^2)[/tex] then it is not.
     
    Last edited: Feb 25, 2007
  4. Feb 25, 2007 #3
    I meant the first, and thanks for the correction.
     
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