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.
Categories: math.NA math.CV physics.data-an