<formula formulatype="inline"><tex Notation="TeX">$\epsilon$</tex> </formula>-Mono-Component: Its Characterization and Construction

Abstract

This paper studies the consistency between the analytic amplitude and the physical amplitude for a mono-component of the form . A special class of mono-components, called -mono-components, are considered and a parameter is introduced to measure the consistency between these two kinds of amplitudes. It is shown that controls the number of zerocrossings of within each monotonic interval of , which means that the oscillation of the analytic amplitude is much slower than that of the phase part at any instant, provided that is sufficiently small. Some sufficient conditions, including the Fourier spectral characterization, for to be an -mono-component are given. Frames and Riesz bases composed of -mono-components are constructed. Finally, applications of -mono-components to signal decomposition and time-frequency analysis are discussed.Index Terms-Mono-component, analytic signal, analytic amplitude, instantaneous frequency, Hardy space.