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Carrier frequencies, holomorphy and unwinding
- Publication Year :
- 2016
-
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)\|_{L^2} \ll \|P_{+}(f)\|_{L^2}.$ This enables us to use techniques from complex analysis, in particular the \textit{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.<br />Comment: 22 pages, 16 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1606.06475
- Document Type :
- Working Paper