This tutorial looks at the basics of time-frequency decomposition of time series such as geophysical signals. Related notebooks also cover the continuous wavelet transform (CWWT) and empirical mode decomposition (EMD). Finally, I include code for reproducing some 'benchmark' time series for exploring and testing decomposition algorithms.

These are the interesting files:

• Manuscript.ipynb — the main notebook, containing the text and code from the manuscript. Start here.
• EMD.ipynb — a quick look at EMD, a time series analysis method in the time domain.
• CWT.ipynb — a quick look at the continuous wavelet transform, which decomposes the signal into scale vs time.
• Natural_signals.ipynb — this notebook extracts a series of natural, real-world digital signals from various sources, including the piano, a bat, a volcano, and an earthquake.
• Synthetic_signals.ipynb — a work in progress, this notebook generates a series of artificial digital signals.

I recommend using conda environments for Python development.

The main notebook, manuscript.ipynb, should run without installing anything except scipy, matplotlib, and (optionally), seaborn.

You will need to install some software:

pip install bruges 

You also need to install PyEMD:

git clone https://github.com/laszukdawid/PyEMD.git cd PyEMD python setup.py sdist pip install dist/EMD-signal-0.2.4.tar.gz 

The notebooks Natural_signals.ipynb requires obspy:

conda config --add channel conda-forge conda install obspy 

The file Manuscript.ipynb contains the manuscript, and all of the code necessary to reproduce it.

Some of the notebook cells contain tags which control the behaviour of nbconvert, the Jupyter command which parses the notebook into other formats. The tags work like so:

• hide: hide this cell completely, as well as any output it generates. (I generally don't include import statements in the manuscript, for example.)
• hidein: hide the input, but keep the output. This includes the figures, but not all the code that's required to generate them. (matplotlib can be rather verbose.)
• hideout: keep the input, but hide the output.

The following steps — which require you to install pandoc and, if you want PDF output, LaTeX too — will first execute the notebook, which saves all of the figures as PNG files, then generate DOCX and PDF manuscript documents from the notebook:

 jupyter nbconvert --execute Manuscript.ipynb --to notebook --output Manuscript.ipynb jupyter nbconvert Manuscript.ipynb --to markdown --output Manuscript.md \ --TagRemovePreprocessor.remove_input_tags={\"hidein\"} \ --TagRemovePreprocessor.remove_all_outputs_tags={\"hideout\"} \ --TagRemovePreprocessor.remove_cell_tags={\"hide\"} pandoc Manuscript.md -o Manuscript.pdf pandoc Manuscript.md -o Manuscript.docx 

Note, if Jupyter complains about NoSuchKernel, add your current environment to the kernelspec, e.g.:

 python -m ipykernel install --name myenv