sinusoid_pwc

signals.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 or None, optional) – The name of the node.

Returns:

The sampled sinusoid.

Return type:

Pwc

See also

Graph.signals.cosine_pulse_pwc: Create a Pwc representing a cosine pulse.
Graph.signals.hann_series_pwc: Create a Pwc representing a sum of Hann window functions.
boulderopal.signals.sinusoid: Create a Signal object representing a sinusoidal oscillation.
Graph.signals.sinusoid_stf: Corresponding operation with Stf output.
Graph.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 = bo.execute_graph(graph=graph, output_node_names="oscillation")
>>> result["output"]["oscillation"]
{
    'durations': array([0.05, 0.05, ..., 0.05, 0.05]),
    'values': array([ 0.99691733,  0.97236992,  ..., -0.97236992, -0.99691733]),
    'time_dimension': 0
}

Define a sinusoid with optimizable parameters.

>>> amplitude = graph.optimizable_scalar(
...     lower_bound=0, upper_bound=4e3, name="amplitude"
... )
>>> angular_frequency = graph.optimizable_scalar(
...     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=()>