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.

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

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.

Returns:

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

Notes

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

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.

Returns:

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

Time Domain Driving Functions

Compute time based driving functions for various systems.

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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

Returns:

• 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

See http://sfstoolbox.org/en/latest/#equation-d.wfs.pw.2.5D

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

Returns:

• 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

See http://sfstoolbox.org/en/latest/#equation-d.wfs.ps.2.5D

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

Returns:

• 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

See http://sfstoolbox.org/en/latest/#equation-d.wfs.fs.2.5D

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.

Returns:

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.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.

Returns:

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).

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.

Returns:

numpy.ndarray – Sound pressure at grid positions.