I have a signal $s(t)$ of duration $T$ with limited bandwidth. In matlab, I use a sampling frequency $fs$ and I have $L=T*fs$. After, I have $r=ones(size(s))+s$. To have a limited bandwidth, I filter with a raised cosine filter: $rr=filter(h,1,r)$ with $h$ the raised cosine filter.
My question: What is the duration for the signal $rr$? Personnally I would have said $T$. How to prove that?