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Qian, Tao

Adaptive Fourier decompositions and rational approximations. I: Theory. (English) Zbl 1304.65283

Int. J. Wavelets Multiresolut. Inf. Process. 12, No. 5, Article ID 1461008, 13 p. (2014).
Summary: In this paper, we give a survey on adaptive Fourier decompositions (AFDs) in one- and multi-dimensions. Theoretical formulations of three different types of AFDs in one-dimension, viz., core AFD, cyclic AFD in conjunction with best rational approximation and unwending AFD are provided.

Cited in 1 Review
Cited in 5 Documents

MSC:

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

Keywords:

Möbius transform; Blaschke form; mono-component; Hardy space; adaptive Fourier decomposition; rational approximation; rational orthogonal system; time-frequency distribution; digital signal processing; uncertainty principle; higher-dimensional signal analysis in several complex variables; Clifford algebra setting; survey
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References:

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