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.

This toolbox includes

  • 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)

A list of papers related to the AFD can be found in Section “Introduction to Adaptive Fourier Decomposition”.

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

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

  1. 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”.

  1. 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.