Intrinsic mono-component decomposition of functions: An advance of Fourier theory
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Publication:3565034
DOI10.1002/mma.1214zbMath1188.42001OpenAlexW1967867504MaRDI QIDQ3565034
Publication date: 27 May 2010
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mma.1214
greedy algorithmTakenaka-Malmquist systemanalytic signalinner and outer functionsNevanlinna factorization theoremcomplex Hardy spaceadaptive decomposition of functionsinstantaneous frequency and amplitudemono-components
Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Conjugate functions, conjugate series, singular integrals (42A50) Other generalizations of function theory of one complex variable (32A30)
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Cites Work
- Orthonormal bases with nonlinear phases
- Rational orthogonal bases satisfying the Bedrosian identity
- Analysis of the intrinsic mode functions
- Boundary derivatives of the phases of inner and outer functions and applications
- The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
- Matching pursuits with time-frequency dictionaries
- The Bedrosian identity for the Hilbert transform of product functions
- Mono‐components for decomposition of signals
