sfs.td.wfs¶
Compute WFS driving functions.
import matplotlib.pyplot as plt
import numpy as np
import sfs
from scipy.signal import unit_impulse
# Plane wave
npw = sfs.util.direction_vector(np.radians(-45))
# Point source
xs = -1.5, 1.5, 0
rs = np.linalg.norm(xs) # distance from origin
ts = rs / sfs.default.c # time-of-arrival at origin
# Focused source
xf = -0.5, 0.5, 0
nf = sfs.util.direction_vector(np.radians(-45)) # normal vector
rf = np.linalg.norm(xf) # distance from origin
tf = rf / sfs.default.c # time-of-arrival at origin
# Impulsive excitation
fs = 44100
signal = unit_impulse(512), fs
# Circular loudspeaker array
N = 32 # number of loudspeakers
R = 1.5 # radius
array = sfs.array.circular(N, R)
grid = sfs.util.xyz_grid([-2, 2], [-2, 2], 0, spacing=0.02)
def plot(d, selection, secondary_source, t=0):
p = sfs.td.synthesize(d, selection, array, secondary_source, grid=grid,
observation_time=t)
sfs.plot2d.level(p, grid)
sfs.plot2d.loudspeakers(array.x, array.n,
selection * array.a, size=0.15)
Functions
|
Get driving signals per secondary source. |
|
Point source by 2.5-dimensional WFS. |
|
Plane wave model by 2.5-dimensional WFS. |
|
Driving function for 2.5-dimensional WFS of a virtual point source. |
|
Driving function for 2.5-dimensional WFS of a virtual point source. |
- sfs.td.wfs.plane_25d(x0, n0, n=[0, 1, 0], xref=[0, 0, 0], c=None)[source]¶
Plane wave model by 2.5-dimensional WFS.
- Parameters
x0 ((N, 3) array_like) – Sequence of secondary source positions.
n0 ((N, 3) array_like) – Sequence of secondary source orientations.
n ((3,) array_like, optional) – Normal vector (propagation direction) of synthesized plane wave.
xref ((3,) array_like, optional) – Reference position
c (float, optional) – Speed of sound
- Returns
delays ((N,) numpy.ndarray) – Delays of secondary sources in seconds.
weights ((N,) numpy.ndarray) – Weights of secondary sources.
selection ((N,) numpy.ndarray) – Boolean array containing
True
orFalse
depending on whether the corresponding secondary source is “active” or not.secondary_source_function (callable) – A function that can be used to create the sound field of a single secondary source. See
sfs.td.synthesize()
.
Notes
2.5D correction factor
\[g_0 = \sqrt{2 \pi |x_\mathrm{ref} - x_0|}\]d using a plane wave as source model
\[d_{2.5D}(x_0,t) = 2 g_0 \scalarprod{n}{n_0} \dirac{t - \frac{1}{c} \scalarprod{n}{x_0}} \ast_t h(t)\]with wfs(2.5D) prefilter h(t), which is not implemented yet.
See https://sfs.rtfd.io/d_wfs/#equation-td-wfs-plane-25d
Examples
delays, weights, selection, secondary_source = \ sfs.td.wfs.plane_25d(array.x, array.n, npw) d = sfs.td.wfs.driving_signals(delays, weights, signal) plot(d, selection, secondary_source)
- sfs.td.wfs.point_25d(x0, n0, xs, xref=[0, 0, 0], c=None)[source]¶
Driving function for 2.5-dimensional WFS of a virtual point source.
Changed in version 0.61: see notes, old handling of
point_25d()
is nowpoint_25d_legacy()
- Parameters
x0 ((N, 3) array_like) – Sequence of secondary source positions.
n0 ((N, 3) array_like) – Sequence of secondary source orientations.
xs ((3,) array_like) – Virtual source position.
xref ((N, 3) array_like or (3,) array_like) – Reference curve of correct amplitude xref(x0)
c (float, optional) – Speed of sound
- Returns
delays ((N,) numpy.ndarray) – Delays of secondary sources in seconds.
weights ((N,) numpy.ndarray) – Weights of secondary sources.
selection ((N,) numpy.ndarray) – Boolean array containing
True
orFalse
depending on whether the corresponding secondary source is “active” or not.secondary_source_function (callable) – A function that can be used to create the sound field of a single secondary source. See
sfs.td.synthesize()
.
Notes
Eq. (2.138) in [Sch16]:
\[d_{2.5D}(x_0, x_{ref}, t) = \sqrt{8\pi} \frac{\scalarprod{(x_0 - x_s)}{n_0}}{|x_0 - x_s|} \sqrt{\frac{|x_0 - x_s||x_0 - x_{ref}|}{|x_0 - x_s|+|x_0 - x_{ref}|}} \cdot \frac{\dirac{t - \frac{|x_0 - x_s|}{c}}}{4\pi |x_0 - x_s|} \ast_t h(t)\]\[h(t) = F^{-1}(\sqrt{\frac{j \omega}{c}})\]with wfs(2.5D) prefilter h(t), which is not implemented yet.
point_25d()
derives WFS from 3D to 2.5D via the stationary phase approximation approach (i.e. the Delft approach). The theoretical link ofpoint_25d()
andpoint_25d_legacy()
was introduced as unified WFS framework in [FFSS17].Examples
delays, weights, selection, secondary_source = \ sfs.td.wfs.point_25d(array.x, array.n, xs) d = sfs.td.wfs.driving_signals(delays, weights, signal) plot(d, selection, secondary_source, t=ts)
- sfs.td.wfs.point_25d_legacy(x0, n0, xs, xref=[0, 0, 0], c=None)[source]¶
Driving function for 2.5-dimensional WFS of a virtual point source.
