cosine_pulse_pwc

signals.cosine_pulse_pwc(duration, segment_count, amplitude, drag=None, start_time=0.0, end_time=None, flat_duration=None, segmentation=SegmentationType.UNIFORM, *, name=None)

Create a Pwc representing a cosine pulse.

Parameters

  • duration (float) – The duration of the signal, TT
  • segment_count (int) – The number of segments in the PWC. Must be at least six.
  • amplitude (float or complex or Tensor) – The amplitude of the pulse, AA
  • drag (float or Tensor or None , optional) – The DRAG parameter, β\beta
  • start_time (float , optional) – The time at which the cosine pulse starts, tstartt_\mathrm{start}
  • end_time (float or None , optional) – The time at which the cosine pulse ends, tendt_\mathrm{end}. Defaults to the given duration TT
  • flat_duration (float or None , optional) – The amount of time to remain constant after the peak of the cosine, tflatt_\mathrm{flat}
  • segmentation (SegmentationType) – The type of segmentation for the signal. With a “MINIMAL” segmentation, most of the segments are placed in the non-constant parts of the signal. Defaults to “UNIFORM”, in which case the segments are uniformly distributed along the signal’s duration.
  • name (str or None , optional) – The name of the node.

Returns

The sampled cosine pulse. If no flat duration is passed then the pulse is evenly sampled between 00 and TT

Return type

Pwc

SEE ALSO

boulderopal.signals.cosine_pulse : Create a Signal object representing a cosine pulse.

Graph.signals.gaussian_pulse_pwc : Create a Pwc representing a Gaussian pulse.

Graph.signals.hann_series_pwc : Create a Pwc representing a sum of Hann window functions.

Graph.signals.sech_pulse_pwc : Create a Pwc representing a hyperbolic secant pulse.

Graph.signals.sinusoid_pwc : Create a Pwc representing a sinusoidal oscillation.

Graph.signals.square_pulse_pwc : Create a Pwc representing a square pulse.

Graph.cos : Calculate the element-wise cosine of an object.

Notes

The cosine pulse is defined as

Cos(t)={0ift<tstartA2[1+cos⁡(ωt−τ−)+iωβsin⁡(ωt−τ−)]iftstart≤t<τ−Aifτ−≤t≤τ+A2[1+cos⁡(ωt−τ+)+iωβsin⁡(ωt−τ+)]ifτ+<t≤tend0ift>tend, \mathop{\mathrm{Cos}}(t) = \begin{cases} 0 &\mathrm{if} \quad t < t_\mathrm{start} \\ \frac{A}{2} \left[1+\cos \left(\omega \\{t-\tau_-\\} \right) + i\omega\beta \sin \left(\omega \\{t-\tau_-\\}\right)\right] &\mathrm{if} \quad t_\mathrm{start} \le t < \tau_- \\ A &\mathrm{if} \quad \tau_- \le t \le \tau_+ \\ \frac{A}{2} \left[1+\cos \left(\omega\\{t-\tau_+\\}\right) + i\omega \beta\sin \left(\omega \\{t-\tau_+\\}\right)\right] &\mathrm{if} \quad \tau_+ < t \le t_\mathrm{end} \\ 0 &\mathrm{if} \quad t > t_\mathrm{end} \\ \end{cases},

where ω=2π/(tend−tstart−tflat)\omega=2\pi /(t_\mathrm{end}-t_\mathrm{start} - t_\mathrm{flat}), τ∓\tau_\mp are the start/end times of the flat segment, with τ∓=(tstart+tend∓tflat)/2\tau_\mp=(t_\mathrm{start}+t_\mathrm{end} \mp t_\mathrm{flat})/2

If the flat duration is zero (the default setting), this reduces to

Cos(t)=A2[1+cos⁡(ωt−τ)+iωβsin⁡(ωt−τ)]θ(t−tstart)θ(tend−t), \mathop{\mathrm{Cos}}(t) = \frac{A}{2} \left[1+\cos \left(\omega \\{t-\tau\\} \right) + i\omega\beta \sin \left(\omega \\{t-\tau\\}\right)\right] \theta(t-t_\mathrm{start}) \theta(t_\mathrm{end}-t),

where now ω=2π/(tend−tstart)\omega=2\pi /(t_\mathrm{end}-t_\mathrm{start}), τ=(tstart+tend)/2\tau=(t_\mathrm{start}+t_\mathrm{end})/2 and θ(t)\theta(t)Heaviside step function.

Examples

Define a cosine PWC pulse.

>>> graph.signals.cosine_pulse_pwc(
...     duration=3.0, segment_count=100, amplitude=1.0, name="cos_pulse"
... )
<Pwc: name="cos_pulse", operation_name="pwc_signal", value_shape=(), batch_shape=()>
>>> result = bo.execute_graph(graph=graph, output_node_names="cos_pulse")
>>> result["output"]["cos_pulse"]
{
    'durations': array([0.03, 0.03, ..., 0.03, 0.03]),
    'values': array([2.46719817e-04, 2.21901770e-03, ..., 2.21901770e-03, 2.46719817e-04]),
    'time_dimension': 0
}

Define a flat-top cosine PWC pulse with a DRAG correction.

>>> graph.signals.cosine_pulse_pwc(
...     duration=3.0,
...     segment_count=100,
...     amplitude=1.0,
...     drag=0.1,
...     start_time=1.0,
...     end_time=2.0,
...     flat_duration=0.3,
...     segmentation="MINIMAL",
...     name="cos_flat",
... )
<Pwc: name="cos_flat", operation_name="pwc_signal", value_shape=(), batch_shape=()>
>>> result = bo.execute_graph(graph=graph, output_node_names="cos_flat")
>>> result["output"]["cos_flat"]
{
    'durations': array([1.        , 0.00729167, ..., 0.00729167, 1.        ]),
    'values': array([0.00000000e+00+0.j        , 2.67706262e-04-0.01468429j, ...,
                     2.67706262e-04+0.01468429j, 0.00000000e+00+0.j        ]),
    'time_dimension': 0
}

Define a cosine pulse with optimizable parameters.

>>> amplitude = graph.optimizable_scalar(
...     lower_bound=0, upper_bound=2.*np.pi, name="amplitude"
... )
>>> drag = graph.optimizable_scalar(
...     lower_bound=0, upper_bound=1., name="drag"
... )
>>> graph.signals.cosine_pulse_pwc(
...     duration=3.0,
...     segment_count=100,
...     amplitude=amplitude,
...     drag=drag,
...     name="cos_pulse",
... )
<Pwc: name="cos_pulse", operation_name="pwc_signal", value_shape=(), batch_shape=()>

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