raised cosine filter
Filter with impulse response defined by
H(f)={1|f|≤1−β2T12[1+cos(2πTβ(|f|−1−β2T))]1−β2T<|f|≤1−β2T0else
The filter takes β, the roll-off length which parametrizes the function. Higher β increases the curved "roll-off" outside the perfect box-car in the frequency domain.
T is the symbol-duration time (1/fs), in 1/baud (a baud is symbol/s).
From wikipedia,
In the frequency domain, the function has symmetry around the 12T, which is why the function can be implemented programmatically be multiplying a signal with a precomputed "up flank" and "down flank."
In the time domain, we can compute the RC's impulse response as (and then apply to the signal by convolution)
h(t)={π4Tsinc(12β)t=±T2β1Tsinc(tT)cos(2βT)1−2βtT2else
The square root of the frequency response of the RC filter is called the root-raised cosine filter.