New in version 0.61:
point_25d()
was renamed topoint_25d_legacy()
(and a new function with the namepoint_25d()
was introduced). See notes below for further details.- Parameters
x0 ((N, 3) array_like) – Sequence of secondary source positions.
n0 ((N, 3) array_like) – Sequence of secondary source orientations.
xs ((3,) array_like) – Virtual source position.
xref ((3,) array_like, optional) – Reference position
c (float, optional) – Speed of sound
- Returns
delays ((N,) numpy.ndarray) – Delays of secondary sources in seconds.
weights ((N,) numpy.ndarray) – Weights of secondary sources.
selection ((N,) numpy.ndarray) – Boolean array containing
True
orFalse
depending on whether the corresponding secondary source is “active” or not.secondary_source_function (callable) – A function that can be used to create the sound field of a single secondary source. See
sfs.td.synthesize()
.
Notes
2.5D correction factor
\[g_0 = \sqrt{2 \pi |x_\mathrm{ref} - x_0|}\]d using a point source as source model
\[d_{2.5D}(x_0,t) = \frac{g_0 \scalarprod{(x_0 - x_s)}{n_0}} {2\pi |x_0 - x_s|^{3/2}} \dirac{t - \frac{|x_0 - x_s|}{c}} \ast_t h(t)\]with wfs(2.5D) prefilter h(t), which is not implemented yet.
See https://sfs.rtfd.io/d_wfs/#equation-td-wfs-point-25d
point_25d_legacy()
derives 2.5D WFS from the 2D Neumann-Rayleigh integral (i.e. the approach by Rabenstein & Spors), cf. [SRA08]. The theoretical link ofpoint_25d()
andpoint_25d_legacy()
was introduced as unified WFS framework in [FFSS17].Examples
delays, weights, selection, secondary_source = \ sfs.td.wfs.point_25d(array.x, array.n, xs) d = sfs.td.wfs.driving_signals(delays, weights, signal) plot(d, selection, secondary_source, t=ts)
- sfs.td.wfs.focused_25d(x0, n0, xs, ns, xref=[0, 0, 0], c=None)[source]¶
Point source by 2.5-dimensional WFS.
- Parameters
x0 ((N, 3) array_like) – Sequence of secondary source positions.
n0 ((N, 3) array_like) – Sequence of secondary source orientations.
xs ((3,) array_like) – Virtual source position.
ns ((3,) array_like) – Normal vector (propagation direction) of focused source. This is used for secondary source selection, see
sfs.util.source_selection_focused()
.xref ((3,) array_like, optional) – Reference position
c (float, optional) – Speed of sound
- Returns
delays ((N,) numpy.ndarray) – Delays of secondary sources in seconds.
weights ((N,) numpy.ndarray) – Weights of secondary sources.
selection ((N,) numpy.ndarray) – Boolean array containing
True
orFalse
depending on whether the corresponding secondary source is “active” or not.secondary_source_function (callable) – A function that can be used to create the sound field of a single secondary source. See
sfs.td.synthesize()
.
Notes
2.5D correction factor
\[g_0 = \sqrt{\frac{|x_\mathrm{ref} - x_0|} {|x_0-x_s| + |x_\mathrm{ref}-x_0|}}\]d using a point source as source model
\[d_{2.5D}(x_0,t) = \frac{g_0 \scalarprod{(x_0 - x_s)}{n_0}} {|x_0 - x_s|^{3/2}} \dirac{t + \frac{|x_0 - x_s|}{c}} \ast_t h(t)\]with wfs(2.5D) prefilter h(t), which is not implemented yet.
See https://sfs.rtfd.io/d_wfs/#equation-td-wfs-focused-25d
Examples
delays, weights, selection, secondary_source = \ sfs.td.wfs.focused_25d(array.x, array.n, xf, nf) d = sfs.td.wfs.driving_signals(delays, weights, signal) plot(d, selection, secondary_source, t=tf)
- sfs.td.wfs.driving_signals(delays, weights, signal)[source]¶
Get driving signals per secondary source.
Returned signals are the delayed and weighted mono input signal (with N samples) per channel (C).
- Parameters
delays ((C,) array_like) – Delay in seconds for each channel, negative values allowed.
weights ((C,) array_like) – Amplitude weighting factor for each channel.
signal ((N,) array_like + float) – Excitation signal consisting of (mono) audio data and a sampling rate (in Hertz). A
DelayedSignal
object can also be used.
- Returns
DelayedSignal
– A tuple containing the driving signals (in anumpy.ndarray
with shape(N, C)
), followed by the sampling rate (in Hertz) and a (possibly negative) time offset (in seconds).