# sinusoid_pwc

The Boulder Opal Toolkits are currently in beta phase of development. Breaking changes may be introduced.

sinusoid_pwc(duration, segment_count, amplitude, angular_frequency, phase=0.0, *, name=None)

Create a Pwc representing a sinusoidal oscillation.

Parameters:
• duration (float) – The duration of the signal, $$T$$.

• segment_count (int) – The number of segments in the PWC.

• amplitude (float or complex or Tensor) – The amplitude of the oscillation, $$A$$. It must either be a scalar or contain a single element.

• angular_frequency (float or Tensor) – The angular frequency of the oscillation, $$\omega$$. It must either be a scalar or contain a single element.

• phase (float or Tensor, optional) – The phase of the oscillation, $$\phi$$. If passed, it must either be a scalar or contain a single element. Defaults to 0.

• name (str, optional) – The name of the node.

Returns:

The sampled sinusoid.

Return type:

Pwc

signals.cosine_pulse_pwc()

Create a Pwc representing a cosine pulse.

signals.hann_series_pwc()

Create a Pwc representing a sum of Hann window functions.

signals.sinusoid()

Function to create a Signal object representing a sinusoidal oscillation.

signals.sinusoid_stf()

Corresponding operation with Stf output.

sin()

Calculate the element-wise sine of an object.

Notes

The sinusoid is defined as

$\mathop{\mathrm{Sinusoid}}(t) = A \sin \left( \omega t + \phi \right) .$

Examples

Define a PWC oscillation.

>>> graph.signals.sinusoid_pwc(
...     duration=5.0,
...     segment_count=100,
...     amplitude=1.0,
...     angular_frequency=np.pi,
...     phase=np.pi/2.0,
...     name="oscillation"
... )
<Pwc: name="oscillation", operation_name="discretize_stf", value_shape=(), batch_shape=()>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["oscillation"])
>>> result.output["oscillation"]
[
{'value': 0.997, 'duration': 0.05},
{'value': 0.972, 'duration': 0.05},
...
{'value': -0.972, 'duration': 0.05},
{'value': -0.996, 'duration': 0.05},
]


Define a sinusoid with optimizable parameters.

>>> amplitude = graph.optimization_variable(
...     count=1, lower_bound=0, upper_bound=4e3, name="amplitude"
... )
>>> angular_frequency = graph.optimization_variable(
...     count=1, lower_bound=5e6, upper_bound=20e6, name="angular_frequency"
... )
>>> phase = graph.optimization_variable(
...     count=1,
...     lower_bound=0,
...     upper_bound=2*np.pi,
...     is_lower_unbounded=True,
...     is_upper_unbounded=True,
...     name="phase",
... )
>>> graph.signals.sinusoid_pwc(
...     duration=3e-6,
...     segment_count=100,
...     amplitude=amplitude,
...     angular_frequency=angular_frequency,
...     phase=phase,
...     name="oscillation"
... )
<Pwc: name="oscillation", operation_name="discretize_stf", value_shape=(), batch_shape=()>