Carrier frequencies, holomorphy and unwinding

2016/06/21 by Ronald R. Coifman, Stefan Steinerberger, Coifman, Ronald R. +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #Data Analysis #FOS: Mathematics #FOS: Physical sciences #Machine Fault Diagnosis Techniques #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems #Statistics and Probability (physics.data-an)

paper · pdf · doi:10.48550/arxiv.1606.06475

openalex publication_date 2016/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that functions of intrinsic-mode type (a classical models for signals) behave essentially like holomorphic functions: adding a pure carrier frequency e^int 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 stabilize and show that the unwinding series can provide a high resolution time-frequency representation, which is robust to noise.

Citations

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• On the Practical Use of Blaschke Decomposition in Nonstationary Signal Analysis

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