  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.
