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Math Help - Proving a symmetric property of the fourier transform

  1. #1
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    Proving a symmetric property of the fourier transform

    Hello!

    I'm trying to prove a symmetric property of the fourier transform, but I'm having some problems with that.
    Here is the failed try of the proof: fourier - MathB.in.

    Any help would be much appreciated! (:
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  2. #2
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    Re: Proving a symmetric property of the fourier transform

    Hey sapsapz.

    I think what you have to do is show that if the final transform has no complex part that the two are equal. If you have a complex variable z = x + iy, then y = 0 implies equality for your problem.

    Recall that -e^(-iwx) = -[cos(-wx) + isin(-wx)] = -cos(-wx) + 0 (if no imaginary component) = -cos(wx) since cos(x) = cos(-x).
    Thanks from topsquark
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  3. #3
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    Re: Proving a symmetric property of the fourier transform

    Quote Originally Posted by chiro View Post
    Hey sapsapz.

    I think what you have to do is show that if the final transform has no complex part that the two are equal. If you have a complex variable z = x + iy, then y = 0 implies equality for your problem.

    Recall that -e^(-iwx) = -[cos(-wx) + isin(-wx)] = -cos(-wx) + 0 (if no imaginary component) = -cos(wx) since cos(x) = cos(-x).
    Thanks chiro, but I can't claim the final transform has no imaginary part, thats what Im trying to prove in the first place, right?
    Did you see any error in the equalities chain in the proof?
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  4. #4
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    Re: Proving a symmetric property of the fourier transform

    Ok, solved, thanks!
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