Carrier frequencies, holomorphy. And unwinding

Ronald R. Coifman; Stefan Steinerberger; Hau Tieng Wu

doi:10.1137/16M1081087

Carrier frequencies, holomorphy. And unwinding

Ronald R. Coifman, Stefan Steinerberger, Hau Tieng Wu

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	4838-4864
Number of pages	27
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	6
DOIs	https://doi.org/10.1137/16M1081087
State	Published - 2017

Keywords

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

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1137/16M1081087

Cite this

@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 = "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",

}

TY - JOUR

T1 - Carrier frequencies, holomorphy. And unwinding

AU - Coifman, Ronald R.

AU - Steinerberger, Stefan

AU - Wu, Hau Tieng

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Blaschkc products

KW - Carrier frequency

KW - Intrinsic-mode type function

KW - Synchrosqucczing transform

KW - Time-frequency representation

KW - Unwinding scries

UR - http://www.scopus.com/inward/record.url?scp=85040071657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040071657&partnerID=8YFLogxK

U2 - 10.1137/16M1081087

DO - 10.1137/16M1081087

M3 - Article

AN - SCOPUS:85040071657

SN - 0036-1410

VL - 49

SP - 4838

EP - 4864

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

Carrier frequencies, holomorphy. And unwinding

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this