Multilevel Discrete Wavelet Transform and Noise Reduction of 1D Time Series: A Real-World Project

How to make multilevel Discrete Wavelet Transform and noise reduction of 1D Time Series signal through a real-world project

In the previous articles, we have displayed the process and methods on how to decompose, reconstruct, and partial reconstruct a 1D signal. In this article, we will use the concepts and methods introduced in these previous articles on a real-world project.

The main objectives of this project are to make a Discrete Wavelet transform on a 1D time series signal of water Dissolved oxygen (DO) collected from a China’s reservoir with sensors. It also encourages you to use your own dataset. The main tasks of the project include:

  • Decompose the signal into multilevel approximation and detail coefficients
  • Visualize the Approximation and Details coefficients
  • Reconstruct the time series signal from these coefficients
  • Reconstruct the Approximation and Details from its coefficients
  • Visualize the Approximation and Details of the signal
  • Reduce data noise at different levels and visualize the results

If you are not familiar with these concepts, process and method, I suggest that you had better read the concerned parts in previous articles.

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