I'm posting this for a friend of mine. We're not sure how to begin with the following problem.
Show that a periodic function $f(t)$ with period $T$ can be written as $$ f(t) = f_T (t) \star \frac{1}{T} \text{comb}\bigg(\frac{t}{T}\bigg) $$ where $f_T (t)$ is one period of $f(t)$.
The book defines the Fourier series representation as $$ \frac{1}{T} \sum_{n=-\infty}^{\infty} \exp(2\pi i n \frac{t}{T}) $$ I believe this plays a role in the problem, but I'm not sure where to begin with it. Any help would be appreciated, thank you.