#
# Copyright 2022 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
import numpy as np
import scipy.fftpack as fftpack
import lc3
import tables as T, appendix_c as C
### ------------------------------------------------------------------------ ###
class Sns:
def __init__(self, dt, sr):
self.dt = dt
self.sr = sr
self.I = T.I[dt][sr]
(self.ind_lf, self.ind_hf, self.shape, self.gain) = \
(None, None, None, None)
(self.idx_a, self.ls_a, self.idx_b, self.ls_b) = \
(None, None, None, None)
def get_data(self):
data = { 'lfcb' : self.ind_lf, 'hfcb' : self.ind_hf,
'shape' : self.shape, 'gain' : self.gain,
'idx_a' : self.idx_a, 'ls_a' : self.ls_a }
if self.idx_b is not None:
data.update({ 'idx_b' : self.idx_b, 'ls_b' : self.ls_b })
return data
def get_nbits(self):
return 38
def spectral_shaping(self, scf, inv, x):
## Scale factors interpolation
scf_i = np.empty(4*len(scf))
scf_i[0 ] = scf[0]
scf_i[1 ] = scf[0]
scf_i[2:62:4] = scf[:15] + 1/8 * (scf[1:] - scf[:15])
scf_i[3:63:4] = scf[:15] + 3/8 * (scf[1:] - scf[:15])
scf_i[4:64:4] = scf[:15] + 5/8 * (scf[1:] - scf[:15])
scf_i[5:64:4] = scf[:15] + 7/8 * (scf[1:] - scf[:15])
scf_i[62 ] = scf[15 ] + 1/8 * (scf[15] - scf[14 ])
scf_i[63 ] = scf[15 ] + 3/8 * (scf[15] - scf[14 ])
nb = len(self.I) - 1
if nb < 32:
n4 = round(abs(1-32/nb)*nb)
n2 = nb - n4
for i in range(n4):
scf_i[i] = np.mean(scf_i[4*i:4*i+4])
for i in range(n4, n4+n2):
scf_i[i] = np.mean(scf_i[2*n4+2*i:2*n4+2*i+2])
scf_i = scf_i[:n4+n2]
elif nb < 64:
n2 = 64 - nb
for i in range(n2):
scf_i[i] = np.mean(scf_i[2*i:2*i+2])
scf_i = np.append(scf_i[:n2], scf_i[2*n2:])
g_sns = np.power(2, [ -scf_i, scf_i ][inv])
## Spectral shaping
y = np.empty(len(x))
I = self.I
for b in range(nb):
y[I[b]:I[b+1]] = x[I[b]:I[b+1]] * g_sns[b]
return y
class SnsAnalysis(Sns):
def __init__(self, dt, sr):
super().__init__(dt, sr)
def compute_scale_factors(self, e, att, nbytes):
dt = self.dt
sr = self.sr
hr = self.sr >= T.SRATE_48K_HR
## Padding
if len(e) < 32:
n4 = round(abs(1-32/len(e))*len(e))
n2 = len(e) - n4
e = np.append(np.zeros(3*n4+n2), e)
for i in range(n4):
e[4*i+0] = e[4*i+1] = \
e[4*i+2] = e[4*i+3] = e[3*n4+n2+i]
for i in range(2*n4, 2*n4+n2):
e[2*i+0] = e[2*i+1] = e[2*n4+n2+i]
elif len(e) < 64:
n2 = 64 - len(e)
e = np.append(np.empty(n2), e)
for i in range(n2):
e[2*i+0] = e[2*i+1] = e[n2+i]
## Smoothing
e_s = np.zeros(len(e))
e_s[0 ] = 0.75 * e[0 ] + 0.25 * e[1 ]
e_s[1:63] = 0.25 * e[0:62] + 0.5 * e[1:63] + 0.25 * e[2:64]
e_s[ 63] = 0.25 * e[ 62] + 0.75 * e[ 63]
## Pre-emphasis
g_tilt = [ 14, 18, 22, 26, 30, 30, 34 ][self.sr]
e_p = e_s * (10 ** ((np.arange(64) * g_tilt) / 630))
## Noise floor
noise_floor = max(np.average(e_p) * (10 ** (-40/10)), 2 ** -32)
e_p = np.fmax(e_p, noise_floor * np.ones(len(e)))
## Logarithm
e_l = np.log2(10 ** -31 + e_p) / 2
## Band energy grouping
w = [ 1/12, 2/12, 3/12, 3/12, 2/12, 1/12 ]
e_4 = np.zeros(len(e_l) // 4)
