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Math Help - Fourier transform properties

  1. #1
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    Fourier transform properties

    well I am having a problem with fourier transforms and their properties, the ones relating the fourier transform of a function and the one of its integral and derivative. in the image I'll link here( http://dl.dropbox.com/u/27392043/IMG_0008.JPG ) I have a solution of a probem witch consists on determining the fourier transform of a funcion x(t) by means of its derivative's or integral's transform. I solve both ways and I somehow get different answers, can anyone tell me what's the problem with my solutions? thank you very much
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  2. #2
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    So you've got a function with a known Fourier transform. If you want the Fourier transform of the derivative, you must use rule 1. If you want the Fourier transform of the integral, you must use rule 2. You can't use the rules interchangeably.

    For the problem in the image you linked to, only rule 2 is applicable. The problem with using rule 1 is that h(t) is not uniquely determined given h'(t). I could define another h by taking your h and adding some constant. My h would be just as legitimate as yours, but would have a different Fourier transform.
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  3. #3
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    I think you missunderstood the porpouse of the exercise I mentioned, the porpouse was to find the foiroer transform of h(t) either by determining his derivative and then determining h'(t)'s F.T.or By determining h(t)'s integral and then hos FT transform. And given that one way or another we got the F.T of the derivative or the integral of a dunction we could then determining the function's FT itself, by using the properties. Ofcourse that if y(t)=h'(t) then the integral of y(t) also is h(t) so we could always use one or other property right?
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  4. #4
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    I got it. You've got a function with a known Fourier transform. You are trying to find the Fourier transform of the integral. You need to use rule 2 to do this. You cannot use rule 1 to do this. That's why your answers don't match up.

    You are saying hey, I've got h'(t) and I know its Fourier transform. I should be able to find the Fourier transform of h(t) using rule 1. The problem is that starting with h'(t), you can't even determine what h(t) is. You can write down the general form of h(t) but it will include an unknown constant of integration.
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