Narrow Results

The concepts of intrinsic mode functions and mono-components are investigated in relation to the empirical mode decomposition. Mono-components are defined to be the functions for which non-negative analytic instantaneous frequency is well defined. We show that a great variety of functions are mono-components based on which adaptive decomposition of signals are theoretically possible. We justify the role of empirical mode decomposition in signal decomposition in relation to mono-components.

In this paper, we will give a survey on adaptive Fourier decompositions (AFDs) in one- and multi-dimensions. Theoretical formulations of three different types of AFDs in one-dimension, viz., Core AFD, Cyclic AFD in conjunction with best rational approximation and Unwending AFD are provided.

A mono-component is a real-variable and complex-valued analytic signal with nonnegative frequency components. The amplitude of an analytic signal is determined by its phase in a canonical amplitude-phase modulation. This paper investigates the amplitude spaces of analytic signals in terms of the Blaschke products with zeros in $(-1,1)$. It is proved that these amplitude spaces are invariant under the Hilbert transform and form a multiresolution analysis in the Hilbert space of signals with finite energy.

This paper reviews some recent progress on adaptive signal decomposition into mono-components that are defined to be the signals of non-negative analytic phase derivatives.