Comparison of adaptive mono-component decompositions

Abstract

As presented in some recent publications, adaptively choosing the parameters of a Takenaka–Malmquist (TM) system according to the given signal gives rise to the so called adaptive Fourier decomposition (AFD). Besides optimal selections of the parameters to ensure the maximal energy gain at each step, AFD produces entries of non-negative analytic instantaneous frequency. The latter enables us to define a reasonable time–frequency distribution with most desired properties. The energy principle together with the unwinding process through factorizing out the inner function factors yields two variations of the standard AFD, both having appeared in the literature. They are referred by this paper as, respectively, unwinding adaptive Fourier decomposition (UAFD) and double sequence unwinding adaptive Fourier decomposition (DSUAFD). After a short summary of the three adaptive decompositions, the present paper makes comparison between them, as well as with the traditional Fourier series decomposition (FD). The related Dirac type time–frequency distributions associated with mono-components and mono-component decompositions of multi-components are introduced with examples. As necessary preparation we recall the concept mono-component and related knowledge in the introduction section.