Formal Definition

$ \lim_{\Delta \rightarrow 0} x_\Delta(t) = \mathrm{comb}_T [x_a(t)] = x_s(t) $

Fourier Properties

The fourier transform of the comb function is the rep function_Old Kiwi.

$ \mathcal{F}\left [\mathrm{comb}_T [x_a(t)] \right ] = \frac{1}{T}\mathrm{rep}_{\frac{1}{T}}\left [ \mathcal{X}_a(f) \right ] $