I'm preparing my signal processing exam and I have come across a question that I really do not know how to prove. It goes like this:
Convolution of two simple periodic signals $x(t)$ and $y(t)$, which have periods $T_x$ and $T_y \ne T_x$ is equal to:
What is the easiest way to obtain this result?
We use the following definition for the convolution: $$x(t)*y(t) = \int_{-\infty}^{+\infty}x(\tau)y(t-\tau)d\tau$$
I checked up with Desmos and it seems that if I pick any sin or cosine functions, I get 0. Based on one of the other posts which I found on the site, this should be correct in general, but I have no knowledge on how to prove it. In the mentioned post, one of the comments proposes writing one of the functions in a complex form, and then calculating the integral. I am not sure am I allowed to do that, because I have no idea what functions am I actually dealing with, given that the it's only said that they are periodic.
I would really appreciate if someone could help me with this. It seems simple enough, but I am unaware of ways of solving it.