Adaptive Fourier decompositions and rational approximations, part I: Theory

DOI10.1142/S0219691314610086zbMath1304.65283OpenAlexW1997626538MaRDI QIDQ2930112

Tao Qian

Publication date: 18 November 2014

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219691314610086

zbMATH Keywords

surveyHardy spaceuncertainty principlerational approximationtime-frequency distributiondigital signal processingMöbius transformmono-componentrational orthogonal systemBlaschke formadaptive Fourier decompositionClifford algebra settinghigher-dimensional signal analysis in several complex variables

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

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On almost-everywhere convergence of Malmquist-Takenaka series ⋮ Blaschke decompositions on weighted Hardy spaces ⋮ Adaptive orthonormal systems for matrix-valued functions ⋮ A novel image encryption scheme with adaptive Fourier decomposition ⋮ Multi-scale analysis of influencing factors for soybean futures price risk: Adaptive Fourier decomposition mathematical model applied for the case of China

Cites Work

• Frequency-domain identification: An algorithm based on an adaptive rational orthogonal system
• A fast adaptive model reduction method based on Takenaka-Malmquist systems
• Adaptive decomposition by weighted inner functions: a generalization of Fourier series
• Hardy-Sobolev spaces decomposition in signal analysis
• Identification and rational \(L^ 2\) approximation: A gradient algorithm
• Non-uniqueness of rational best approximants
• Comparison of adaptive mono-component decompositions
• Adaptive Fourier series---a variation of greedy algorithm
• Analysis of the intrinsic mode functions
• Adaptive Fourier decomposition of functions in quaternionic Hardy spaces
• Analytic Phase Derivatives, All-Pass Filters and Signals of Minimum Phase
• Algorithm of Adaptive Fourier Decomposition
• Optimal approximation by Blaschke forms
• Cyclic AFD algorithm for the best rational approximation
• Mono‐components for decomposition of signals

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