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?