The adaptive Fourier decomposition algorithm provides a robust method for signal expansion with efficient energy decay and computational complexity comparable to DFT.
AFD supports robust signal expansion with DFT-like efficiency; leaves open validation for cardiovascular applications.
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 HardyH2and theL2spaces. 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.
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Qian et al. (2011) studied this question.
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