e_4[0 ] = w[0] * e_l[0] + np.sum(w[1:] * e_l[:5])
e_4[1:15] = [ np.sum(w * e_l[4*i-1:4*i+5]) for i in range(1, 15) ]
e_4[ 15] = np.sum(w[:5] * e_l[59:64]) + w[5] * e_l[63]
## Mean removal and scaling, attack handling
cf = [ 0.85, 0.6 ][hr]
if hr and nbytes * 8 > [ 1150, 2300, 0, 4400 ][self.dt]:
cf *= [ 0.25, 0.35 ][ self.dt == T.DT_10M ]
scf = cf * (e_4 - np.average(e_4))
scf_a = np.zeros(len(scf))
scf_a[0 ] = np.mean(scf[:3])
scf_a[1 ] = np.mean(scf[:4])
scf_a[2:14] = [ np.mean(scf[i:i+5]) for i in range(12) ]
scf_a[ 14] = np.mean(scf[12:])
scf_a[ 15] = np.mean(scf[13:])
scf_a = (0.5 if self.dt != T.DT_7M5 else 0.3) * \
(scf_a - np.average(scf_a))
return scf_a if att else scf
def enum_mpvq(self, v):
sign = None
index = 0
x = 0
for (n, vn) in enumerate(v[::-1]):
if sign is not None and vn != 0:
index = 2*index + sign
if vn != 0:
sign = 1 if vn < 0 else 0
index += T.SNS_MPVQ_OFFSETS[n][x]
x += abs(vn)
return (index, bool(sign))
def quantize(self, scf):
## Stage 1
dmse_lf = [ np.sum((scf[:8] - T.SNS_LFCB[i]) ** 2) for i in range(32) ]
dmse_hf = [ np.sum((scf[8:] - T.SNS_HFCB[i]) ** 2) for i in range(32) ]
self.ind_lf = np.argmin(dmse_lf)
self.ind_hf = np.argmin(dmse_hf)
st1 = np.append(T.SNS_LFCB[self.ind_lf], T.SNS_HFCB[self.ind_hf])
r1 = scf - st1
## Stage 2
t2_rot = fftpack.dct(r1, norm = 'ortho')
x = np.abs(t2_rot)
## Stage 2 Shape search, step 1
K = 6
proj_fac = (K - 1) / sum(np.abs(t2_rot))
y3 = np.floor(x * proj_fac).astype(int)
## Stage 2 Shape search, step 2
corr_xy = np.sum(y3 * x)
energy_y = np.sum(y3 * y3)
k0 = sum(y3)
for k in range(k0, K):
q_pvq = ((corr_xy + x) ** 2) / (energy_y + 2*y3 + 1)
n_best = np.argmax(q_pvq)
corr_xy += x[n_best]
energy_y += 2*y3[n_best] + 1
y3[n_best] += 1
## Stage 2 Shape search, step 3
K = 8
y2 = y3.copy()
for k in range(sum(y2), K):
q_pvq = ((corr_xy + x) ** 2) / (energy_y + 2*y2 + 1)
n_best = np.argmax(q_pvq)
corr_xy += x[n_best]
energy_y += 2*y2[n_best] + 1
y2[n_best] += 1
## Stage 2 Shape search, step 4
y1 = np.append(y2[:10], [0] * 6)
## Stage 2 Shape search, step 5
corr_xy -= sum(y2[10:] * x[10:])
energy_y -= sum(y2[10:] * y2[10:])
## Stage 2 Shape search, step 6
K = 10
for k in range(sum(y1), K):
q_pvq = ((corr_xy + x[:10]) ** 2) / (energy_y + 2*y1[:10] + 1)
n_best = np.argmax(q_pvq)
corr_xy += x[n_best]
energy_y += 2*y1[n_best] + 1
y1[n_best] += 1
## Stage 2 Shape search, step 7
y0 = np.append(y1[:10], [ 0 ] * 6)
q_pvq = ((corr_xy + x[10:]) ** 2) / (energy_y + 2*y0[10:] + 1)
n_best = 10 + np.argmax(q_pvq)
y0[n_best] += 1
## Stage 2 Shape search, step 8
y0 *= np.sign(t2_rot).astype(int)
y1 *= np.sign(t2_rot).astype(int)
y2 *= np.sign(t2_rot).astype(int)
y3 *= np.sign(t2_rot).astype(int)
## Stage 2 Shape search, step 9
xq = [ y / np.sqrt(sum(y ** 2)) for y in (y0, y1, y2, y3) ]
## Shape and gain combination determination
G = [ T.SNS_VQ_REG_ADJ_GAINS, T.SNS_VQ_REG_LF_ADJ_GAINS,
