Amplitude Spaces Of Mono-Components From Blaschke Products And An Intrinsic Multiresolution Analysis

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.