Algorithm of Adaptive Fourier Decomposition

The present paper is a continuing work on the recently established adaptive Fourier decomposition (AFD) mainly stressing on the algorithm aspect, including algorithm analysis and numerical examples. AFD is a variation and realization of greedy algorithm (matching pursuit) suitable for the Hardy H² and the L² spaces. Applying AFD to a given signal, one obtains a series expansion in the basic signals, called mono-components, that possess non-negative analytic phase derivatives (functions), or, equivalently, meaningful analytic instantaneous frequencies. AFD is shown to be robust with computational complexity comparable with DFT. Consistent to the greedy algorithm principle experiments show that AFD produces (pre-) mono-component series with efficient energy decay that also leads to efficient pointwise convergence, both in terms of computer running time.