sech_pulse_pwc
- signals.sech_pulse_pwc(duration, segment_count, amplitude, width=None, center_time=None, *, name=None)
Create a Pwc representing a hyperbolic secant pulse.
- 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 pulse, \(A\). It must either be a scalar or contain a single element.
width (float or Tensor or None, optional) – The characteristic time for the hyperbolic secant pulse, \(t_\mathrm{pulse}\). If passed, it must either be a scalar or contain a single element. Defaults to \(T/12\), giving the pulse a full width at half maximum (FWHM) of \(0.22 T\).
center_time (float or Tensor or None, optional) – The time at which the pulse peaks, \(t_\mathrm{peak}\). If passed, it must either be a scalar or contain a single element. Defaults to \(T/2\).
name (str or None, optional) – The name of the node.
- Returns:
The sampled hyperbolic secant pulse.
- Return type:
See also
Graph.signals.cosine_pulse_pwc
Create a Pwc representing a cosine pulse.
Graph.signals.gaussian_pulse_pwc
Create a Pwc representing a Gaussian pulse.
boulderopal.signals.sech_pulse
Create a Signal object representing a hyperbolic secant pulse.
Graph.signals.sech_pulse_stf
Corresponding operation with Stf output.
Graph.signals.square_pulse_pwc
Create a Pwc representing a square pulse.
Notes
The hyperbolic secant pulse is defined as
\[\mathop{\mathrm{Sech}}(t) = \frac{A}{\cosh\left((t - t_\mathrm{peak}) / t_\mathrm{pulse} \right)} .\]The FWHM of the pulse is about \(2.634 t_\mathrm{pulse}\).
Examples
Define a simple sech PWC pulse.
>>> graph.signals.sech_pulse_pwc( ... duration=5, segment_count=50, amplitude=1, name="sech" ... ) <Pwc: name="sech", operation_name="discretize_stf", value_shape=(), batch_shape=()> >>> result = bo.execute_graph(graph=graph, output_node_names="sech") >>> result["output"]["sech"] { 'durations': array([0.1, 0.1, ..., 0.1, 0.1]), 'values': array([0.00558953, 0.00710565, ..., 0.00710565, 0.00558953]), 'time_dimension': 0 }
Define a displaced sech PWC pulse.
>>> graph.signals.sech_pulse_pwc( ... duration=3e-6, ... segment_count=60, ... amplitude=20e6, ... width=0.15e-6, ... center_time=1e-6, ... name="displaced", ... ) <Pwc: name="displaced", operation_name="discretize_stf", value_shape=(), batch_shape=()> >>> result = bo.execute_graph(graph=graph, output_node_names="sech_displaced") >>> result["output"]["sech_displaced"] { 'durations': array([5.e-08, 5.e-08, ..., 5.e-08, 5.e-08]), 'values': array([6.01374318e+04, 8.39283672e+04, ..., 1.06810547e+02, 7.65331014e+01]), 'time_dimension': 0 }
Define a sech pulse with optimizable parameters.
>>> amplitude = graph.optimizable_scalar( ... lower_bound=0, upper_bound=10e6, name="amplitude" ... ) >>> width = graph.optimizable_scalar( ... lower_bound=0.1e-6, upper_bound=0.5e-6, name="width" ... ) >>> center_time = graph.optimizable_scalar( ... lower_bound=1e-6, upper_bound=2e-6, name="center_time" ... ) >>> graph.signals.sech_pulse_pwc( ... duration=3e-6, ... segment_count=32, ... amplitude=amplitude, ... width=width, ... center_time=center_time, ... name="sech_pulse", ... ) <Pwc: name="sech_pulse", operation_name="discretize_stf", value_shape=(), batch_shape=()>