hann_series_pwc
- signals.hann_series_pwc(duration, segment_count, coefficients, *, name=None)
Create a Pwc representing a sum of Hann window functions.
The piecewise-constant function is sampled from Hann functions that start and end at zero.
- Parameters:
duration (float) – The duration of the signal, \(T\).
segment_count (int) – The number of segments in the PWC.
coefficients (np.ndarray or Tensor) – The coefficients for the different Hann window functions, \(c_n\). It must be a 1D array or Tensor and it can’t contain more than segment_count elements.
name (str or None, optional) – The name of the node.
- Returns:
The sampled Hann window functions series.
- Return type:
See also
Graph.signals.cosine_pulse_pwc
Create a Pwc representing a cosine pulse.
Graph.signals.sinusoid_pwc
Create a Pwc representing a sinusoidal oscillation.
boulderopal.signals.hann_series
Create a Signal object representing a sum of Hann window functions.
Graph.signals.hann_series_stf
Corresponding operation with Stf output.
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.
>>> graph.signals.hann_series_pwc( ... duration=5.0, ... segment_count=50, ... coefficients=np.array([0.5, 1, 0.25]), ... name="hann_series", ... ) <Pwc: name="hann_series", operation_name="pwc_signal", value_shape=(), batch_shape=()> >>> result = bo.execute_graph(graph=graph, output_node_names="hann_series") >>> result["output"]["hann_series"] { 'durations': array([0.1, 0.1, ..., 0.1, 0.1]), 'values': array([0.00665006, 0.05899895, ..., 0.05899895, 0.00665006]), 'time_dimension': 0 }
Define a Hann series with optimizable coefficients.
>>> coefficients = graph.optimization_variable( ... count=8, lower_bound=-3.5e6, upper_bound=3.5e6, name="coefficients" ... ) >>> graph.signals.hann_series_pwc( ... duration=2.0e-6, ... segment_count=128, ... coefficients=coefficients, ... name="hann_series", ... ) <Pwc: name="hann_series", operation_name="pwc_signal", value_shape=(), batch_shape=()>