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Fourier transform of sin

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Hey guys.
    I need to find the Fourier transform of sin, is this right?

    http://img156.imageshack.us/img156/5531/scan0004r.jpg [Broken]

    I searched the internet but all I could find is the answer with the dirac delta and I don't need that.

    Thanks.


    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 3, 2009 #2

    dx

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    The Fourier transform of sin(t) involves the Dirac delta function. What do you mean by "I don't need that"? And why did you change the limits from -∞ to ∞ to -π to π in your integral?
     
  4. May 3, 2009 #3
    Oh, sorry, I need to find it from -pi to pi.
    Is there something wrong with what I did?

    Thanks.
     
  5. May 3, 2009 #4

    dx

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    I didn't read your whole solution, but there is a mistake in your first step. The Fourier transform integral goes from -∞ to ∞. Why did you change those limits?
     
  6. May 3, 2009 #5
    Yeah, I need to find it from -pi to pi.
    Is that way it doesn't involves Dirac function?

    Thanks.
     
  7. May 3, 2009 #6

    dx

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    No! It's not from -pi to pi. It's -∞ to ∞.
     
  8. May 3, 2009 #7
    :smile:

    But that is the question.
    Find Fourier transform of sin in -pi<t<pi.

    What do you mean?

    Thanks.
     
  9. May 3, 2009 #8

    Cyosis

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    Your question is to transform the function [tex]f(t) = \left\{ \begin{matrix} \sin t & \mathrm{if}\; -\pi < t < \pi \\ 0 & \mathrm{otherwise} \end{matrix} \right[/tex] ?
     
  10. May 3, 2009 #9
    Yeah, sorry for the misconfusion.
     
  11. May 3, 2009 #10

    Cyosis

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    Then your approach is correct since the function is zero outside -pi<t<pi anyway so you may as well integrate from -pi to pi.
     
  12. May 3, 2009 #11

    dx

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    Ah, now it makes sense! Thanks Cyosis!
     
  13. May 3, 2009 #12

    Cyosis

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    You're welcome.
     
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