# sfs.fd.sdm¶

Compute SDM driving functions.

import matplotlib.pyplot as plt
import numpy as np
import sfs

plt.rcParams['figure.figsize'] = 6, 6

xs = -1.5, 1.5, 0
# normal vector for plane wave:
f = 300  # Hz
omega = 2 * np.pi * f

grid = sfs.util.xyz_grid([-2, 2], [-2, 2], 0, spacing=0.02)

array = sfs.array.linear(32, 0.2, orientation=[0, -1, 0])

def plot(d, selection, secondary_source):
p = sfs.fd.synthesize(d, selection, array, secondary_source, grid=grid)
sfs.plot2d.amplitude(p, grid)
sfs.plot2d.loudspeakers(array.x, array.n, selection * array.a, size=0.15)


Functions

 line_2d(omega, x0, n0, xs, *[, c]) Driving function for 2-dimensional SDM for a virtual line source. plane_25d(omega, x0, n0[, n, xref, c]) Driving function for 2.5-dimensional SDM for a virtual plane wave. plane_2d(omega, x0, n0[, n, c]) Driving function for 2-dimensional SDM for a virtual plane wave. point_25d(omega, x0, n0, xs, *[, xref, c]) Driving function for 2.5-dimensional SDM for a virtual point source.
sfs.fd.sdm.line_2d(omega, x0, n0, xs, *, c=None)[source]

Driving function for 2-dimensional SDM for a virtual line source.

Parameters
• omega (float) – Angular frequency of line source.

• x0 ((N, 3) array_like) – Sequence of secondary source positions.

• n0 ((N, 3) array_like) – Sequence of normal vectors of secondary sources.

• xs ((3,) array_like) – Position of line source.

• c (float, optional) – Speed of sound.

Returns

• d ((N,) numpy.ndarray) – Complex weights of secondary sources.

• selection ((N,) numpy.ndarray) – Boolean array containing True or False 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.fd.synthesize().

Notes

The secondary sources have to be located on the x-axis (y0=0). Derived from [SA09], Eq.(9), Eq.(4).

Examples

d, selection, secondary_source = sfs.fd.sdm.line_2d(
omega, array.x, array.n, xs)
plot(d, selection, secondary_source)

sfs.fd.sdm.plane_2d(omega, x0, n0, n=[0, 1, 0], *, c=None)[source]

Driving function for 2-dimensional SDM for a virtual plane wave.

Parameters
• omega (float) – Angular frequency of plane wave.

• x0 ((N, 3) array_like) – Sequence of secondary source positions.

• n0 ((N, 3) array_like) – Sequence of normal vectors of secondary sources.

• n ((3,) array_like, optional) – Normal vector (traveling direction) of plane wave.

• c (float, optional) – Speed of sound.

Returns

• d ((N,) numpy.ndarray) – Complex weights of secondary sources.

• selection ((N,) numpy.ndarray) – Boolean array containing True or False 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.fd.synthesize().

Notes

The secondary sources have to be located on the x-axis (y0=0). Derived from [Ahr12], Eq.(3.73), Eq.(C.5), Eq.(C.11):

$D(\x_0,k) = k_\text{pw,y} \e{-\i k_\text{pw,x} x}$

Examples

d, selection, secondary_source = sfs.fd.sdm.plane_2d(
omega, array.x, array.n, npw)
plot(d, selection, secondary_source)

sfs.fd.sdm.plane_25d(omega, x0, n0, n=[0, 1, 0], *, xref=[0, 0, 0], c=None)[source]

Driving function for 2.5-dimensional SDM for a virtual plane wave.

Parameters
• omega (float) – Angular frequency of plane wave.

• x0 ((N, 3) array_like) – Sequence of secondary source positions.

• n0 ((N, 3) array_like) – Sequence of normal vectors of secondary sources.

• n ((3,) array_like, optional) – Normal vector (traveling direction) of plane wave.

• xref ((3,) array_like, optional) – Reference point for synthesized sound field.

• c (float, optional) – Speed of sound.

Returns

• d ((N,) numpy.ndarray) – Complex weights of secondary sources.

• selection ((N,) numpy.ndarray) – Boolean array containing True or False 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.fd.synthesize().

Notes

The secondary sources have to be located on the x-axis (y0=0). Eq.(3.79) from [Ahr12].

Examples

d, selection, secondary_source = sfs.fd.sdm.plane_25d(
omega, array.x, array.n, npw, xref=[0, -1, 0])
plot(d, selection, secondary_source)

sfs.fd.sdm.point_25d(omega, x0, n0, xs, *, xref=[0, 0, 0], c=None)[source]

Driving function for 2.5-dimensional SDM for a virtual point source.

Parameters
• omega (float) – Angular frequency of point source.

• x0 ((N, 3) array_like) – Sequence of secondary source positions.

• n0 ((N, 3) array_like) – Sequence of normal vectors of secondary sources.

• xs ((3,) array_like) – Position of virtual point source.

• xref ((3,) array_like, optional) – Reference point for synthesized sound field.

• c (float, optional) – Speed of sound.

Returns

• d ((N,) numpy.ndarray) – Complex weights of secondary sources.

• selection ((N,) numpy.ndarray) – Boolean array containing True or False 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.fd.synthesize().

Notes

The secondary sources have to be located on the x-axis (y0=0). Driving function from [SA10], Eq.(24).

Examples

d, selection, secondary_source = sfs.fd.sdm.point_25d(
omega, array.x, array.n, xs, xref=[0, -1, 0])
plot(d, selection, secondary_source)