Toolbox-for-Adaptive-Fourier-Decomposition

This toolbox is intended to help users use the adaptive Fourier decomposition (AFD) easily.

This toolbox contains multiple implementations of the AFD for different types of processed signals and different decomposition process.

There is a online version based on Python version v2.0. You can try the AFD quickly.

Please check the document for detailed information.

Advantages of AFD

• Adaptive decomposition:
  • Adaptive basis;
  • Orthogonal decomposition components;
  • Decomposition components are mono-components that only contain non-negative analytic phase derivatives;
  • Fast energy convergence;
  • Rigorous mathematical foundation.
• Provide the transient time-frequency distribution:
  • Correct total energy;
  • Non-negative real-valuedness;
  • Weak and strong finite suports.

AFD methods included in the toolbox

• Core AFD:
  • Single channel
    • without FFT (slow)
    • with FFT (fast)
  • Multi-channel
    • without FFT (slow)
    • with FFT (fast)
• Unwinding AFD:
  • Single channel
    • without FFT (slow)
    • with FFT (fast)
  • Multi-channel
    • without FFT (slow)
    • with FFT (fast)

Related Papers

A list of papers related to the mathematical Foundation, implementations, and applications of the AFD can be found in the document.

If you use the single-channel AFD method in this toolbox, please at least cite these papers:

T. Qian, L. Zhang, and Z. Li, “Algorithm of adaptive Fourier decomposition,” IEEE Trans. Signal Process., vol. 59, no. 12, pp. 5899–5906, 2011.

T. Qian, Y. B. Wang, “Adaptive Fourier series -- a variation of greedy algorithm," Adv. Comput. Math., vol. 34, no. 3, pp. 279–293, 2011.

If you use the multi-channel AFD method in this toolbox, please at least cite “Adaptive Fourier decomposition for multi-channel signal analysis”.

Z. Wang, C. M. Wong, A. Rosa, T. Qian, and F. Wan, “Adaptive Fourier decomposition for multi-channel signal analysis,” IEEE Trans. Signal Process., vol. 70, pp. 903–918, 2022.

License

This toolbox follows "Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)".