signal_decomposition.py

https://github.com/marimo-team/gallery-examples/blob/main/notebooks/education/signal_decomposition.py

Signal Decomposition
This app is a hands-on introduction to signal decomposition, an
age-old problem about breaking down a complex signal, also known as a
time series, into the sum of simpler interpretable ones.
The simpler signals that come out of a decomposition are called
components. When doing a signal decomposition, we have to specify
two things:


    

  1. How many components do we want?
    2. 

  2. What kinds of components, or "component classes", do we want?
    3. 

Part 1: Understanding components

Let's build a decomposition for this signal:

    

  • Every decomposition needs at least two components. We'll make
2 components.
    • 

  • We have to choose the component classes out of a library of
available classes.
    • 

  • Noise component: The first component always represents noise,
or a residual; we typically want it to be small.
    • 

  • Other components: What to choose for
the other components depends on what properties we suspect the
underlying simpler signals to have.
    • 


Use the radio buttons to try a few options for the second
 component.
Part 2: More Decompositions
''
More about Signal Decomposition


This tutorial is based on the research book, ,
by Bennet Meyers and Stephen Boyd. It uses the  Python library to
compute decompositions.


We hope this app shows that math can be intuitive, actionable,
and fun.
This material is based upon work supported by the U.S. Department of
Energy's Office of Energy Efficiency and Renewable Energy (EERE)
under the Solar Energy Technologies Office Award Number 38529.