sfs.fd.nfchoa¶

Compute NFC-HOA driving functions.

\[\gdef\dirac#1{\mathop{{}\delta}\left(#1\right)} \gdef\e#1{\operatorname{e}^{#1}} \gdef\Hankel#1#2#3{\mathop{{}H_{#2}^{(#1)}}\!\left(#3\right)} \gdef\hankel#1#2#3{\mathop{{}h_{#2}^{(#1)}}\!\left(#3\right)} \gdef\i{\mathrm{i}} \gdef\scalarprod#1#2{\left\langle#1,#2\right\rangle} \gdef\vec#1{\mathbf{#1}} \gdef\wc{\frac{\omega}{c}} \gdef\w{\omega} \gdef\x{\vec{x}} \gdef\n{\vec{n}}\]

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:
npw = sfs.util.direction_vector(np.radians(-45))
f = 300  # Hz
omega = 2 * np.pi * f
R = 1.5  # Radius of circular loudspeaker array

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

array = sfs.array.circular(N=32, R=R)

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

`plane_25d`(omega, x0, r0[, n, max_order, c])	Driving function for 2.5-dimensional NFC-HOA for a virtual plane wave.
`plane_2d`(omega, x0, r0[, n, max_order, c])	Driving function for 2-dimensional NFC-HOA for a virtual plane wave.
`point_25d`(omega, x0, r0, xs, *[, max_order, c])	Driving function for 2.5-dimensional NFC-HOA for a virtual point source.

sfs.fd.nfchoa.plane_2d(omega, x0, r0, n=[0, 1, 0], *, max_order=None, c=None)[source]¶

Driving function for 2-dimensional NFC-HOA for a virtual plane wave.

Parameters

omega (float) – Angular frequency of plane wave.
x0 ((N, 3) array_like) – Sequence of secondary source positions.
r0 (float) – Radius of circular secondary source distribution.
n ((3,) array_like, optional) – Normal vector (traveling direction) of plane wave.
max_order (float, optional) – Maximum order of circular harmonics used for the calculation.
c (float, optional) – Speed of sound.

Returns

d ((N,) numpy.ndarray) – Complex weights of secondary sources.
selection ((N,) numpy.ndarray) – Boolean array containing only True indicating that all secondary source are “active” for NFC-HOA.
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

\[D(\phi_0, \omega) = -\frac{2\i}{\pi r_0} \sum_{m=-M}^M \frac{\i^{-m}}{\Hankel{2}{m}{\wc r_0}} \e{\i m (\phi_0 - \phi_\text{pw})}\]

See https://sfs.rtfd.io/d_nfchoa/#equation-fd-nfchoa-plane-2d

Examples

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

sfs.fd.nfchoa.point_25d(omega, x0, r0, xs, *, max_order=None, c=None)[source]¶

Driving function for 2.5-dimensional NFC-HOA for a virtual point source.

Parameters

omega (float) – Angular frequency of point source.
x0 ((N, 3) array_like) – Sequence of secondary source positions.
r0 (float) – Radius of circular secondary source distribution.
xs ((3,) array_like) – Position of point source.
max_order (float, optional) – Maximum order of circular harmonics used for the calculation.
c (float, optional) – Speed of sound.

Returns

d ((N,) numpy.ndarray) – Complex weights of secondary sources.
selection ((N,) numpy.ndarray) – Boolean array containing only True indicating that all secondary source are “active” for NFC-HOA.
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

\[D(\phi_0, \omega) = \frac{1}{2 \pi r_0} \sum_{m=-M}^M \frac{\hankel{2}{|m|}{\wc r}}{\hankel{2}{|m|}{\wc r_0}} \e{\i m (\phi_0 - \phi)}\]

See https://sfs.rtfd.io/d_nfchoa/#equation-fd-nfchoa-point-25d

Examples

d, selection, secondary_source = sfs.fd.nfchoa.point_25d(
    omega, array.x, R, xs)
plot(d, selection, secondary_source)

sfs.fd.nfchoa.plane_25d(omega, x0, r0, n=[0, 1, 0], *, max_order=None, c=None)[source]¶

Driving function for 2.5-dimensional NFC-HOA for a virtual plane wave.

Parameters

omega (float) – Angular frequency of point source.
x0 ((N, 3) array_like) – Sequence of secondary source positions.
r0 (float) – Radius of circular secondary source distribution.
n ((3,) array_like, optional) – Normal vector (traveling direction) of plane wave.
max_order (float, optional) – Maximum order of circular harmonics used for the calculation.
c (float, optional) – Speed of sound.

Returns

d ((N,) numpy.ndarray) – Complex weights of secondary sources.
selection ((N,) numpy.ndarray) – Boolean array containing only True indicating that all secondary source are “active” for NFC-HOA.
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

\[D(\phi_0, \omega) = \frac{2\i}{r_0} \sum_{m=-M}^M \frac{\i^{-|m|}}{\wc \hankel{2}{|m|}{\wc r_0}} \e{\i m (\phi_0 - \phi_\text{pw})}\]

See https://sfs.rtfd.io/d_nfchoa/#equation-fd-nfchoa-plane-25d

Examples

d, selection, secondary_source = sfs.fd.nfchoa.plane_25d(
    omega, array.x, R, npw)
plot(d, selection, secondary_source)