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Fourier transform

  1. Jan 15, 2014 #1
    I have an exercise with a function of the form:

    h(t) = f(t)g(t)

    and f(t) and g(t) both have discrete fourier series, which implies that h does too. I want to find the fourier series of h, so my teacher said I should apply the convolution theorem which would turn the product above into a convolution in the frequency domain.

    ωnf(a-ωn)g(ωn)

    But the problem for me is that it seems arbitrary for me what the constant a should be? How is that determined?

    The problem also arises in the case where I have a product as above but I want to find the fourier transform (i.e. now not series but proper integral transform).
    The FT will be a convolution but what determines the constant in the convolution?
     
    Last edited: Jan 15, 2014
  2. jcsd
  3. Jan 16, 2014 #2
    I suppose you have [tex]\hat{h}(a)=\sum_{\omega_n}\hat{f}(a-\omega_n)\hat{g}(\omega_n)[/tex],

    so that a is the argument of h.
     
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