PyHHT Tutorials

The Hilbert Huang transform (HHT) is a time series analysis technique that is designed to handle nonlinear and nonstationary time series data. PyHHT is a Python module based on NumPy and SciPy which implements the HHT. These tutorials introduce HHT, the common vocabulary associated with it and the usage of the PyHHT module itself to analyze time series data.

This series of tutorials goes through the philosophy of the Hilbert Huang transform in detail. The first two tutorials lay the groundwork for the HHT, providing the motivation first for the Hilbert spectral analysis and then for the empirical mode decomposition algorithm. The third tutorial is an introduction to the PyHHT module. You may skip the first two sections if you are comfortable with the theory of HHT and if you want to start coding Python applications with PyHHT.

Contents:

• Limitations of the Fourier Transform: Need For a Data Driven Approach
  • The Problem
  • A note on time-frequency analysis
  • Time-Frequency representations of the signal
  • A counterexample
• Motivation for Hilbert Spectral Analysis
  • 1. The Uncertainty Principle
  • 2. Instantaneous Frequency
  • 3. Two Views of Nonlinear Phenomena
  • 4. Conclusion
• Using PyHHT: EMD and Hilbert Spectral Analysis