def rakeOneForcingFilters(self, sources, interferers, R_n, epsilon=5e-3):
'''
Compute the time-domain filters of a beamformer with unit response
towards multiple sources.
'''
dist_mat = distance(self.R, sources.images)
s_time = dist_mat / constants.get('c')
s_dmp = 1./(4*np.pi*dist_mat)
dist_mat = distance(self.R, interferers.images)
i_time = dist_mat / constants.get('c')
i_dmp = 1./(4*np.pi*dist_mat)
# compute offset needed for decay of sinc by epsilon
offset = np.maximum(s_dmp.max(), i_dmp.max())/(np.pi*self.Fs*epsilon)
t_min = np.minimum(s_time.min(), i_time.min())
t_max = np.maximum(s_time.max(), i_time.max())
# adjust timing
s_time -= t_min - offset
i_time -= t_min - offset
Lh = np.ceil((t_max - t_min + 2*offset)*float(self.Fs))
# the channel matrix
K = sources.images.shape[1]
Lg = self.Lg
off = (Lg - Lh)/2
L = self.Lg + Lh - 1
H = np.zeros((Lg*self.M, 2*L))
As = np.zeros((Lg*self.M, K))
for r in np.arange(self.M):
# build constraint matrix
hs = u.lowPassDirac(s_time[r,:,np.newaxis], s_dmp[r,:,np.newaxis], self.Fs, Lh)[:,::-1]
As[r*Lg+off:r*Lg+Lh+off,:] = hs.T
# build interferer RIR matrix
hx = u.lowPassDirac(s_time[r,:,np.newaxis], s_dmp[r,:,np.newaxis], self.Fs, Lh).sum(axis=0)
H[r*Lg:(r+1)*Lg,:L] = u.convmtx(hx, Lg).T
# build interferer RIR matrix
hq = u.lowPassDirac(i_time[r,:,np.newaxis], i_dmp[r,:,np.newaxis], self.Fs, Lh).sum(axis=0)
H[r*Lg:(r+1)*Lg,L:] = u.convmtx(hq, Lg).T
ones = np.ones((K,1))
# We first assume the sample are uncorrelated
K_x = np.dot(H[:,:L], H[:,:L].T)
K_nq = np.dot(H[:,L:], H[:,L:].T) + R_n
# Compute the TD filters
K_nq_inv = np.linalg.inv(K_x+K_nq)
C = np.dot(K_nq_inv, As)
B = np.linalg.inv(np.dot(As.T, C))
g_val = np.dot(C, np.dot(B, ones))
self.filters = g_val.reshape((self.M,Lg))
# compute and return SNR
A = np.dot(g_val.T, H[:,:L])
num = np.dot(A, A.T)
denom = np.dot(np.dot(g_val.T, K_nq), g_val)
return num/denom
def buildRIRMatrix(mics, sources, Lg, Fs, epsilon=5e-3, unit_damping=False):
"""
A function to build the channel matrix for many sources and microphones
mics is a dim-by-M ndarray where each column is the position of a microphone
sources is a list of SoundSource objects
Lg is the length of the beamforming filters
Fs is the sampling frequency
epsilon determines how long the sinc is let to decay. Defaults to epsilon=5e-3
unit_damping determines if the wall damping parameters are used or not. Default to false.
returns the RIR matrix H =
--------------------
| H_{11} H_{12} ...
| ...
|
--------------------
where H_{ij} is channel matrix between microphone i and source j.
H is of type (M*Lg)x((Lg+Lh-1)*S) where Lh is the channel length (determined by epsilon),
and M, S are the number of microphones, sources, respectively.