T.SNS_VQ_NEAR_ADJ_GAINS, T.SNS_VQ_FAR_ADJ_GAINS ]
dMSE = [ [ sum((t2_rot - G[j][i] * xq[j]) ** 2)
for i in range(len(G[j])) ] for j in range(4) ]
self.shape = np.argmin([ np.min(dMSE[j]) for j in range(4) ])
self.gain = np.argmin(dMSE[self.shape])
gain = G[self.shape][self.gain]
## Enumeration of the selected PVQ pulse configurations
if self.shape == 0:
(self.idx_a, self.ls_a) = self.enum_mpvq(y0[:10])
(self.idx_b, self.ls_b) = self.enum_mpvq(y0[10:])
elif self.shape == 1:
(self.idx_a, self.ls_a) = self.enum_mpvq(y1[:10])
(self.idx_b, self.ls_b) = (None, None)
elif self.shape == 2:
(self.idx_a, self.ls_a) = self.enum_mpvq(y2)
(self.idx_b, self.ls_b) = (None, None)
elif self.shape == 3:
(self.idx_a, self.ls_a) = self.enum_mpvq(y3)
(self.idx_b, self.ls_b) = (None, None)
## Synthesis of the Quantized scale factor
scf_q = st1 + gain * fftpack.idct(xq[self.shape], norm = 'ortho')
return scf_q
def run(self, eb, att, nbytes, x):
scf = self.compute_scale_factors(eb, att, nbytes)
scf_q = self.quantize(scf)
y = self.spectral_shaping(scf_q, False, x)
return y
def store(self, b):
shape = self.shape
gain_msb_bits = np.array([ 1, 1, 2, 2 ])[shape]
gain_lsb_bits = np.array([ 0, 1, 0, 1 ])[shape]
b.write_uint(self.ind_lf, 5)
b.write_uint(self.ind_hf, 5)
b.write_bit(shape >> 1)
b.write_uint(self.gain >> gain_lsb_bits, gain_msb_bits)
b.write_bit(self.ls_a)
if self.shape == 0:
sz_shape_a = 2390004
index_joint = self.idx_a + \
(2 * self.idx_b + self.ls_b + 2) * sz_shape_a
elif self.shape == 1:
sz_shape_a = 2390004
index_joint = self.idx_a + (self.gain & 1) * sz_shape_a
elif self.shape == 2:
index_joint = self.idx_a
elif self.shape == 3:
sz_shape_a = 15158272
index_joint = sz_shape_a + (self.gain & 1) + 2 * self.idx_a
b.write_uint(index_joint, 14 - gain_msb_bits)
b.write_uint(index_joint >> (14 - gain_msb_bits), 12)
class SnsSynthesis(Sns):
def __init__(self, dt, sr):
super().__init__(dt, sr)
def deenum_mpvq(self, index, ls, npulses, n):
y = np.zeros(n, dtype=np.intc)
pos = 0
for i in range(len(y)-1, -1, -1):
if index > 0:
yi = 0
while index < T.SNS_MPVQ_OFFSETS[i][npulses - yi]: yi += 1
index -= T.SNS_MPVQ_OFFSETS[i][npulses - yi]
else:
yi = npulses
y[pos] = [ yi, -yi ][int(ls)]
pos += 1
npulses -= yi
if npulses <= 0:
break
if yi > 0:
ls = index & 1
index >>= 1
return y
def unquantize(self):
## SNS VQ Decoding
y = np.empty(16, dtype=np.intc)
if self.shape == 0:
y[:10] = self.deenum_mpvq(self.idx_a, self.ls_a, 10, 10)
y[10:] = self.deenum_mpvq(self.idx_b, self.ls_b, 1, 6)
elif self.shape == 1:
y[:10] = self.deenum_mpvq(self.idx_a, self.ls_a, 10, 10)
y[10:] = np.zeros(6, dtype=np.intc)
elif self.shape == 2:
y = self.deenum_mpvq(self.idx_a, self.ls_a, 8, 16)
elif self.shape == 3:
y = self.deenum_mpvq(self.idx_a, self.ls_a, 6, 16)
## Unit energy normalization
y = y / np.sqrt(sum(y ** 2))
