Hi Crostophe, thank you for this wonderful tutorial.
You may want to use the more standard terms:
"pre-envelope" m_+(t) = m(t) + j \hat{m}(t)
(ie, the signal you currently denote as \tilde{m}(t))
"complex-envelope", \tilde{m}(t)
(for the signal you currently denote as m^{bb}(t) )
thank you again for your efforts,
Achilleas
