def __init__(self, J, Q, audio_length):
super(Scatter, self).__init__()
self.J = J
self.Q = Q
self.T = audio_length
self.meta = Scattering1D.compute_meta_scattering(self.J, self.Q)
self.order0_indices = (self.meta['order'] == 0)
self.order1_indices = (self.meta['order'] == 1)
self.order2_indices = (self.meta['order'] == 2)
self.scattering = Scattering1D(self.J, self.T, self.Q).cuda()
self.output_size = self.scattering.output_size()
def normalised_frquency_vector(x,
J,
Q,
epsilon_order_1=1 * 10**-6,
epsilon_order_2=1 * 10**-6):
x = torch.from_numpy(x).float()
x /= x.abs().max()
x = x.view(1, -1)
T = x.shape[-1]
scattering = Scattering1D(J,
T,
Q=Q,
average=True,
oversampling=0,
vectorize=True)
Sx = scattering.forward(x)
Sx_abs = scattering.forward(np.abs(x))
meta = Scattering1D.compute_meta_scattering(J, Q)
order0 = (meta['order'] == 0)
order1 = (meta['order'] == 1)
order2 = (meta['order'] == 2)
Sx1 = normalise_order1(Sx,
Sx_abs,
order0,
order1,
order2,
epsilon_order_1,
frequency_normalisation_order_1_vector=[])
Sx2 = normalise_order2(J,
Q,
Sx,
order0,
order1,
order2,
epsilon_order_2,
frequency_normalisation_order_2_vector=[])
return np.mean(scale_value(Sx1.numpy()),
axis=1), np.mean(scale_value(Sx2.numpy()), axis=1)
def plot_multi_order_scattering(x,
J,
Q,
order1_frequency_axis=[],
normalise_1=False,
normalise_2=False,
epsilon_order_1=1 * 10**-6,
epsilon_order_2=1 * 10**-6,
frequency_normalisation_order_1_vector=None,
frequency_normalisation_order_2_vector=None):
x = torch.from_numpy(x).float()
x /= x.abs().max()
x = x.view(1, -1)
T = x.shape[-1]
scattering = Scattering1D(J,
T,
Q=Q,
average=True,
oversampling=0,
vectorize=True)
Sx = scattering.forward(x)
Sx_abs = scattering.forward(np.abs(x))
meta = Scattering1D.compute_meta_scattering(J, Q)
order0 = (meta['order'] == 0)
order1 = (meta['order'] == 1)
order2 = (meta['order'] == 2)
fig = make_subplots(
rows=3,
cols=6,
column_widths=[0.4, 0.4, 0.4, 0.4, 0.4, 0.4],
row_heights=[0.2, 0.2, 0.2],
specs=[[{
"type": "Scatter"
}, {
"type": "Heatmap"
}, {
"type": "Heatmap"
}, {
"type": "Heatmap"
}, {
"type": "Heatmap"
}, {
"type": "Heatmap"
}],
[{
"type": "Scatter"
}, {
"type": "Scatter"
}, {
"type": "Scatter"
}, {
"type": "Scatter"
}, {
"type": "Scatter"
}, {
"type": "Scatter"
}],
[
None, {
"type": "Scatter"
}, {
"type": "Scatter"
}, {
"type": "Scatter"
}, {
"type": "Scatter"
}, {
"type": "Scatter"
}
]],
subplot_titles=(
'Temporal signal', 'Scattering Order 1',
'Scattering Order 1 Normalised', 'Scattering Order 2',
'Scattering Order 2 Normalised', 'Order 2 Frequency',
"Scattering Order 0", 'Scattering Order 1 mean',
'Scattering Order 1 mean Normalised', 'Scattering Order 2 mean',
'Scattering Order 2 mean Normalised', 'Order 2 Frequency mean',
None, 'Scattering Order 1 max',
'Scattering Order 1 max Normalised', 'Scattering Order 2 max',
'Scattering Order 2 max Normalised', 'Order 2 Frequency max'))
fig.add_trace(go.Scatter(y=x[0, :].numpy(), name="Negative"), row=1, col=1)
fig.add_trace(go.Scatter(y=Sx[0, order0, :].numpy().ravel(),
name="Negative"),
row=2,
col=1)
if normalise_1:
Sx1 = normalise_order1(Sx,
Sx_abs,
order0,
order1,
order2,
epsilon_order_1,
frequency_normalisation_order_1_vector=
frequency_normalisation_order_1_vector)
else:
Sx1 = Sx[0, order1, :]
if (len(order1_frequency_axis) != 0):
fig.add_trace(go.Heatmap(z=scale_value(Sx[0, order1, :].numpy()),
