I am asked to explain the effect of filtering a general input time function $f(t)$ by $g(t)$ (which is just the convolution of $f(t)$ with $g(t)$), with $g(t)$ being the Gaussian function as below: $$g(t)=\frac{1}{\sqrt{\pi}t_{H}}e^{-(t/t_{H})^2}$$ where $t_H$ is the half duration, a constant.
I have no idea how to answer this since I am very new to concepts like convolution and Gaussian functions. Is there any help or hint?