We know that $f(t)*δ(t-a)=f(t-a)$. How about $f(t-a)*δ(t-a)$? (where * is convolution and $δ(t)$ is dirac delta function)
I think it's $f(t-a)*δ(t-a) = f(t-a)$ because convolution with delta function shifts the function to where the delta is. So if the function has already shifted to the same location as the delta - nothing happens and it stays the same shifted function. What do you think?
Thank you.