From c74e34a8b64f0c283be0624d2808e20ec70f0da5 Mon Sep 17 00:00:00 2001
From: Frank Schultz <scf175@googlemail.com>
Date: Thu, 14 Mar 2019 20:36:46 +0100
Subject: [PATCH] new Point Source 2.5D WFS handling, old one becomes legacy
-old handling was Spors/Rabenstein, 2D to 2.5D
-new one is Delft, 3D to 2.5D
---
doc/references.bib | 26 ++++++++++
sfs/mono/wfs.py | 115 ++++++++++++++++++++++++++++++++++++++++++---
2 files changed, 135 insertions(+), 6 deletions(-)
diff --git a/doc/references.bib b/doc/references.bib
index 3b510c86..8b149bac 100644
--- a/doc/references.bib
+++ b/doc/references.bib
@@ -70,3 +70,29 @@ @article{Borish1984
year = {1984},
doi = {10.1121/1.390983}
}
+@article{Firtha2017,
+ author = {Gergely Firtha AND P{\'e}ter Fiala AND Frank Schultz AND
+ Sascha Spors},
+ title = {{Improved Referencing Schemes for 2.5D Wave Field Synthesis
+ Driving Functions}},
+ journal = {IEEE/ACM Trans. Audio Speech Language Process.},
+ volume = {25},
+ number = {5},
+ pages = {1117-1127},
+ year = {2017},
+ doi = {10.1109/TASLP.2017.2689245}
+}
+@phdthesis{Start1997,
+ author = {Evert W. Start},
+ title = {{Direct Sound Enhancement by Wave Field Synthesis}},
+ school = {Delft University of Technology},
+ year = {1997}
+}
+@phdthesis{Schultz2016,
+ author = {Frank Schultz},
+ title = {{Sound Field Synthesis for Line Source Array Applications in
+ Large-Scale Sound Reinforcement}},
+ school = {University of Rostock},
+ year = {2016},
+ doi = {10.18453/rosdok_id00001765}
+}
diff --git a/sfs/mono/wfs.py b/sfs/mono/wfs.py
index a05aa0fa..3e5762a6 100644
--- a/sfs/mono/wfs.py
+++ b/sfs/mono/wfs.py
@@ -155,8 +155,102 @@ def _point(omega, x0, n0, xs, c=None):
def point_25d(omega, x0, n0, xs, xref=[0, 0, 0], c=None, omalias=None):
+ r"""Driving function for 2.5-dimensional WFS of a virtual point source.
+
+ .. versionchanged:: 0.5
+ see notes, old handling of `point_25d()` is now `point_25d_legacy()`
+
+ Parameters
+ ----------
+ omega : float
+ Angular frequency of point source.
+ x0 : (N, 3) array_like
+ Sequence of secondary source positions.
+ n0 : (N, 3) array_like
+ Sequence of normal vectors of secondary sources.
+ xs : (3,) array_like
+ Position of virtual point source.
+ xref : (3,) array_like, optional
+ Reference point xref or contour xref(x0) for amplitude correct
+ synthesis.
+ c : float, optional
+ Speed of sound in m/s.
+ omalias: float, optional
+ Angular frequency where spatial aliasing becomes prominent.
+
+ Returns
+ -------
+ d : (N,) numpy.ndarray
+ Complex weights of secondary sources.
+ selection : (N,) numpy.ndarray
+ Boolean array containing ``True`` or ``False`` depending on
+ whether the corresponding secondary source is "active" or not.
+ secondary_source_function : callable
+ A function that can be used to create the sound field of a
+ single secondary source. See `sfs.mono.synthesize()`.
+
+ Notes
+ -----
+ `point_25d()` derives 2.5D WFS from the 3D
+ Neumann-Rayleigh integral (i.e. the TU Delft approach).
+ The eq. (3.10), (3.11) in :cite:`Start1997`, equivalent to
+ Eq. (2.137) in :cite:`Schultz2016`
+
+ .. math::
+
+ D(\x_0,\w) = \sqrt{8 \pi \, \i\wc}
+ \sqrt{\frac{|\x_\text{ref}-\x_0| \cdot
+ |\x_0-\x_\text{s}|}{|\x_\text{ref}-\x_0| + |\x_0-\x_\text{s}|}}
+ \scalarprod{\frac{\x_0-\x_\text{s}}{|\x_0-\x_\text{s}|}}{\n_0}
+ \frac{\e{-\i\wc |\x_0-\x_\text{s}|}}{4\pi\,|\x_0-\x_\text{s}|}
+
+ is implemented.
