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