Carrier frequencies, holomorphy. And unwinding


Journal Article

© 2017 Society for Industrial and Applied Mathematics. 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.

Full Text

Duke Authors

Cited Authors

  • Coifman, RR; Steinerberger, S; Wu, HT

Published Date

  • January 1, 2017

Published In

Volume / Issue

  • 49 / 6

Start / End Page

  • 4838 - 4864

Electronic International Standard Serial Number (EISSN)

  • 1095-7154

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/16M1081087

Citation Source

  • Scopus