# Time Domain¶

## Time Domain Sources¶

Compute the sound field generated by a sound source.

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

sfs.time.source.point(xs, signal, observation_time, grid, c=None)

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

Notes

$g(x-x_s,t) = \frac{1}{4 \pi |x - x_s|} \dirac{t - \frac{|x - x_s|}{c}}$
sfs.time.source.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. numpy.ndarray – Scalar sound pressure field, evaluated at positions given by grid.

## Time Domain Driving Functions¶

Compute time based driving functions for various systems.

sfs.time.drivingfunction.apply_delays(signal, delays)

Apply delays for every channel.

Parameters: 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. delays ((C,) array_like) – Delay in seconds for each channel (C), negative values allowed. DelayedSignal – A tuple containing the delayed signals (in a numpy.ndarray with shape (N, C)), followed by the sampling rate (in Hertz) and a (possibly negative) time offset (in seconds).
sfs.time.drivingfunction.driving_signals(delays, weights, signal)

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. DelayedSignal – A tuple containing the driving signals (in a numpy.ndarray with shape (N, C)), followed by the sampling rate (in Hertz) and a (possibly negative) time offset (in seconds).
sfs.time.drivingfunction.wfs_25d_focused(x0, n0, xs, xref=[0, 0, 0], c=None)

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. xref ((3,) array_like, optional) – Reference position c (float, optional) – Speed of sound delays ((N,) numpy.ndarray) – Delays of secondary sources in seconds. weights ((N,) numpy.ndarray) – Weights of secondary sources.

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

$d_{2.5D}(x_0,t) = h(t) \frac{g_0 \scalarprod{(x_0 - x_s)}{n_0}} {|x_0 - x_s|^{3/2}} \dirac{t + \frac{|x_0 - x_s|}{c}}$

with wfs(2.5D) prefilter h(t), which is not implemented yet.

References

sfs.time.drivingfunction.wfs_25d_plane(x0, n0, n=[0, 1, 0], xref=[0, 0, 0], c=None)

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 delays ((N,) numpy.ndarray) – Delays of secondary sources in seconds. weights ((N,) numpy.ndarray) – Weights of secondary sources.

Notes

2.5D correction factor

$g_0 = \sqrt{2 \pi |x_\mathrm{ref} - x_0|}$

d using a plane wave as source model

$d_{2.5D}(x_0,t) = h(t) 2 g_0 \scalarprod{n}{n_0} \dirac{t - \frac{1}{c} \scalarprod{n}{x_0}}$

with wfs(2.5D) prefilter h(t), which is not implemented yet.

References

sfs.time.drivingfunction.wfs_25d_point(x0, n0, xs, xref=[0, 0, 0], c=None)

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. xref ((3,) array_like, optional) – Reference position c (float, optional) – Speed of sound delays ((N,) numpy.ndarray) – Delays of secondary sources in seconds. weights ((N,) numpy.ndarray) – Weights of secondary sources.

Notes

2.5D correction factor

$g_0 = \sqrt{2 \pi |x_\mathrm{ref} - x_0|}$

d using a point source as source model

$d_{2.5D}(x_0,t) = h(t) \frac{g_0 \scalarprod{(x_0 - x_s)}{n_0}} {2\pi |x_0 - x_s|^{3/2}} \dirac{t - \frac{|x_0 - x_s|}{c}}$

with wfs(2.5D) prefilter h(t), which is not implemented yet.

References

## Time Domain Sound Fields¶

Compute sound field.

sfs.time.soundfield.p_array(x0, signals, weights, observation_time, grid, source=<function point>, c=None)

Compute sound field for an array of secondary sources.

Parameters: x0 ((N, 3) array_like) – Sequence of secondary source positions. signals ((N, C) array_like + float) – Driving signals consisting of audio data (C channels) and a sampling rate (in Hertz). A DelayedSignal object can also be used. weights ((C,) array_like) – Additional weights applied during integration, e.g. source tapering. observation_time (float) – Simulation point in time (seconds). grid (triple of array_like) – The grid that is used for the sound field calculations. See sfs.util.xyz_grid(). source (function, optional) – Source type is a function, returning scalar field. For default, see sfs.time.source.point(). c (float, optional) – Speed of sound. numpy.ndarray – Sound pressure at grid positions.