When designing a root raised cosine filter on Matlab, there is an option to set its "roll-off factor". What does this mean? I have been looking around for a while but I can't seem to find a clear explanation. Any help will be appreciated.
Think of the root-raised cosine as a family of functions. The roll-off factor is a parameter that chooses one of the possible functions.
All root-raised cosine pulses look similar to the sinc pulse. The interesting thing about the roll-off factor is that it controls two features of the function:
The rate at which the function's lobes (or ripples) decrease. At one extreme, with roll-off set to 0, they decrease slowly (as $1/t$, with $t$ equal to time). At the other end, when the roll-off factor is 1, they decrease as $1/t^3$.
As the roll-off factor increases, so does the function's bandwith. Basically, if the function's bandwidth is $B$ when the roll-off is 0, then it becomes $2B$ when the roll-off is 1.
You can choose any value for the roll-off factor between 0 and 1, so you can select the function with the ripple and bandwidth that are best suited to your needs.