I'm currently trying to solve a problem on my "Signals and Systems" class and I'm stumped.The question has 2 parts:
1-) The function T.I can be defined as: $$ T\cdot I(t) = \sum_{n=-\infty}^{\infty}\delta(t-na) $$
Where $ \delta $ is the delta Dirac function. Make a sketch of the function.
2-) What happens if I make the convolution of any function $f(x)$ with the function T.I? Sketch the result of the convolution.
I can't visualize how the graph of the T.I function will look like. The best I can think is that it'll be an infinite number of delta-dirac functions all throughout -infinity to + infinity. However, I don't know how I would be able to sketch that and how a convolution involving the T.I function would ever look like in a graph.