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komm.SincPulse

Sinc pulse. It is a pulse with waveform given by $$ p(t) = \frac{\sin(\pi t)}{\pi t} = \sinc(t). $$

The waveform of the sinc pulse is depicted below.

Sinc pulse.

Attributes:

(No attributes)

waveform()

The waveform $p(t)$ of the pulse.

For the sinc pulse, it is given by $$ p(t) = \sinc(t). $$

Examples:

>>> pulse = komm.SincPulse()
>>> pulse.waveform(
...     [-1.0, -0.75, -0.5, -0.25, 0.0, 0.25, 0.5, 0.75, 1.0],
... ).round(3)
array([0.   , 0.3  , 0.637, 0.9  , 1.   , 0.9  , 0.637, 0.3  , 0.   ])

spectrum()

The spectrum $\hat{p}(f)$ of the pulse.

For the sinc pulse, it is given by $$ \hat{p}(f) = \rect(f). $$

Examples:

>>> pulse = komm.SincPulse()
>>> np.abs(pulse.spectrum(
...     [-1.0, -0.75, -0.5, -0.25, 0.0, 0.25, 0.5, 0.75, 1.0],
... ))
array([0., 0., 1., 1., 1., 1., 0., 0., 0.])

autocorrelation()

The autocorrelation function $R(\tau)$ of the pulse.

For the sinc pulse, it is given by $$ R(\tau) = \sinc(\tau). $$

Examples:

>>> pulse = komm.SincPulse()
>>> pulse.autocorrelation(
...     [-1.0, -0.75, -0.5, -0.25, 0.0, 0.25, 0.5, 0.75, 1.0],
... ).round(3)
array([0.   , 0.3  , 0.637, 0.9  , 1.   , 0.9  , 0.637, 0.3  , 0.   ])

energy_density_spectrum()

The energy density spectrum $S(f)$ of the pulse.

For the sinc pulse, it is given by $$ S(f) = \rect(f). $$

Examples:

>>> pulse = komm.SincPulse()
>>> pulse.energy_density_spectrum(
...     [-1.0, -0.75, -0.5, -0.25, 0.0, 0.25, 0.5, 0.75, 1.0],
... )
array([0., 0., 1., 1., 1., 1., 0., 0., 0.])

support tuple[float, float] cached property

The support of the pulse waveform $p(t)$, defined as the interval $[a, b]$ where $p(t)$ is non-zero.

For the sinc pulse, the support is given by $(-\infty, \infty)$.

Examples:

>>> pulse = komm.SincPulse()
>>> pulse.support
(-inf, inf)

taps()

Returns the FIR taps of the pulse.

Parameters:

  • samples_per_symbol (int) –

    The number of samples per symbol.

  • span (tuple[int, int] | None) –

    The time span to consider for the taps. This parameter is optional for pulses with finite support (defaults to $[0, 1]$), but required for pulses with infinite support.

Examples:

>>> pulse = komm.SincPulse()
>>> pulse.taps(samples_per_symbol=4, span=(-1, 1)).round(3)
array([0.   , 0.3  , 0.637, 0.9  , 1.   , 0.9  , 0.637, 0.3  , 0.   ])
>>> pulse.taps(samples_per_symbol=4, span=(-16, 16)).shape
(129,)