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move example into dedicated jupyter notebook
- more convenient to have this in a notebbok - the wfs.py examples remain minimal and straightforward - the proposed notebook can be extended to referencing schemes for linear SSDs and in general for other potential referencing schemes
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‎doc/examples.rst

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:maxdepth: 1
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examples/sound-field-synthesis
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examples/wfs-referencing
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examples/modal-room-acoustics
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examples/mirror-image-source-model
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examples/animations-pulsating-sphere

‎doc/examples/wfs-referencing.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# WFS Referencing Schemes\n",
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"\n",
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"Illustrates the usage of the SFS toolbox for the simulation of different sound fields using 2.5D WFS and referencing schemes for contours that exhibit amplitude correct synthesis, cf. Ch. 4.1.3 in Gergely Firtha's doctoral thesis [A Generalized Wave Field Synthesis Framework with Application for Moving Virtual Sources](https://last.hit.bme.hu/download/firtha/PhD_thesis/firtha_phd_thesis.pdf) of 2019.\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Circular loudspeaker arrays"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"import sfs\n",
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"\n",
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"R = 1.5 # Radius of circular loudspeaker array\n",
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"array = sfs.array.circular(N=64, R=R)\n",
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"grid = sfs.util.xyz_grid([-2, 2], [-2, 2], 0, spacing=0.02)\n",
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"\n",
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"xs = -4, 0, 0 # point source on negative x-axis\n",
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"normalize_gain = 4 * np.pi * np.linalg.norm(xs)\n",
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"lmb = 1 / 4 # m\n",
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"f = sfs.default.c / lmb # Hz\n",
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"omega = 2 * np.pi * f # rad/s"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def sound_field(d, xref, selection,\n",
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" secondary_source, array, grid, tapering=True):\n",
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" if tapering:\n",
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" tapering_window = sfs.tapering.kaiser(selection, beta=1)\n",
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" else:\n",
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" tapering_window = sfs.tapering.none(selection)\n",
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"\n",
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" p = sfs.fd.synthesize(d, tapering_window,\n",
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" array, secondary_source, grid=grid)\n",
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"\n",
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" fig, axs = plt.subplots(1, 2, figsize=(10, 8))\n",
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" sfs.plot2d.amplitude(p, grid, vmax=2, vmin=-2, ax=axs[0])\n",
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" sfs.plot2d.level(p, grid, vmax=6, vmin=-6, ax=axs[1],\n",
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" cmap='seismic', colorbar_kwargs={'label': 'dB'})\n",
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" for i in range(axs.shape[0]):\n",
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" sfs.plot2d.loudspeakers(array.x, array.n,\n",
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" tapering_window,\n",
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" size=0.125, ax=axs[i])\n",
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" axs[i].plot(xref[:, 0][selection],\n",
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" xref[:, 1][selection], 'C5o', ms=4)\n",
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" axs[i].grid(True)\n",
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" plt.tight_layout()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Line as reference contour\n",
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"\n",
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"The reference contour is calculated according to https://github.com/spatialaudio/wfs_chapter_hda/blob/master/python/wfs25d_circSSD.py#L91 for a virtual point source on x-axis."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# reference contour is a straight line\n",
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"xref_line = 0\n",
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"# calc reference contour xref(x0):\n",
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"x0_tmp = array.x.T[np.newaxis, :]\n",
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"xs_tmp = np.array(xs)[np.newaxis, :, np.newaxis]\n",
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"x0xs = x0_tmp - xs_tmp\n",
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"x0xs_length = np.linalg.norm(x0xs, axis=1)\n",
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"x0xs_unit = x0xs / x0xs_length\n",
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"n0_ = array.n.T[np.newaxis, :]\n",
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"xref = np.zeros_like(x0_tmp)\n",
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"# code assumes that virtual point source is on x-axis:\n",
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"for i in range(array.x.shape[0]):\n",
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" cosbeta = np.dot(-n0_[0, :, i], [-1, 0, 0]) # use outward SSD normal\n",
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" tmp = x0xs_unit[0, :, i]\n",
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" tmp *= -x0xs_length[0, i]\n",
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" tmp *= xref_line + R * cosbeta\n",
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" tmp /= xs_tmp[0, 0, 0] + R * cosbeta\n",
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" xref[0, :, i] = x0_tmp[0, :, i] + tmp\n",
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"xref = np.squeeze(xref).T\n",
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"\n",
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"d, selection, secondary_source = sfs.fd.wfs.point_25d(\n",
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" omega, array.x, array.n, xs, xref=xref)\n",
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"sound_field(d * normalize_gain, xref, selection,\n",
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" secondary_source, array, grid, tapering=False)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Circle as reference contour\n",
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"\n",
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"This reference contour is a circle with origin xs and a radius, such that the origin is on this circle. This contour is straightforward with some obvious vector calculus."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# reference contour is a circle with origin xs\n",
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"xref_dist = np.linalg.norm(xs)\n",
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"# calc reference contour xref(x0):\n",
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"x0_tmp = array.x.T[np.newaxis, :]\n",
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"xs_tmp = np.array(xs)[np.newaxis, :, np.newaxis]\n",
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"x0xs = x0_tmp - xs_tmp\n",
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"x0xs_length = np.linalg.norm(x0xs, axis=1)\n",
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"x0xs_unit = x0xs / x0xs_length\n",
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"xref = x0_tmp + (xref_dist - x0xs_length) * x0xs_unit\n",
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"xref = np.squeeze(xref).T\n",
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"\n",
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"d, selection, secondary_source = sfs.fd.wfs.point_25d(\n",
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" omega, array.x, array.n, xs, xref=xref)\n",
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"sound_field(d * normalize_gain, xref, selection,\n",
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" secondary_source, array, grid, tapering=False)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "sfs",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.13.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎sfs/fd/wfs.py

