komm.RootRaisedCosinePulse

Root raised cosine pulse. It is a pulse with waveform given by $$ h(t) = \frac{\sin ( 2 \pi f_1 t ) + 4 \alpha t \cos ( 2 \pi f_2 t )}{\pi t ( 1 - (4 \alpha t)^2 )}, $$ where $\alpha$ is the roll-off factor (which must satisfy $0 \leq \alpha \leq 1$), $f_1 = (1 - \alpha) / 2$, and $f_2 = (1 + \alpha) / 2$. Its spectrum is given by the square root of the spectrum of the raised cosine pulse.

The root raised cosine pulse is depicted below for $\alpha = 0.25$, and for $\alpha = 0.75$.

Attributes:

• rolloff (float) –

  The roll-off factor $\alpha$ of the pulse. Must satisfy $0 \leq \alpha \leq 1$. The default value is 0.0.

Examples:

>>> pulse = komm.RootRaisedCosinePulse(rolloff=0.25)
>>> pulse.waveform([-0.75, -0.50, -0.25,  0.00,  0.25,  0.50,  0.75]).round(4)
array([0.2379, 0.6218, 0.9432, 1.0683, 0.9432, 0.6218, 0.2379])
>>> pulse.spectrum([-0.75, -0.50, -0.25,  0.00,  0.25,  0.50,  0.75]).round(4)
array([0.    , 0.7071, 1.    , 1.    , 1.    , 0.7071, 0.    ])