## Reconstruction of the quantized scale factors
G = [ T.SNS_VQ_REG_ADJ_GAINS, T.SNS_VQ_REG_LF_ADJ_GAINS,
T.SNS_VQ_NEAR_ADJ_GAINS, T.SNS_VQ_FAR_ADJ_GAINS ]
gain = G[self.shape][self.gain]
scf = np.append(T.SNS_LFCB[self.ind_lf], T.SNS_HFCB[self.ind_hf]) \
+ gain * fftpack.idct(y, norm = 'ortho')
return scf
def load(self, b):
self.ind_lf = b.read_uint(5)
self.ind_hf = b.read_uint(5)
shape_msb = b.read_bit()
gain_msb_bits = 1 + shape_msb
self.gain = b.read_uint(gain_msb_bits)
self.ls_a = b.read_bit()
index_joint = b.read_uint(14 - gain_msb_bits)
index_joint |= b.read_uint(12) << (14 - gain_msb_bits)
if shape_msb == 0:
sz_shape_a = 2390004
if index_joint >= sz_shape_a * 14:
raise ValueError('Invalide SNS joint index')
self.idx_a = index_joint % sz_shape_a
index_joint = index_joint // sz_shape_a
if index_joint >= 2:
self.shape = 0
self.idx_b = (index_joint - 2) // 2
self.ls_b = (index_joint - 2) % 2
else:
self.shape = 1
self.gain = (self.gain << 1) + (index_joint & 1)
else:
sz_shape_a = 15158272
if index_joint >= sz_shape_a + 1549824:
raise ValueError('Invalide SNS joint index')
if index_joint < sz_shape_a:
self.shape = 2
self.idx_a = index_joint
else:
self.shape = 3
index_joint -= sz_shape_a
self.gain = (self.gain << 1) + (index_joint % 2)
self.idx_a = index_joint // 2
def run(self, x):
scf = self.unquantize()
y = self.spectral_shaping(scf, True, x)
return y
### ------------------------------------------------------------------------ ###
def check_analysis(rng, dt, sr):
ok = True
analysis = SnsAnalysis(dt, sr)
for i in range(10):
ne = T.I[dt][sr][-1]
x = rng.random(ne) * 1e4
e = rng.random(len(T.I[dt][sr]) - 1) * 1e10
if sr >= T.SRATE_48K_HR:
for nbits in (1144, 1152, 2296, 2304, 4400, 4408):
y = analysis.run(e, False, nbits // 8, x)
data = analysis.get_data()
(y_c, data_c) = lc3.sns_analyze(
dt, sr, nbits // 8, e, False, x)
for k in data.keys():
ok = ok and data_c[k] == data[k]
ok = ok and lc3.sns_get_nbits() == analysis.get_nbits()
ok = ok and np.amax(np.abs(y - y_c)) < 1e-1
else:
for att in (0, 1):
y = analysis.run(e, att, 0, x)
data = analysis.get_data()
(y_c, data_c) = lc3.sns_analyze(dt, sr, 0, e, att, x)
for k in data.keys():
ok = ok and data_c[k] == data[k]
ok = ok and lc3.sns_get_nbits() == analysis.get_nbits()
ok = ok and np.amax(np.abs(y - y_c)) < 1e-1
return ok
def check_synthesis(rng, dt, sr):
ok = True
synthesis = SnsSynthesis(dt, sr)
for i in range(100):
synthesis.ind_lf = rng.integers(0, 32)
synthesis.ind_hf = rng.integers(0, 32)
shape = rng.integers(0, 4)
sz_shape_a = [ 2390004, 2390004, 15158272, 774912 ][shape]
sz_shape_b = [ 6, 1, 0, 0 ][shape]
synthesis.shape = shape
synthesis.gain = rng.integers(0, [ 2, 4, 4, 8 ][shape])
synthesis.idx_a = rng.integers(0, sz_shape_a, endpoint=True)
synthesis.ls_a = bool(rng.integers(0, 1, endpoint=True))
synthesis.idx_b = rng.integers(0, sz_shape_b, endpoint=True)
synthesis.ls_b = bool(rng.integers(0, 1, endpoint=True))
