"""Weights (tapering) for the driving function.
.. plot::
:context: reset
import sfs
import matplotlib.pyplot as plt
import numpy as np
plt.rcParams['figure.figsize'] = 8, 3 # inch
plt.rcParams['axes.grid'] = True
active1 = np.zeros(101, dtype=bool)
active1[5:-5] = True
# The active part can wrap around from the end to the beginning:
active2 = np.ones(101, dtype=bool)
active2[30:-10] = False
"""
import numpy as _np
def none(active):
"""No tapering window.
Parameters
----------
active : array_like, dtype=bool
A boolean array containing ``True`` for active loudspeakers.
Returns
-------
type(active)
The input, unchanged.
Examples
--------
.. plot::
:context: close-figs
plt.plot(sfs.tapering.none(active1))
plt.axis([-3, 103, -0.1, 1.1])
.. plot::
:context: close-figs
plt.plot(sfs.tapering.none(active2))
plt.axis([-3, 103, -0.1, 1.1])
"""
return active
def tukey(active, *, alpha):
"""Tukey tapering window.
This uses a function similar to :func:`scipy.signal.tukey`, except
that the first and last value are not zero.
Parameters
----------
active : array_like, dtype=bool
A boolean array containing ``True`` for active loudspeakers.
alpha : float
Shape parameter of the Tukey window, see
:func:`scipy.signal.tukey`.
Returns
-------
(len(active),) `numpy.ndarray`
Tapering weights.
Examples
--------
.. plot::
:context: close-figs
plt.plot(sfs.tapering.tukey(active1, alpha=0), label='alpha = 0')
plt.plot(sfs.tapering.tukey(active1, alpha=0.25), label='alpha = 0.25')
plt.plot(sfs.tapering.tukey(active1, alpha=0.5), label='alpha = 0.5')
plt.plot(sfs.tapering.tukey(active1, alpha=0.75), label='alpha = 0.75')
plt.plot(sfs.tapering.tukey(active1, alpha=1), label='alpha = 1')
plt.axis([-3, 103, -0.1, 1.1])
plt.legend(loc='lower center')
.. plot::
:context: close-figs
plt.plot(sfs.tapering.tukey(active2, alpha=0.3))
plt.axis([-3, 103, -0.1, 1.1])
"""
idx = _windowidx(active)
alpha = _np.clip(alpha, 0, 1)
if alpha == 0:
return none(active)
# design Tukey window
x = _np.linspace(0, 1, len(idx) + 2)
tukey = _np.ones_like(x)
first_part = x < alpha / 2
tukey[first_part] = 0.5 * (
1 + _np.cos(2 * _np.pi / alpha * (x[first_part] - alpha / 2)))
third_part = x >= (1 - alpha / 2)
tukey[third_part] = 0.5 * (
1 + _np.cos(2 * _np.pi / alpha * (x[third_part] - 1 + alpha / 2)))
# fit window into tapering function
result = _np.zeros(len(active))
result[idx] = tukey[1:-1]
return result
def kaiser(active, *, beta):
"""Kaiser tapering window.
This uses :func:`numpy.kaiser`.
Parameters
----------
active : array_like, dtype=bool
A boolean array containing ``True`` for active loudspeakers.
alpha : float
Shape parameter of the Kaiser window, see :func:`numpy.kaiser`.
Returns
-------
(len(active),) `numpy.ndarray`
Tapering weights.
Examples
--------
.. plot::
:context: close-figs
plt.plot(sfs.tapering.kaiser(active1, beta=0), label='beta = 0')
plt.plot(sfs.tapering.kaiser(active1, beta=2), label='beta = 2')
plt.plot(sfs.tapering.kaiser(active1, beta=6), label='beta = 6')
plt.plot(sfs.tapering.kaiser(active1, beta=8.6), label='beta = 8.6')
plt.plot(sfs.tapering.kaiser(active1, beta=14), label='beta = 14')
plt.axis([-3, 103, -0.1, 1.1])
plt.legend(loc='lower center')
.. plot::
:context: close-figs
plt.plot(sfs.tapering.kaiser(active2, beta=7))
plt.axis([-3, 103, -0.1, 1.1])
"""
idx = _windowidx(active)
window = _np.zeros(len(active))
window[idx] = _np.kaiser(len(idx), beta)
return window
def _windowidx(active):
"""Return list of connected indices for window function.
Note: Gaps within the active part are not allowed.
"""
# find index where active loudspeakers begin (works for connected contours)
if (active[0] and not active[-1]) or _np.all(active):
first_idx = 0
else:
first_idx = _np.argmax(_np.diff(active.astype(int))) + 1
# shift generic index vector to get a connected list of indices
idx = _np.roll(_np.arange(len(active)), -first_idx)
# remove indices of inactive secondary sources
return idx[:_np.count_nonzero(active)]
