Carrier Frequencies, Holomorphy, and Unwinding

We prove that functions of intrinsic-mode type (a classical models for signals) behave essentially like holomorphic functions: adding a pure carrier frequency eint ensures that the anti-holomorphic part is much smaller than the holomorphic part ‖P−(f)‖L2 ‖P+(f)‖L2 . This enables us to use techniques from complex analysis, in particular the unwinding series. We study its stability and convergence properties and show that the unwinding series can provide a high-resolution, noise-robust time-frequency representation.