Wavelet Cookbook

This Project Pythia Cookbook covers how to work with wavelets in Python

Motivation

Wavelets are a powerful tool to analyze time-series data. When data frequencies vary over time, wavelets can be applied to analysis trends and overcome the time/frequency limitations of Fourier Transforms

Authors

Cora Schneck

Contributors

Structure

This cookbook is broken into two main sections:

• Foundations
• Example Workflows

Foundations

"Wavelet Basics" covers the motivation and background for wavelet analysis by reviewing time-series data and the strengths and weaknesses of other signal analysis tools like Fourier Transform

Example Workflows

• "PyWavelets and Jingle Bells": Learn how to use PyWavelets, a Python implementation of wavelet analysis, to determine the order of notes in a simple musical piece
• "Spy Keypad": Learn how to use wavelets to undercover the frequency and order of notes in an unknown piece of audio data
• "Atmospheric Data: Nino 3 SST Index": Learn how to apply wavelets to real atmospheric and oceanic data to generate a power wavelet scalogram, similiar to the 1999 paper "A Practical Guide to Wavelet Analysis" by Torrence and Compo in Python

Running the Notebooks

You can either run the notebook using Binder or on your local machine.

Running on Binder

The simplest way to interact with a Jupyter Notebook is through Binder, which enables the execution of a Jupyter Book in the cloud. The details of how this works are not important for now. All you need to know is how to launch a Pythia Cookbooks chapter via Binder. Simply navigate your mouse to the top right corner of the book chapter you are viewing and click on the rocket ship icon, (see figure below), and be sure to select “launch Binder”. After a moment you should be presented with a notebook that you can interact with. I.e. you’ll be able to execute and even change the example programs. You’ll see that the code cells have no output at first, until you execute them by pressing {kbd}Shift+{kbd}Enter. Complete details on how to interact with a live Jupyter notebook are described in Getting Started with Jupyter.

Running on Your Own Machine

If you are interested in running this material locally on your computer, you will need to follow this workflow:

(Replace "cookbook-example" with the title of your cookbooks)

1. Clone the https://github.com/ProjectPythia/cookbook-example repository:

    git clone https://github.com/ProjectPythia/cookbook-example.git

2. Move into the cookbook-example directory

   cd cookbook-example

3. Create and activate your conda environment from the environment.yml file

   conda env create -f environment.yml
   conda activate cookbook-dev

4. Move into the notebooks directory and start up Jupyterlab

   cd notebooks/
   jupyter lab