A Theory on Non-Constant Frequency Decompositions and Applications
From MaRDI portal
Publication:3296691
DOI10.1007/978-3-030-40120-7_1zbMath1494.94015OpenAlexW3026329270MaRDI QIDQ3296691
Tao Qian, Li-Hui Tan, Qiu-hui Chen
Publication date: 1 July 2020
Published in: Advancements in Complex Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-030-40120-7_1
Hardy spaceHilbert transformClifford algebraBlaschke productreproducing kernel Hilbert spaceMöbius transformseveral complex variablesmono-componentNevanlinna factorizationrational orthogonal systemBeurling-Lax theoreminner and outer functionsadaptive Fourier decompositionpre-orthogonal AFD
Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Research exposition (monographs, survey articles) pertaining to information and communication theory (94-02) Approximation by rational functions (41A20) Hardy spaces (30H10)
Related Items (9)
Analytic phase retrieval based on intensity measurements ⋮ Sparse representation of approximation to identity ⋮ Sparse representations of random signals ⋮ Matching pursuit with unbounded parameter domains ⋮ Adaptive Fourier decomposition‐type sparse representations versus the Karhunen–Loève expansion for decomposing stochastic processes ⋮ Reproducing kernel representation of the solution of second order linear three‐point boundary value problem ⋮ Reproducing kernel sparse representations in relation to operator equations ⋮ Best kernel approximation in Bergman spaces ⋮ Adaptive decompositions in monogenic reproducing kernel Hilbert spaces of Paley-Wiener type
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- New aspects of Beurling-Lax shift invariant subspaces
- Phase derivative of monogenic signals in higher dimensional spaces
- The Fueter primitive of biaxially monogenic functions
- Frequency-domain identification: An algorithm based on an adaptive rational orthogonal system
- A fast adaptive model reduction method based on Takenaka-Malmquist systems
- Blaschke products and their applications. Proceedings based on the presentations at the conference, Toronto, Canada, July 25--29, 2011
- Approximation of monogenic functions by higher order Szegő kernels on the unit ball and half space
- Discrete orthogonality of the Malmquist Takenaka system of the upper half plane and rational interpolation
- Adaptive decomposition by weighted inner functions: a generalization of Fourier series
- Orthonormal bases with nonlinear phases
- Analytic unit quadrature signals with nonlinear phase
- Analytic signals with nonnegative instantaneous frequency
- Hardy-Sobolev spaces decomposition in signal analysis
- Fourier spectrum characterizations of \(H^{p}\) spaces on tubes over cones for \(1\leq p \leq \infty \)
- Extracting outer function part from Hardy space function
- Identification and rational \(L^ 2\) approximation: A gradient algorithm
- System identification by discrete rational atoms
- The structure of instantaneous frequencies of periodic analytic signals
- The Bedrosian identity and homogeneous semi-convolution equations
- Simple proofs of the Bedrosian equality for the Hilbert transform
- The Cauchy kernel, the Szegö kernel, and the Riemann mapping function
- Greedy algorithm and \(m\)-term trigonometric approximation
- A martingale proof of \(L_ 2\) boundedness of Clifford-valued singular integrals
- Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces
- Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space
- Characterizations of mono-components: the Blaschke and starlike types
- Uncertainty principle and phase-amplitude analysis of signals on the unit sphere
- Adaptative decomposition: the case of the Drury-Arveson space
- Comparison of adaptive mono-component decompositions
- Rational orthogonal bases satisfying the Bedrosian identity
- Fourier spectrum of Clifford \(H^p\) spaces on \(\mathbb{R}_+^{n + 1}\) for \(1 \leq p \leq \infty \)
- Numerical stability of circular Hilbert transform and its application to signal decomposition
- An enhancement algorithm for cyclic adaptive Fourier decomposition
- Nonlinear phase unwinding of functions
- Phase unwinding, or invariant subspace decompositions of Hardy spaces
- Adaptive Fourier series---a variation of greedy algorithm
- A sharper uncertainty principle
- Analysis of the intrinsic mode functions
- Matching pursuits among shifted Cauchy kernels in higher-dimensional spaces
- Multivalent starlike functions
- Clifford and harmonic analysis on cylinders and tori
- Analytic signals and harmonic measures
- Characterization of boundary values of functions in Hardy spaces with applications in signal analysis
- Rational approximation of functions in Hardy spaces
- Hilbert transforms on the sphere with the Clifford algebra setting
- Hardy space decomposition of on the unit circle:
- Backward shift invariant subspaces with applications to band preserving and phase retrieval problems
- TRANSIENT TIME-FREQUENCY DISTRIBUTION BASED ON MONO-COMPONENT DECOMPOSITIONS
- Instantaneous frequency estimation and representation of the audio signal through Complex Wavelet Additive Synthesis
- Adaptive orthonormal systems for matrix-valued functions
- General Theory for Integer-Type Algorithm for Higher Order Differential Equations
- The Fueter mapping theorem in integral form and the ℱ-functional calculus
- Practical Implementation and Error Bound of Integer-Type Algorithm for Higher-Order Differential Equations
- Adaptive Fourier decomposition of functions in quaternionic Hardy spaces
- Aveiro method in reproducing kernel Hilbert spaces under complete dictionary
- ADAPTIVE DECOMPOSITION OF FUNCTIONS INTO PIECES OF NON-NEGATIVE INSTANTANEOUS FREQUENCIES
- Intrinsic mono-component decomposition of functions: An advance of Fourier theory
- Boundary derivatives of the phases of inner and outer functions and applications
- Fourier spectrum characterization of Hardy spaces and applications
- Hilbert transforms and the Cauchy integral in euclidean space
- Fourier Multipliers on Lipschitz Curves
- Convolution Singular Integrals on Lipschitz Surfaces
- Matrix RationalH2Approximation: A Gradient Algorithm Based on Schur Analysis
- The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
- Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves
- Analytic Phase Derivatives, All-Pass Filters and Signals of Minimum Phase
- Algorithm of Adaptive Fourier Decomposition
- A Tighter Uncertainty Principle for Linear Canonical Transform in Terms of Phase Derivative
- Carrier Frequencies, Holomorphy, and Unwinding
- Hardy-Hodge decomposition of vector fields in ℝⁿ
- A Class of Intrinsic Trigonometric Mode Polynomials
- Greedy Algorithms and Rational Approximation in One and Several Variables
- Rational approximation in Hardy spaces on strips
- On a Conjecture of M. S. Robertson
- Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves
- Matching pursuits with time-frequency dictionaries
- Optimal approximation by Blaschke forms
- Two-Dimensional Frequency-Domain System Identification
- Directional quaternionic hilbert operators
- A novel 2D partial unwinding adaptive Fourier decomposition method with application to frequency domain system identification
- 2D Partial Unwinding—A Novel Non-Linear Phase Decomposition of Images
- Reproducing kernel approximation in weighted Bergman spaces: Algorithm and applications
- Adaptive Fourier decomposition‐based Dirac type time‐frequency distribution
- Cyclic AFD algorithm for the best rational approximation
- Rational orthogonal systems are Schauder bases
- Mono‐components for decomposition of signals
- STABILITY OF FRAMES GENERATED BY NONLINEAR FOURIER ATOMS
- Two‐dimensional adaptive Fourier decomposition
- Fourier analysis on starlike Lipschitz surfaces
- Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces
This page was built for publication: A Theory on Non-Constant Frequency Decompositions and Applications
