Carrier frequencies, holomorphy. And unwinding

Ronald R. Coifman, Stefan Steinerberger, Hau Tieng Wu

Research output: Contribution to journalArticlepeer-review


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 lP-(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 scries can provide a high-resolution, noise- robust time-frequency representation.

Original languageEnglish (US)
Pages (from-to)4838-4864
Number of pages27
JournalSIAM Journal on Mathematical Analysis
Issue number6
StatePublished - 2017


  • Blaschkc products
  • Carrier frequency
  • Intrinsic-mode type function
  • Synchrosqucczing transform
  • Time-frequency representation
  • Unwinding scries

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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