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Math Help - Fourier transform properties

  1. #1
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    Fourier transform properties

    I am having trouble with the proof of the time shifting property in the fourier transform. The property states that if x(t) has a fourier transform X(jw) then, x(at) has a transform (abs(a^-1)X(jw/a). My problem is with the abs!! why does it have a abs there? The proof of the property is in a file stored on dropbox( http://dl.dropbox.com/u/27392043/ooooo.jpg ) because i cant upload it here dunno why. If you look at the picture what I dont understand is the - signal where a<0 why is it there if when T=at dT/a=dt never dT/-a=dt!!! please help me.
    Thanks.
    Last edited by mr fantastic; May 14th 2011 at 02:20 PM. Reason: Bad language deleted.
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  2. #2
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    If a < 0 then the limits in the integral will be reversed since \tau = at, i.e. you'll have \int_{+\infty}^{-\infty} instead of \int_{-\infty}^{+\infty}

    Switching the limits back will also switch the sign of the integral.
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  3. #3
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    Oh thanks a lot!!! I was looking at it for 1 hour and couldn't see the most obvious answer.Thanks a lot man
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