# Source code for sfs.td.source

"""Compute the sound field generated by a sound source.

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

.. include:: math-definitions.rst

.. plot::
:context: reset

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)

"""
import numpy as _np

from .. import default as _default
from .. import util as _util

[docs]def point(xs, signal, observation_time, grid, c=None):
r"""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
-----
.. math::

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

Examples
--------
.. plot::
:context: close-figs

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

"""
xs = _util.asarray_1d(xs)
data, samplerate, signal_offset = _util.as_delayed_signal(signal)
data = _util.asarray_1d(data)
grid = _util.as_xyz_components(grid)
if c is None:
c = _default.c
r = _np.linalg.norm(grid - xs)
# If r is +-0, the sound pressure is +-infinity
with _np.errstate(divide='ignore'):
weights = 1 / (4 * _np.pi * r)
delays = r / c
base_time = observation_time - signal_offset
points_at_time = _np.interp(base_time - delays,
_np.arange(len(data)) / samplerate,
data, left=0, right=0)
# weights can be +-infinity
with _np.errstate(invalid='ignore'):
return weights * points_at_time

[docs]def point_image_sources(x0, signal, observation_time, grid, L, max_order,
coeffs=None, c=None):
"""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
--------
.. plot::
:context: close-figs

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)

"""
if coeffs is None:
coeffs = _np.ones(6)

positions, order = _util.image_sources_for_box(x0, L, max_order)
source_strengths = _np.prod(coeffs**order, axis=1)

p = 0
for position, strength in zip(positions, source_strengths):
if strength != 0:
p += strength * point(position, signal, observation_time, grid, c)

return p