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Fourier transform - what integral limits

  1. Mar 2, 2012 #1
    Find the fourier transform of the unit rectangular distribution f(t) = 1 for ltl<1 else 0
    Since e-iωt is zero except for t in ]-1;1[ it must be an integral over this interval. But should I take the boundaries as -1 and 1? Because they are not included in the interval where e-iωt is not zero but rather supremum and infimum for it. Would it better to put the limits lim t->1 and lim t->-1?
     
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  3. Mar 2, 2012 #2

    MathematicalPhysicist

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    What?
    The exponent never vanishes for finite values.
     
  4. Mar 2, 2012 #3
    umm the fourier transform is:

    -∞f(t)e-iωtdt

    But since f(t)=0 for t≥1, t≤-1 you integrate from -1 to 1?
     
  5. Mar 2, 2012 #4

    LCKurtz

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    Yes.
     
  6. Mar 2, 2012 #5

    vela

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    I think you meant f(t) where you wrote e-iωt.

    Regarding your question about the limits, it turns out it doesn't matter. You can look up some statement about the uniqueness of Fourier transforms. I think it's something like two functions have the same Fourier transform if they differ over a set of points of measure 0.
     
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