I have trouble trying to work out a fourier transform of sampling function. I also looked at other questions on math stackexchange but they just don't make much sense to me.
\begin{equation} f(t)=\sum_{j=0}^{\frac{T}{\Delta t}-1} \delta(t-j\Delta t) \text{ where, } T=n\Delta t \end{equation}
I'm not even sure how to approach this problem - I'm not sure how the delta function inside of the sum works out to be when you apply the fourier transform. I think that you should get something like this - but also, I'm not really sure.
\begin{equation} f(\omega)=\sum_{j=0}^{\Delta t-1} \delta(\omega-j\frac{T}{\Delta t}) \end{equation}