+ The theoretical link of `point_25d()` and `point_25d_legacy()` was
+ introduced as *unified WFS framework* in :cite:`Firtha2017`.
+
+ Examples
+ --------
+ .. plot::
+ :context: close-figs
+
+ d, selection, secondary_source = sfs.mono.wfs.point_25d(
+ omega, array.x, array.n, xs)
+ normalize_gain = 4 * np.pi * np.linalg.norm(xs)
+ plot(normalize_gain * d, selection, secondary_source)
+
+ """
+ x0 = util.asarray_of_rows(x0)
+ n0 = util.asarray_of_rows(n0)
+ xs = util.asarray_1d(xs)
+ xref = util.asarray_1d(xref)
+ k = util.wavenumber(omega, c)
+
+ ds = x0 - xs
+ dr = xref - x0
+ s = np.linalg.norm(ds, axis=1)
+ r = np.linalg.norm(dr, axis=1)
+
+ d = (
+ preeq_25d(omega, omalias, c) *
+ np.sqrt(8 * np.pi) *
+ np.sqrt((r * s) / (r + s)) *
+ inner1d(n0, ds) / s *
+ np.exp(-1j * k * s) / (4 * np.pi * s))
+ selection = util.source_selection_point(n0, x0, xs)
+ return d, selection, secondary_source_point(omega, c)
+
+
+point_3d = _point
+
+
+def point_25d_legacy(omega, x0, n0, xs, xref=[0, 0, 0], c=None, omalias=None):
r"""Driving function for 2.5-dimensional WFS for a virtual point source.
+ .. versionadded:: 0.5
+ `point_25d()` was renamed to `point_25d_legacy()` (and a new
+ function with the name `point_25d()` was introduced). See notes for
+ further details.
+
Parameters
----------
omega : float
@@ -171,6 +265,8 @@ def point_25d(omega, x0, n0, xs, xref=[0, 0, 0], c=None, omalias=None):
Reference point for synthesized sound field.
c : float, optional
Speed of sound.
+ omalias: float, optional
+ Angular frequency where spatial aliasing becomes prominent.
Returns
-------
@@ -185,6 +281,10 @@ def point_25d(omega, x0, n0, xs, xref=[0, 0, 0], c=None, omalias=None):
Notes
-----
+ `point_25d_legacy()` derives 2.5D WFS from the 2D
+ Neumann-Rayleigh integral (i.e. the approach by Rabenstein & Spors), cf.
+ :cite:`Spors2008`.
+
.. math::
D(\x_0,\w) = \sqrt{\i\wc |\x_\text{ref}-\x_0|}
@@ -192,14 +292,19 @@ def point_25d(omega, x0, n0, xs, xref=[0, 0, 0], c=None, omalias=None):
{|\x_0-\x_\text{s}|^\frac{3}{2}}
\e{-\i\wc |\x_0-\x_\text{s}|}
+ The theoretical link of `point_25d()` and `point_25d_legacy()` was
+ introduced as *unified WFS framework* in :cite:`Firtha2017`.
+ Also cf. Eq. (2.145)-(2.147) :cite:`Schultz2016`.
+
Examples
--------
.. plot::
:context: close-figs
- d, selection, secondary_source = sfs.mono.wfs.point_25d(
+ d, selection, secondary_source = sfs.mono.wfs.point_25d_legacy(
omega, array.x, array.n, xs)
- plot(d, selection, secondary_source)
+ normalize_gain = np.linalg.norm(xs)
+ plot(normalize_gain * d, selection, secondary_source)
"""
x0 = util.asarray_of_rows(x0)
@@ -217,9 +322,6 @@ def point_25d(omega, x0, n0, xs, xref=[0, 0, 0], c=None, omalias=None):
return d, selection, secondary_source_point(omega, c)
-point_3d = _point
-
-
def _plane(omega, x0, n0, n=[0, 1, 0], c=None):
r"""Driving function for 2/3-dimensional WFS for a virtual plane wave.
@@ -499,7 +601,8 @@ def preeq_25d(omega, omalias, c):
H(\w) = \begin{cases}
\sqrt{\i \wc} & \text{for } \w \leq \w_\text{alias} \\
- \sqrt{\i \frac{\w_\text{alias}}{c}} & \text{for } \w > \w_\text{alias}
+ \sqrt{\i \frac{\w_\text{alias}}{c}} &
+ \text{for } \w > \w_\text{alias}
\end{cases}
"""