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Bessel Parseval Relation?

  1. Jun 18, 2008 #1
  2. jcsd
  3. Jun 19, 2008 #2
    If you have an L2(R) (complex) function [tex]f[/tex] whose Fourier transform writes
    [tex] \tilde{f}(q) = \int_{-\infty}^{+ \infty} dq f(x) e^{-2 \pi i qx } [/tex]
    then the Bessel-Parseval theorem states that
    [tex] \int_{-\infty}^{+\infty} \left| f(x) \right|^2 dx = \int_{-\infty}^{+\infty} \left| \tilde{f}(q) \right|^2 dq [/tex]

    This theorem also works (and is simpler to understand) in the discret case i.e. considering the Fourier series of [tex] f [/tex] as a specific case of the general Pythagore theorem.
  4. Jun 19, 2008 #3
    Wowww... are you serious? The theorem must be ridiculously helpful then...
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