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arXiv · 1212.3886

Amplitudes of mono-components and representation by generalized sampling functions

Qiuhui Chen·Luoqing Li·Yi Wang
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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.

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Qiuhui Chen, Luoqing Li, Yi Wang. 2012-12-17. Amplitudes of mono-components and representation by generalized sampling functions. https://arxiv.org/abs/1212.3886

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