Amplitudes of mono-components and representation by generalized sampling functions
Information Theory
2012-12-18 v1 math.IT
Abstract
A mono-component is a real-valued signal of finite energy that has non-negative instantaneous frequencies, which may be defined as the derivative of the phase function of the given real-valued signal through the approach of canonical amplitude-phase modulation. We study in this article how the amplitude is determined by its phase in a canonical amplitude-phase modulation. Our finding is that such an amplitude can be perfectly reconstructed by a sampling formula using the so-called generalized sampling functions and their Hilbert transforms. The regularity of such an amplitude is identified to be at least continuous. Meanwhile, we also make a very interesting and new characterization of the band-limited functions.
Cite
@article{arxiv.1212.3886,
title = {Amplitudes of mono-components and representation by generalized sampling functions},
author = {Qiuhui Chen and Luoqing Li and Yi Wang},
journal= {arXiv preprint arXiv:1212.3886},
year = {2012}
}