Question: Fourier transform of impulse train

I would like to compute the Fourier transform of a impulse train for applications in signal processing.  I expect to get an impulse train as a result, but do not:

delta__t:=t->sum(Dirac(t-k*T__0),k=-infinity..infinity) assuming T__0>0

I will note that Mathematica has the DiracComb function since 2008.  It also computes the result as an impulse

train: which is what I would expect.  Is there something I should be doing that I'm not aware of?

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