This is a question about producing a time/period (1/frequency) plot from a CWT, instead of the time/scale output. I am trying to use the ssqueezepy python library to perform the CWTs. Then I understand I need to convert the scales into pseudo-frequencies to make the plot.

I have a dataset which I want to transform here. The sampling rate is fs = 1 sample per day (not Hz). I want to generate a time/period plot, with period = 1/frequency. I am specifically searching for signals in the 30-60 day period band, so I would like to have that range visible on the y axis.

My dataset has a number of peaks, so I am using the Mexican hat wavelet. In particular I am interested in the periods of the smaller amplitude peaks in the 30-60 day band.

Below are plots of the CWT (top) SSQ_CWT (middle) and original time series (bottom). The SSQ_CWT from ssqueezepy returns normalized frequencies, and I tried to plot 1/(f*fs) on the vertical axis of the middle panel to get period in days, as fs=1 sample per day. However it doesn't seem to work correctly.

enter image description here

I would be grateful for help from anyone familiar with CWTs and the ssqueezepy library to explain how to convert the CWT output into pseudo-frequencies and then plot a time/period map. The code I am using is:

import numpy as np
import matplotlib.pyplot as plt
from ssqueezepy import ssq_cwt, ssq_stft

# read signal
x = np.loadtxt("data.txt")

Tx, Wx, freqs, scales, *_ = ssq_cwt(x, wavelet='cmhat')

fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex=True)

extent = 0, 2954, np.max(scales), np.min(scales)
ax1.imshow(np.abs(Wx), aspect='auto', cmap='turbo', extent=extent)

extent = 0, 2954, 1 / np.min(freqs), 1 / np.max(freqs)
ax2.imshow(np.abs(Tx), aspect='auto', vmin=0, vmax=20, cmap='turbo', extent=extent)



1 Answer 1

  1. CWT freqs are log scaled, extent assumes linear; must pass values explicitly
  2. Period is as simple as 1/freq. I also advise "center frequency" over "pseudo"; once properly interpreted, they're very real (else SSQ wouldn't work). An explanation

ssqueezepy.visuals actually has a built-in support for such plotting:

visuals.imshow(Wx, abs=1, yticks=1/freqs)  # I don't have your data, took randn

You can inspect its source code (starting here) and replicate for yourself.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.