# Wavelet Scattering (Kymatio) Zero Divison Error

I'm attempting to make use of wavelet scattering to analyse my signal samples.

The example IQ Wav file I am using is as follows: https://www.dropbox.com/s/dd6fr4va4alpazj/move_x_movedist_1_speed_25k_sample_6.wav?dl=0

Currently, following a guide from the Kymatio documentation, I have the following code:

import scipy.io.wavfile
import numpy as np
import matplotlib.pyplot as plt
from kymatio.numpy import Scattering1D

path = r"move_x_movedist_1_speed_25k_sample_6.wav"

# Read in the sample WAV file
fs, x = scipy.io.wavfile.read(path)
x = x.T
print(fs)
# Once the recording is in memory, we normalise it to +1/-1
x = x / np.max(np.abs(x))
print(x)
# Set up parameters for the scattering transform
## number of samples, T
N = x.shape[-1]
print(N)
## Averaging scale as power of 2, 2**J, for averaging
## scattering scale of 2**6 = 64 samples
J = 6
## No. of wavelets per octave (resolve frequencies at
## a resolution of 1/16 octaves)
Q = 16
# Create object to compute scattering transform
scattering = Scattering1D(J, N, Q)
# Compute scattering transform of our signal sample
Sx = scattering(x)
# Extract meta information to identify scattering coefficients
meta = scattering.meta()
# Zeroth-order
order0 = np.where(meta['order'] == 0)
# First-order
order1 = np.where(meta['order'] == 1)
# Second-order
order2 = np.where(meta['order'] == 2)

#%%
# Plot original signal
plt.figure(figsize=(8, 2))
plt.plot(x)
plt.title('Original Signal')
plt.show()

# Plot zeroth-order scattering coefficient (average of
# original signal at scale 2**J)
plt.figure(figsize=(8,8))
plt.subplot(3, 1, 1)
plt.plot(Sx[order0][0])
plt.title('Zeroth-Order Scattering')
# Plot first-order scattering coefficient (arrange
# along time and log-frequency)
plt.subplot(3, 1, 2)
plt.imshow(Sx[order1], aspect='auto')
plt.title('First-order scattering')
# Plot second-order scattering coefficient (arranged
# along time but has two log-frequency indicies -- one
# first- and one second-order frequency. Both are mixed
# along the vertical axis)
plt.subplot(3, 1, 3)
plt.imshow(Sx[order2], aspect='auto')
plt.title('Second-order scattering')
plt.show()


The print statements for the sample rate, the normalised X (data) and the number of samples are as follows:

2000000
[[-0.65671316  0.40170009]
[-0.67349608  0.50152572]
[-0.62685266  0.54555362]
...
[-0.59829991 -0.11006975]
[-0.64930253 -0.03116827]
[-0.6619442   0.05557977]]
2


There seems to be 2 samples as the main signal was split up into chunks of 2s using pydub's make_chunks and exporting them as wav format. The sample rate is 2MHz as these recordings are of RF signals stored in IQ WAV files.

However, the problem here is that I am getting the following error, from which I read seems to potentially be an issue with my J value (averaging scale):

Traceback (most recent call last): File "analyse.py", line 38, in scattering = Scattering1D(J, T, Q) File "C:\Users\xwb18152\AppData\Roaming\Python\Python38\site-packages\kymatio\scattering1d\frontend\numpy_frontend.py", line 19, in init ScatteringBase1D.build(self) File "C:\Users\xwb18152\AppData\Roaming\Python\Python38\site-packages\kymatio\scattering1d\frontend\base_frontend.py", line 55, in build min_to_pad = compute_minimum_support_to_pad( File "C:\Users\xwb18152\AppData\Roaming\Python\Python38\site-packages\kymatio\scattering1d\utils.py", line 125, in compute_minimum_support_to_pad _, _, _, t_max_phi = scattering_filter_factory( File "C:\Users\xwb18152\AppData\Roaming\Python\Python38\site-packages\kymatio\scattering1d\filter_bank.py", line 676, in scattering_filter_factory psi_f[0] = morlet_1d( File "C:\Users\xwb18152\AppData\Roaming\Python\Python38\site-packages\kymatio\scattering1d\filter_bank.py", line 135, in morlet_1d morlet_f *= get_normalizing_factor(morlet_f, normalize=normalize) File "C:\Users\xwb18152\AppData\Roaming\Python\Python38\site-packages\kymatio\scattering1d\filter_bank.py", line 157, in get_normalizing_factor raise ValueError('Zero division error is very likely to occur, ' + ValueError: Zero division error is very likely to occur, aborting computations now.

Any help would be appreciated to understand what's going on!

EDIT: I can get to "the next step" if I use Q=1,J=1, however I get the following warning:

warnings.warn('Signal support is too small to avoid border effects'

And when trying to plot I get the error:

File "analyse.py", line 100, in <module>
plt.imshow(Sx[order1], aspect='auto')
[....]
raise TypeError("Invalid shape {} for image data"
TypeError: Invalid shape (2, 3, 1) for image data

• Updated the OP with some recent attempts! Mar 14, 2022 at 12:22

Latest release is incomplete. Use dev

pip install git+https://github.com/kymatio/kymatio.git@dev


or latest stable branch with all functionality

pip install git+https://github.com/kymatio/kymatio.git@refs/pull/674/head


And when trying to plot I get the error:

is due to

There seems to be 2 samples as the main signal was split up

so an option is to iterate over the batch axis (0) and plot one by one.

• I used the second option (all functionality latest stable) and running the code gives the error AssertionError: must have at least 3 filters in filterbank (got 1) Mar 14, 2022 at 13:44
• Increasing Q to 3 gives the error: ValueError: max() arg is an empty sequence Mar 14, 2022 at 13:47
• @rshah I do not reproduce your errors. Running your code gave different errors, so I edited the working version into your question. Data loads batches into axis 1, but must be axis 0 as mentioned (also in docs). Mar 14, 2022 at 16:21
• @rshah That's right. And, they're here in help(Scattering1D). Unfortunately there aren't built-in visuals (or examples) for properly visualizing the second order; the true structure is shown here under "CWT, second order". Mar 15, 2022 at 14:27
• @rshah That's expanding the scope of the question, but briefly, order0 and order1 are fully proper, order2 is "unrolled". Mar 15, 2022 at 14:38