# hann_series¶

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

hann_series(duration, coefficients)

Create a Pulse object representing a sum of Hann window functions.

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

• coefficients (np.ndarray) – The coefficients for the different Hann window functions, $$c_n$$. It must be a 1D array.

Returns

The Hann window functions series.

Return type

Pulse

pulses.cosine_pulse()

Create a Pulse object representing a cosine pulse.

pulses.sinusoid()

Create a Pulse object representing a sinusoidal oscillation.

pulses.hann_series_pwc()

Graph operation to create a Pwc representing a sum of Hann window functions.

pulses.hann_series_stf()

Graph operation to create an Stf representing a sum of Hann window functions.

Notes

The series is defined as

$\mathop{\mathrm{Hann}}(t) = \sum_{n=1}^N c_n \sin^2 \left( \frac{\pi n t}{T} \right) ,$

where $$N$$ is the number of coefficients.

Examples

Define a simple Hann series.

>>> pulse = graph.pulses.hann_series(
...     duration=5.0,
...     coefficients=np.array([0.5, 1, 0.25]),
... )
>>> pulse.export_with_time_step(time_step=0.5)
array([0.15925422, 1.00144425, 1.375     , 1.05757275, 0.78172879,
0.78172879, 1.05757275, 1.375     , 1.00144425, 0.15925422])