sfs.td.source¶

Compute the sound field generated by a sound source.

The Green’s function describes the spatial sound propagation over time.

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

import matplotlib.pyplot as plt
import numpy as np
from scipy.signal import unit_impulse
import sfs

xs = 1.5, 1, 0  # source position
rs = np.linalg.norm(xs)  # distance from origin
ts = rs / sfs.default.c  # time-of-arrival at origin

# Impulsive excitation
fs = 44100
signal = unit_impulse(512), fs

grid = sfs.util.xyz_grid([-2, 3], [-1, 2], 0, spacing=0.02)

Functions

`point`(xs, signal, observation_time, grid[, c])	Source model for a point source: 3D Green’s function.
`point_image_sources`(x0, signal, …[, coeffs, c])	Point source in a rectangular room using the mirror image source model.

sfs.td.source.point(xs, signal, observation_time, grid, c=None)[source]¶

Source model for a point source: 3D Green’s function.

Calculates the scalar sound pressure field for a given point in time, evoked by source excitation signal.

Parameters

xs ((3,) array_like) – Position of source in cartesian coordinates.
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.
observation_time (float) – Observed point in time.
grid (triple of array_like) – The grid that is used for the sound field calculations. See sfs.util.xyz_grid().
c (float, optional) – Speed of sound.

Returns

numpy.ndarray – Scalar sound pressure field, evaluated at positions given by grid.

Notes

\[g(x-x_s,t) = \frac{1}{4 \pi |x - x_s|} \dirac{t - \frac{|x - x_s|}{c}}\]

Examples

p = sfs.td.source.point(xs, signal, ts, grid)
sfs.plot2d.level(p, grid)

sfs.td.source.point_image_sources(x0, signal, observation_time, grid, L, max_order, coeffs=None, c=None)[source]¶

Point source in a rectangular room using the mirror image source model.

Parameters

x0 ((3,) array_like) – Position of source in cartesian coordinates.
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.
observation_time (float) – Observed point in time.
grid (triple of array_like) – The grid that is used for the sound field calculations. See sfs.util.xyz_grid().
L ((3,) array_like) – Dimensions of the rectangular room.
max_order (int) – Maximum number of reflections for each image source.
coeffs ((6,) array_like, optional) – Reflection coeffecients of the walls. If not given, the reflection coefficients are set to one.
c (float, optional) – Speed of sound.

Returns

numpy.ndarray – Scalar sound pressure field, evaluated at positions given by grid.

Examples

room = 5, 3, 1.5  # room dimensions
order = 2  # image source order
coeffs = .8, .8, .6, .6, .7, .7  # wall reflection coefficients
grid = sfs.util.xyz_grid([0, room[0]], [0, room[1]], 0, spacing=0.01)
p = sfs.td.source.point_image_sources(
        xs, signal, 1.5 * ts, grid, room, order, coeffs)
sfs.plot2d.level(p, grid)