# sinusoid_stf

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

sinusoid_stf(amplitude, angular_frequency, phase=0.0)

Create an Stf representing a sinusoidal oscillation.

Parameters
• 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.

Returns

The sampleable sinusoid.

Return type

Stf

signals.hann_series_stf()

Create an Stf representing a sum of Hann window functions.

signals.sinusoid()

Function to create a Signal object representing a sinusoidal oscillation.

signals.sinusoid_pwc()

Corresponding operation with Pwc 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 an STF oscillation.

>>> oscillation = graph.signals.sinusoid_stf(
...     amplitude=1.0, angular_frequency=np.pi, phase=np.pi/2.0
... )
>>> oscillation
<Stf: operation_name="multiply", value_shape=(), batch_shape=()>
>>> graph.sample_stf(stf=oscillation, sample_times=np.linspace(0, 1, 5), name="oscillation")
<Tensor: name="oscillation", operation_name="sample_stf", shape=(5,)>
>>> graph.discretize_stf(
...     oscillation, duration=10, segment_count=100, name="discretized_oscillation"
... )
<Pwc: name="discretized_oscillation", operation_name="discretize_stf", value_shape=(), batch_shape=()>
>>> result = qctrl.functions.calculate_graph(
...     graph=graph, output_node_names=["oscillation", "discretized_oscillation"]
... )
>>> result.output["oscillation"]["value"]
array([ 1.000e+00,  7.071e-01,  1.225e-16, -7.071e-01, -1.000e+00])


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_stf(
...     amplitude=amplitude, angular_frequency=angular_frequency, phase=phase
... )
<Stf: operation_name="multiply", value_shape=(), batch_shape=()>