y=order1_frequency_axis,
colorscale='Viridis',
showscale=False),
row=1,
col=2)
fig.add_trace(go.Heatmap(z=scale_value(Sx1.numpy()),
y=order1_frequency_axis,
colorscale='Viridis',
showscale=False),
row=1,
col=3)
else:
fig.add_trace(go.Heatmap(z=scale_value(Sx[0, order1, :].numpy()),
colorscale='Viridis',
showscale=False),
row=1,
col=2)
fig.update_yaxes(autorange="reversed", row=1, col=2)
fig.add_trace(go.Heatmap(z=scale_value(Sx1.numpy()),
colorscale='Viridis',
showscale=False),
row=1,
col=3)
fig.update_yaxes(autorange="reversed", row=1, col=3)
fig.add_trace(go.Scatter(y=np.mean(scale_value(Sx[0, order1, :].numpy()),
axis=1),
name="Negative"),
row=2,
col=2)
fig.add_trace(go.Scatter(y=np.max(scale_value(Sx[0, order1, :].numpy()),
axis=1),
name="Negative"),
row=3,
col=2)
fig.add_trace(go.Scatter(y=np.mean(scale_value(Sx1.numpy()), axis=1),
name="Negative"),
row=2,
col=3)
fig.add_trace(go.Scatter(y=np.max(scale_value(Sx1.numpy()), axis=1),
name="Negative"),
row=3,
col=3)
if normalise_2:
Sx2 = normalise_order2(J,
Q,
Sx,
order0,
order1,
order2,
epsilon_order_2,
frequency_normalisation_order_2_vector=
frequency_normalisation_order_2_vector)
else:
Sx2 = Sx[0, order2, :]
fig.add_trace(go.Heatmap(z=scale_value(Sx[0, order2, :].numpy()),
colorscale='Viridis',
showscale=False),
row=1,
col=4)
fig.update_yaxes(autorange="reversed", row=1, col=4)
fig.add_trace(go.Heatmap(z=scale_value(Sx2.numpy()),
colorscale='Viridis',
showscale=False),
row=1,
col=5)
fig.update_yaxes(autorange="reversed", row=1, col=5)
fig.add_trace(go.Scatter(y=np.mean(scale_value(Sx[0, order2, :].numpy()),
axis=1),
name="Negative"),
row=2,
col=4)
fig.add_trace(go.Scatter(y=np.max(scale_value(Sx[0, order2, :].numpy()),
axis=1),
name="Negative"),
row=3,
col=4)
fig.add_trace(go.Scatter(y=np.mean(scale_value(Sx2.numpy()), axis=1),
name="Negative"),
row=2,
col=5)
fig.add_trace(go.Scatter(y=np.max(scale_value(Sx2.numpy()), axis=1),
name="Negative"),
row=3,
col=5)
fig.update_layout(showlegend=False)
Sx2_Bis = select_frequency(Sx2, T, J, Q, index_frequency=None)
fig.add_trace(go.Heatmap(z=scale_value(Sx2_Bis),
colorscale='Viridis',
showscale=False),
row=1,
col=6)
fig.update_yaxes(autorange="reversed", row=1, col=6)
fig.add_trace(go.Scatter(y=np.mean(scale_value(Sx2_Bis), axis=1),
name="Negative"),
row=2,
col=6)
fig.add_trace(go.Scatter(y=np.max(scale_value(Sx2_Bis), axis=1),
name="Negative"),
row=3,
col=6)
fig.show()
# -----------
# Let's take a look at the signal spectrogram
plt.figure(figsize=(10, 10))
plt.specgram(x.numpy().ravel(), Fs=1024)
plt.title("Time-Frequency spectrogram of signal")
###############################################################################
# Doing the scattering transform
# ------------------------------
J = 6
Q = 16
scattering = Scattering1D(T, J, Q)
# get the metadata on the coordinates of the scattering
meta = Scattering1D.compute_meta_scattering(J, Q)
order0 = (meta['order'] == 0)
order1 = (meta['order'] == 1)
order2 = (meta['order'] == 2)
s = scattering.forward(x)[0]
plt.figure(figsize=(10, 10), dpi=300)
plt.subplot(3, 1, 1)
plt.plot(s[order0].numpy())
plt.title("Scattering order 0")
plt.subplot(3, 1, 2)
plt.imshow(s[order1].numpy(), aspect='auto')
plt.title("Scattering order 1")
plt.subplot(3, 1, 3)
plt.imshow(s[order2].numpy(), aspect='auto')
plt.title("Scattering order 2")