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komm.RectangularPulse

Rectangular pulse. It is a pulse with waveform given by $$ h(t) = \begin{cases} 1, & 0 \leq t < w, \\ 0, & \text{otherwise}. \end{cases} = \mathrm{rect}\left(\frac{t}{w}\right), $$ where $w$ is the width of the pulse, which must satisfy $0 \leq w \leq 1$. Its spectrum is given by $$ \hat{h}(f) = w \, \operatorname{sinc}(w f). $$

The rectangular pulse is depicted below for $w = 1$, and for $w = 0.5$.

Rectangular NRZ pulse. Rectangular RZ pulse.

Notes
  • For $w = 1$ it is also called the NRZ pulse.
  • For $w = 0.5$ it is also called the halfway RZ pulse.

Attributes:

  • width (Optional[float]) –

    The width $w$ of the pulse. Must satisfy $0 \leq w \leq 1$. The default value is 1.0.

Examples:

>>> pulse = komm.RectangularPulse(width=1.0)  # NRZ pulse
>>> pulse.waveform([-0.50, -0.25,  0.00,  0.25,  0.50,  0.75,  1.00])
array([0., 0., 1., 1., 1., 1., 0.])
>>> pulse.spectrum([-0.75, -0.50, -0.25,  0.00,  0.25,  0.50,  0.75]).round(4)
array([0.3001, 0.6366, 0.9003, 1.    , 0.9003, 0.6366, 0.3001])

>>> pulse = komm.RectangularPulse(width=0.5)  # Halfway RZ pulse
>>> pulse.waveform([-0.50, -0.25,  0.00,  0.25,  0.50,  0.75,  1.00])
array([0., 0., 1., 1., 0., 0., 0.])
>>> pulse.spectrum([-0.75, -0.50, -0.25,  0.00,  0.25,  0.50,  0.75]).round(4)
array([0.3921, 0.4502, 0.4872, 0.5   , 0.4872, 0.4502, 0.3921])