Improving Energy Compaction of Adaptive Fourier Decomposition

Adaptive Fourier decomposition (AFD) provides an expansion of an analytic function into a sum of basic signals, called mono-components. Unlike the Fourier series decomposition, the AFD is based on an adaptive rational orthogonal system, hence it is better suited for analyzing non-stationary data. The most popular algorithm for the AFD decomposes any signal in such a way that the energy of the low-frequency components is maximized. Unfortunately, this results in poor energy compaction of high-frequency components. In this paper, we develop a novel algorithm for the AFD. The key idea is to maximize the energy of any components no matter how big or small the corresponding frequencies are. A comparative evaluation was conducted of the signal reconstruction efficiency of the proposed approach and several conventional algorithms by using speech recordings. The experimental results show that with the new algorithm, it is possible to get a better performance in terms of the reconstruction quality and energy compaction property.