For a typical wireless communication system, we use modulation schemes and filters before transmitting the signal. The main purpose of using it is to transmit a proper waveform so that we can recover the signal at the receiving end more accurately.
If the roll-off factor is α, then
Bandwidth (B) = (1 + α) / (2 * T)
where T is the time interval. The filter response is zero outside that.
The roll-off factor is a parameter used to shape the spectrum of a digital signal in communication systems, and it is not just the product of time and bandwidth. It affects both the time and frequency domain characteristics of the signal.
Application
A raised cosine filter is used for pulse shaping. You might have noticed in most of the diagrams of 'communication systems.' It is common to use this type of filter after the modulation module.