@article{10c545962848400a8bdb69037294f6d8,
title = "Carrier frequencies, holomorphy. And unwinding",
abstract = "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.",
keywords = "Blaschkc products, Carrier frequency, Intrinsic-mode type function, Synchrosqucczing transform, Time-frequency representation, Unwinding scries",
author = "Coifman, {Ronald R.} and Stefan Steinerberger and Wu, {Hau Tieng}",
note = "Funding Information: ∗Received by the editors June 22, 2016; accepted for publication (in revised form) June 7, 2017; published electronically November 30, 2017. http://www.siam.org/journals/sima/49-6/M108108.html Funding: The work of the second author was supported by the Institute of New Economic Thinking, INET 0015-0038. The work of the third author was supported by Sloan Research Fellowship FR-2015-65363. †Program in Applied Mathematics, Department of Mathematics, Yale University, New Haven, CT 06511 (coifman@math.yale.edu, stefan.steinerberger@yale.edu). ‡Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada (hauwu@ math.toronto.edu). Publisher Copyright: {\textcopyright} 2017 Society for Industrial and Applied Mathematics.",
year = "2017",
doi = "10.1137/16M1081087",
language = "English (US)",
volume = "49",
pages = "4838--4864",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "6",
}