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@@ -218,112 +218,6 @@ def point_25d(omega, x0, n0, xs, xref=[0, 0, 0], c=None, omalias=None):
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normalize_gain = 4 * np.pi * np.linalg.norm(xs)
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plot(normalize_gain * d, selection, secondary_source)
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.. plot::
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:context: close-figs
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xs = -4, 0, 0 # point source on negative x-axis
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xref_line = 0 # reference contour is a straight line
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lmb = 1 / 4 # m
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f_tmp = sfs.default.c / lmb # Hz
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omega_tmp = 2 * np.pi * f_tmp # rad/s
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# calc reference contour xref(x0):
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x0_tmp = array2.x.T[np.newaxis, :]
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xs_tmp = np.array(xs)[np.newaxis, :, np.newaxis]
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x0xs = x0_tmp - xs_tmp
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x0xs_length = np.linalg.norm(x0xs, axis=1)
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x0xs_unit = x0xs / x0xs_length
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n0_ = array2.n.T[np.newaxis, :]
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xref = np.zeros_like(x0_tmp)
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# cf. https://github.com/spatialaudio/wfs_chapter_hda/blob/master/python/wfs25d_circSSD.py#L91 # noqa
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# code is valid for a virtual point source on negative x-axis:
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for i in range(array2.x.shape[0]):
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cosbeta = np.dot(-n0_[0, :, i], [-1, 0, 0]) # use outward SSD normal
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tmp = x0xs_unit[0, :, i]
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tmp *= -x0xs_length[0, i]
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tmp *= xref_line + R * cosbeta
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tmp /= xs_tmp[0, 0, 0] + R * cosbeta
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xref[0, :, i] = x0_tmp[0, :, i] + tmp
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xref = np.squeeze(xref).T
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d, selection, secondary_source = sfs.fd.wfs.point_25d(
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omega_tmp, array2.x, array2.n, xs, xref=xref)
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normalize_gain = 4 * np.pi * np.linalg.norm(xs)
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p = sfs.fd.synthesize(d * normalize_gain,
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selection,
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array2,
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secondary_source,
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grid=grid)
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plt.rcParams['figure.figsize'] = 10, 8
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ax_amp, ax_lvl = plt.subplot(2, 2, 1), plt.subplot(2, 2, 2)
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sfs.plot2d.amplitude(p, grid, vmax=2, vmin=-2, ax=ax_amp,
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colorbar_kwargs={'label': 'lin'})
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sfs.plot2d.level(p, grid, vmax=6, vmin=-6,
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cmap='seismic', ax=ax_lvl,
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colorbar_kwargs={'label': 'dB'})
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sfs.plot2d.loudspeakers(array2.x, array2.n,
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selection * array2.a,
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size=0.125, ax=ax_amp)
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sfs.plot2d.loudspeakers(array2.x, array2.n,
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selection * array2.a,
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size=0.125, ax=ax_lvl)
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# plot xref(x0) contour:
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ax_amp.plot(xref[:, 0][selection],
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xref[:, 1][selection], 'C5o', ms=4)
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ax_lvl.plot(xref[:, 0][selection],
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xref[:, 1][selection], 'C5o', ms=4)
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ax_amp.grid(True), ax_lvl.grid(True)
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.. plot::
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:context: close-figs
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xs = -4, 0, 0 # point source on negative x-axis
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xref_dist = 4 # radius for reference contour circle with origin xs
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lmb = 1 / 4 # m
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f_tmp = sfs.default.c / lmb # Hz
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omega_tmp = 2 * np.pi * f_tmp # rad/s
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# calc reference contour xref(x0):
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x0_tmp = array2.x.T[np.newaxis, :]
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xs_tmp = np.array(xs)[np.newaxis, :, np.newaxis]
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x0xs = x0_tmp - xs_tmp
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x0xs_length = np.linalg.norm(x0xs, axis=1)
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x0xs_unit = x0xs / x0xs_length
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xref = x0_tmp + (xref_dist - x0xs_length) * x0xs_unit
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xref = np.squeeze(xref).T
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d, selection, secondary_source = sfs.fd.wfs.point_25d(
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omega_tmp, array2.x, array2.n, xs, xref=xref)
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normalize_gain = 4 * np.pi * np.linalg.norm(xs)
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p = sfs.fd.synthesize(d * normalize_gain,
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selection,
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array2,
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secondary_source,
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grid=grid)
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plt.rcParams['figure.figsize'] = 10, 8
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ax_amp, ax_lvl = plt.subplot(2, 2, 1), plt.subplot(2, 2, 2)
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sfs.plot2d.amplitude(p, grid, vmax=2, vmin=-2, ax=ax_amp,
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colorbar_kwargs={'label': 'lin'})
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sfs.plot2d.level(p, grid, vmax=6, vmin=-6,
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cmap='seismic', ax=ax_lvl,
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colorbar_kwargs={'label': 'dB'})
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sfs.plot2d.loudspeakers(array2.x, array2.n,
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selection * array2.a,
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size=0.125, ax=ax_amp)
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sfs.plot2d.loudspeakers(array2.x, array2.n,
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selection * array2.a,
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size=0.125, ax=ax_lvl)
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# plot xref(x0) contour:
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ax_amp.plot(xref[:, 0][selection],
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xref[:, 1][selection], 'C5o', ms=4)
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ax_lvl.plot(xref[:, 0][selection],
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xref[:, 1][selection], 'C5o', ms=4)
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ax_amp.grid(True), ax_lvl.grid(True)
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"""
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x0 = _util.asarray_of_rows(x0)
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n0 = _util.asarray_of_rows(n0)

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