I am having trouble with the following proof.
Let $y(t) = x(t) \ast h(t)$ (where $\ast$ denotes convolution of two functions).
Prove that if $x(t)$ is periodic, then $y(t)$ is periodic.
So I started off assuming $x(t)$ has some fundamental period, called $T$. But then, the question gives me no information about $h(t)$ and whether it is periodic, so I'm kind of stuck on how to go further with this question. I'm also pretty new to convolution, so I'm not super rock solid on all the convolution properties.
Let $x(t+T)=x(t)$ and: $$y(t)=\int_{-\infty}^\infty x(t-\tau)h(\tau) \, d\tau$$ Then: $$y(t+T)=\int_{-\infty}^\infty x(t+T-\tau)h(\tau) \, d\tau = \int_{-\infty}^\infty x(t-\tau)h(\tau) \, d\tau=y(t)$$