10000 NFC-HOA second-order-section filters by narahahn · Pull Request #45 · sfstoolbox/sfs-python · GitHub
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NFC-HOA second-order-section filters #45

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Mar 11, 2019
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NFC-HOA second-order-section filters #45

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50 changes: 50 additions & 0 deletions doc/examples/time_domain_nfchoa.py
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Original file line number Diff line number Diff line change
@@ -0,0 +1,50 @@
"""Create some examples of time-domain NFC-HOA."""

import numpy as np
import matplotlib.pyplot as plt
import sfs
from scipy.signal import unit_impulse

# Parameters
fs = 44100 # sampling frequency
grid = sfs.util.xyz_grid([-2, 2], [-2, 2], 0, spacing=0.005)
N = 60 # number of secondary sources
R = 1.5 # radius of circular array
array = sfs.array.circular(N, R)

# Excitation signal
signal = unit_impulse(512), fs, 0

# Plane wave
max_order = None
npw = [0, -1, 0] # propagating direction
t = 0 # observation time
delay, weight, sos, phaseshift, selection, secondary_source = \
sfs.time.drivingfunction.nfchoa_25d_plane(array.x, R, npw, fs, max_order)
d = sfs.time.drivingfunction.nfchoa_25d_driving_signals(
delay, weight, sos, phaseshift, signal)
p = sfs.time.synthesize(d, selection, array, secondary_source,
observation_time=t, grid=grid)

plt.figure()
sfs.plot.level(p, grid)
sfs.plot.loudspeaker_2d(array.x, array.n)
sfs.plot.virtualsource_2d([0, 0], ns=npw, type='plane')
plt.savefig('impulse_pw_nfchoa_25d.png')

# Point source
max_order = 100
xs = [1.5, 1.5, 0] # position
t = np.linalg.norm(xs) / sfs.default.c # observation time
delay, weight, sos, phaseshift, selection, secondary_source = \
sfs.time.drivingfunction.nfchoa_25d_point(array.x, R, xs, fs, max_order)
d = sfs.time.drivingfunction.nfchoa_25d_driving_signals(
delay, weight, sos, phaseshift, signal)
p = sfs.time.synthesize(d, selection, array, secondary_source,
observation_time=t, grid=grid)

plt.figure()
sfs.plot.level(p, grid)
sfs.plot.loudspeaker_2d(array.x, array.n)
sfs.plot.virtualsource_2d(xs, type='point')
plt.savefig('impulse_ps_nfchoa_25d.png')
29 changes: 15 additions & 14 deletions sfs/mono/drivingfunction.py
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Original file line number Diff line number Diff line change
Expand Up @@ -325,14 +325,16 @@ def nfchoa_2d_plane(omega, x0, r0, n=[0, 1, 0], max_order=None, c=None):
plot(d, selection, secondary_source)

"""
if max_order is None:
max_order = util.max_order_circular_harmonics(len(x0))

x0 = util.asarray_of_rows(x0)
k = util.wavenumber(omega, c)
n = util.normalize_vector(n)
phi, _, r = util.cart2sph(*n)
phi0 = util.cart2sph(*x0.T)[0]
M = _max_order_circular_harmonics(len(x0), max_order)
d = 0
for m in range(-M, M + 1):
for m in range(-max_order, max_order + 1):
d += 1j**-m / hankel2(m, k * r0) * np.exp(1j * m * (phi0 - phi))
selection = util.source_selection_all(len(x0))
return -2j / (np.pi*r0) * d, selection, secondary_source_point(omega, c)
Expand Down Expand Up @@ -361,16 +363,18 @@ def nfchoa_25d_point(omega, x0, r0, xs, max_order=None, c=None):
plot(d, selection, secondary_source)

"""
if max_order is None:
max_order = util.max_order_circular_harmonics(len(x0))

x0 = util.asarray_of_rows(x0)
k = util.wavenumber(omega, c)
xs = util.asarray_1d(xs)
phi, _, r = util.cart2sph(*xs)
phi0 = util.cart2sph(*x0.T)[0]
M = _max_order_circular_harmonics(len(x0), max_order)
hr = util.spherical_hn2(range(0, M + 1), k * r)
hr0 = util.spherical_hn2(range(0, M + 1), k * r0)
hr = util.spherical_hn2(range(0, max_order + 1), k * r)
hr0 = util.spherical_hn2(range(0, max_order + 1), k * r0)
d = 0
for m in range(-M, M + 1):
for m in range(-max_order, max_order + 1):
d += hr[abs(m)] / hr0[abs(m)] * np.exp(1j * m * (phi0 - phi))
selection = util.source_selection_all(len(x0))
return d / (2 * np.pi * r0), selection, secondary_source_point(omega, c)
Expand Down Expand Up @@ -399,15 +403,17 @@ def nfchoa_25d_plane(omega, x0, r0, n=[0, 1, 0], max_order=None, c=None):
plot(d, selection, secondary_source)

"""
if max_order is None:
max_order = util.max_order_circular_harmonics(len(x0))

x0 = util.asarray_of_rows(x0)
k = util.wavenumber(omega, c)
n = util.normalize_vector(n)
phi, _, r = util.cart2sph(*n)
phi0 = util.cart2sph(*x0.T)[0]
M = _max_order_circular_harmonics(len(x0), max_order)
d = 0
hn2 = util.spherical_hn2(range(0, M + 1), k * r0)
for m in range(-M, M + 1):
hn2 = util.spherical_hn2(range(0, max_order + 1), k * r0)
for m in range(-max_order, max_order + 1):
d += (-1j)**abs(m) / (k * hn2[abs(m)]) * np.exp(1j * m * (phi0 - phi))
selection = util.source_selection_all(len(x0))
return 2*1j / r0 * d, selection, secondary_source_point(omega, c)
Expand Down Expand Up @@ -782,8 +788,3 @@ def secondary_source(position, _, grid):
return _source.line(omega, position, grid, c)

return secondary_source


def _max_order_circular_harmonics(N, max_order):
"""Compute order of 2D HOA."""
return N // 2 if max_order is None else max_order
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