  We prove that functions of intrinsic-mode type (a classical models for
signals) behave essentially like holomorphic functions: adding a pure carrier
frequency $e^{int}$ ensures that the anti-holomorphic part is much smaller than
the holomorphic part $ \| P_{-}(f)\|_{L^2} \ll \|P_{+}(f)\|_{L^2}.$ This
enables us to use techniques from complex analysis, in particular the
\textit{unwinding series}. We study its stability and convergence properties
and show that the unwinding series can stabilize and show that the unwinding
series can provide a high resolution time-frequency representation, which is
robust to noise.
