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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.

∑

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?

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.

∑

_{ωn}f(a-ω_{n})g(ω_{n})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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