Orthonormal bases with nonlinear phases

DOI10.1007/s10444-009-9120-0zbMath1213.42126OpenAlexW1978770402MaRDI QIDQ541599

Yuesheng Xu, Haizhang Zhang, Tao Qian, Rui Wang

Publication date: 7 June 2011

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-009-9120-0

zbMATH Keywords

Hilbert transformHardy spacestime-frequency analysisorthonormal basesthe empirical mode decomposition

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30)

Related Items (19)

A class of iterative greedy algorithms related to Blaschke product ⋮ Positive-instantaneous frequency and approximation ⋮ Best two‐parameter rational approximation algorithm of given order: a variation of adaptive Fourier decomposition ⋮ Characterizations of mono-components: the Blaschke and starlike types ⋮ Adaptive Fourier series---a variation of greedy algorithm ⋮ Rational orthogonal bases satisfying the Bedrosian identity ⋮ Multidimensional analytic signals and the Bedrosian identity ⋮ The Bedrosian identity for \(\mathbf H^p\) functions ⋮ A Theory on Non-Constant Frequency Decompositions and Applications ⋮ Constructions of \(\epsilon\)-mono-components and mathematical analysis on signal decomposition algorithm ⋮ Intrinsic mono-component decomposition of functions: An advance of Fourier theory ⋮ Adaptive decomposition by weighted inner functions: a generalization of Fourier series ⋮ Two‐dimensional adaptive Fourier decomposition ⋮ Spectra of rational orthonormal systems ⋮ Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis ⋮ Chirp transforms and chirp series ⋮ The circular Bedrosian identity and multidimensional periodic analytic signals ⋮ Expansions of functions based on rational orthogonal basis with nonnegative instantaneous frequencies ⋮ ANALYTIC SAMPLING APPROXIMATION BY PROJECTION OPERATOR WITH APPLICATION IN DECOMPOSITION OF INSTANTANEOUS FREQUENCY

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analytic unit quadrature signals with nonlinear phase
• Translation invariant spaces
• The Bedrosian identity and homogeneous semi-convolution equations
• A B-spline approach for empirical mode decompositions
• Two families of unit analytic signals with nonlinear phase
• Characterization of boundary values of functions in Hardy spaces with applications in signal analysis
• On two problems concerning linear transformations in Hilbert space
• Two-dimensional empirical mode decomposition by finite elements
• The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
• Piecewise linear spectral sequences
• The Bedrosian identity for the Hilbert transform of product functions

This page was built for publication: Orthonormal bases with nonlinear phases