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Fourier transform

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  • #1
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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?
 
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Answers and Replies

  • #2
661
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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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