"""
from beamforming import distance
from utilities import lowPassDirac, convmtx
from scipy.linalg import toeplitz
# set the boundaries of RIR filter for given epsilon
d_min = np.inf
d_max = 0.0
dmp_max = 0.0
for s in xrange(len(sources)):
dist_mat = distance(mics, sources[s].images)
if unit_damping == True:
dmp_max = np.maximum((1.0 / (4 * np.pi * dist_mat)).max(), dmp_max)
else:
dmp_max = np.maximum((sources[s].damping[np.newaxis, :] / (4 * np.pi * dist_mat)).max(), dmp_max)
d_min = np.minimum(dist_mat.min(), d_min)
d_max = np.maximum(dist_mat.max(), d_max)
t_max = d_max / constants.get("c")
t_min = d_min / constants.get("c")
offset = dmp_max / (np.pi * Fs * epsilon)
# RIR length
Lh = int((t_max - t_min + 2 * offset) * float(Fs))
# build the channel matrix
L = Lg + Lh - 1
H = np.zeros((Lg * mics.shape[1], len(sources) * L))
for s in xrange(len(sources)):
for r in np.arange(mics.shape[1]):
dist = sources[s].distance(mics[:, r])
time = dist / constants.get("c") - t_min + offset
if unit_damping == True:
dmp = 1.0 / (4 * np.pi * dist)
else:
dmp = sources[s].damping / (4 * np.pi * dist)
h = lowPassDirac(time[:, np.newaxis], dmp[:, np.newaxis], Fs, Lh).sum(axis=0)
H[r * Lg : (r + 1) * Lg, s * L : (s + 1) * L] = convmtx(h, Lg).T
return H
def buildRIRMatrix(mics, sources, Lg, Fs, epsilon=5e-3, unit_damping=False):
'''
A function to build the channel matrix for many sources and microphones
mics is a dim-by-M ndarray where each column is the position of a microphone
sources is a list of SoundSource objects
Lg is the length of the beamforming filters
Fs is the sampling frequency
epsilon determines how long the sinc is let to decay. Defaults to epsilon=5e-3
unit_damping determines if the wall damping parameters are used or not. Default to false.
returns the RIR matrix H =
--------------------
| H_{11} H_{12} ...
| ...
|
--------------------
where H_{ij} is channel matrix between microphone i and source j.
H is of type (M*Lg)x((Lg+Lh-1)*S) where Lh is the channel length (determined by epsilon),
and M, S are the number of microphones, sources, respectively.
'''
from beamforming import distance
from utilities import lowPassDirac, convmtx
from scipy.linalg import toeplitz
# set the boundaries of RIR filter for given epsilon
d_min = np.inf
d_max = 0.
dmp_max = 0.
for s in xrange(len(sources)):
dist_mat = distance(mics, sources[s].images)
if unit_damping == True:
dmp_max = np.maximum((1. / (4 * np.pi * dist_mat)).max(), dmp_max)
else:
dmp_max = np.maximum((sources[s].damping[np.newaxis, :] /
(4 * np.pi * dist_mat)).max(), dmp_max)
d_min = np.minimum(dist_mat.min(), d_min)
d_max = np.maximum(dist_mat.max(), d_max)
t_max = d_max / constants.get('c')
t_min = d_min / constants.get('c')
offset = dmp_max / (np.pi * Fs * epsilon)
# RIR length
Lh = int((t_max - t_min + 2 * offset) * float(Fs))
# build the channel matrix
L = Lg + Lh - 1
H = np.zeros((Lg * mics.shape[1], len(sources) * L))
for s in xrange(len(sources)):
for r in np.arange(mics.shape[1]):
dist = sources[s].distance(mics[:, r])
time = dist / constants.get('c') - t_min + offset
if unit_damping == True:
dmp = 1. / (4 * np.pi * dist)
else:
dmp = sources[s].damping / (4 * np.pi * dist)
h = lowPassDirac(time[:, np.newaxis], dmp[:, np.newaxis], Fs,
Lh).sum(axis=0)
H[r * Lg:(r + 1) * Lg, s * L:(s + 1) * L] = convmtx(h, Lg).T
return H