ne = T.I[dt][sr][-1]
x = rng.random(ne) * 1e4
y = synthesis.run(x)
y_c = lc3.sns_synthesize(dt, sr, synthesis.get_data(), x)
ok = ok and np.amax(np.abs(1 - y/y_c)) < 1e-5
return ok
def check_analysis_appendix_c(dt):
i0 = dt - T.DT_7M5
sr = T.SRATE_16K
ok = True
for i in range(len(C.E_B[i0])):
scf = lc3.sns_compute_scale_factors(dt, sr, 0, C.E_B[i0][i], False)
ok = ok and np.amax(np.abs(scf - C.SCF[i0][i])) < 1e-4
(lf, hf) = lc3.sns_resolve_codebooks(scf)
ok = ok and lf == C.IND_LF[i0][i] and hf == C.IND_HF[i0][i]
(y, yn, shape, gain) = lc3.sns_quantize(scf, lf, hf)
ok = ok and np.any(y[0][:16] - C.SNS_Y0[i0][i] == 0)
ok = ok and np.any(y[1][:10] - C.SNS_Y1[i0][i] == 0)
ok = ok and np.any(y[2][:16] - C.SNS_Y2[i0][i] == 0)
ok = ok and np.any(y[3][:16] - C.SNS_Y3[i0][i] == 0)
ok = ok and shape == 2*C.SUBMODE_MSB[i0][i] + C.SUBMODE_LSB[i0][i]
ok = ok and gain == C.G_IND[i0][i]
scf_q = lc3.sns_unquantize(lf, hf, yn[shape], shape, gain)
ok = ok and np.amax(np.abs(scf_q - C.SCF_Q[i0][i])) < 1e-5
x = lc3.sns_spectral_shaping(dt, sr, C.SCF_Q[i0][i], False, C.X[i0][i])
ok = ok and np.amax(np.abs(1 - x/C.X_S[i0][i])) < 1e-5
(x, data) = lc3.sns_analyze(dt, sr, 0, C.E_B[i0][i], False, C.X[i0][i])
ok = ok and data['lfcb'] == C.IND_LF[i0][i]
ok = ok and data['hfcb'] == C.IND_HF[i0][i]
ok = ok and data['shape'] == 2*C.SUBMODE_MSB[i0][i] + \
C.SUBMODE_LSB[i0][i]
ok = ok and data['gain'] == C.G_IND[i0][i]
ok = ok and data['idx_a'] == C.IDX_A[i0][i]
ok = ok and data['ls_a'] == C.LS_IND_A[i0][i]
ok = ok and (C.IDX_B[i0][i] is None or
data['idx_b'] == C.IDX_B[i0][i])
ok = ok and (C.LS_IND_B[i0][i] is None or
data['ls_b'] == C.LS_IND_B[i0][i])
ok = ok and np.amax(np.abs(1 - x/C.X_S[i0][i])) < 1e-5
return ok
def check_synthesis_appendix_c(dt):
i0 = dt - T.DT_7M5
sr = T.SRATE_16K
ok = True
for i in range(len(C.X_HAT_TNS[i0])):
data = {
'lfcb' : C.IND_LF[i0][i], 'hfcb' : C.IND_HF[i0][i],
'shape' : 2*C.SUBMODE_MSB[i0][i] + C.SUBMODE_LSB[i0][i],
'gain' : C.G_IND[i0][i],
'idx_a' : C.IDX_A[i0][i],
'ls_a' : C.LS_IND_A[i0][i],
'idx_b' : C.IDX_B[i0][i] if C.IDX_B[i0][i] is not None else 0,
'ls_b' : C.LS_IND_B[i0][i] if C.LS_IND_B[i0][i] is not None else 0,
}
x = lc3.sns_synthesize(dt, sr, data, C.X_HAT_TNS[i0][i])
ok = ok and np.amax(np.abs(x - C.X_HAT_SNS[i0][i])) < 1e0
return ok
def check():
rng = np.random.default_rng(1234)
ok = True
for dt in range(T.NUM_DT):
for sr in range(T.SRATE_8K, T.SRATE_48K + 1):
ok = ok and check_analysis(rng, dt, sr)
ok = ok and check_synthesis(rng, dt, sr)
for dt in ( T.DT_2M5, T.DT_5M, T.DT_10M ):
for sr in ( T.SRATE_48K_HR, T.SRATE_96K_HR ):
ok = ok and check_analysis(rng, dt, sr)
ok = ok and check_synthesis(rng, dt, sr)
for dt in ( T.DT_7M5, T.DT_10M ):
check_analysis_appendix_c(dt)
check_synthesis_appendix_c(dt)
return ok
### ------------------------------------------------------------------------ ###