Roll-off factor bandwidth and bit rate

1. What is the roll off factor?
2. How do you calculate bit rate from bandwidth?
3. What is the roll off factor of an ideal LPF?
4. Why do we use raised cosine filter?

What is the roll off factor?

Roll-off is the steepness of a transfer function with frequency, particularly in electrical network analysis, and most especially in connection with filter circuits in the transition between a passband and a stopband.

How do you calculate bit rate from bandwidth?

C(bps) = 2B * log₂M (Nyquist)

C is the capacity in bits per second, B is the frequency bandwidth in Hertz, and M is the number of levels a single symbol can take on. This "idealized" capacity equation shows us that data rate is proportional to twice the bandwidth and logarithmically proportional to M.

What is the roll off factor of an ideal LPF?

A better compromise would be a roll off factor somewhere between 0.25 and 0.5 (B and C). Here the impulse response decays relatively quickly with small lobes, requiring a pulse shaping filter with a small number of taps, while still keeping the required bandwidth reasonable.

Why do we use raised cosine filter?

Raised cosine filters are used for pulse shaping, where the signal is upsampled. Therefore, we also need to specify the upsampling factor.