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Fourier Transform of Rect fn

  1. Apr 15, 2009 #1
    Hi all,

    How is the fourier transform applied to non-periodic functions, such as the Rect function?

    Any help would be greatly appreciated,

    Cheers,

    Jamie :)
     
  2. jcsd
  3. Apr 15, 2009 #2

    mathman

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    I think you are confusing Fourier series, which apply to periodic functions, and Fourier transforms, which apply to integrable (in some sense) functions.
     
  4. Apr 16, 2009 #3
    OK, i can see why my post appeared to sound like that, but I know what the differnce is.

    What i mean is, say, how would you show that the FT transform of {1} is a delta function??

    Cheers
     
  5. Apr 16, 2009 #4
    Let A be a ( large ) positive real number

    The transform you specified will lead you to integrate exp( - i * w * t ) with t ranging from -A to A, and letting A approaching +∞. When A approaches +∞, this will give you a function similar to one of these :

    http://en.wikipedia.org/wiki/Impulse_function#Representations_of_the_delta_function

    I let you try the computation and identify which one corresponds to the Fourier transform of 1.
     
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