Math @ Duke
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Publications [#331926] of Hau-Tieng Wu
Papers Published
- Wu, H; Steinerberger, S; Coifman, R, Carrier frequencies, holomorphy and unwinding,
SIAM Journal on Mathematical Analysis, vol. 49 no. 6
(January, 2017),
pp. 4838-4864, Society for Industrial and Applied Mathematics [doi]
(last updated on 2024/03/28)
Abstract: We prove that functions of intrinsic-mode type (a classical models for signals) behave essentially like holomorphic functions: Adding a pure carrier frequency eint ensures that the anti- holomorphic part is much smaller than the holomorphic part lP-(f)||L ≪||-P+(f)||L . 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. 2 2
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