Frequency-domain identification: An algorithm based on an adaptive rational orthogonal system

Int. J. Wavelets Multiresolut Inf. Process.

2014

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Section: T Qianmentioning

confidence: 99%

Adaptive Fourier decompositions and rational approximations, part I: Theory

Int. J. Wavelets Multiresolut Inf. Process.

2014

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“…These properties distinguish AFD from the traditional studies of TM systems, Downloaded by [New York University] at 07: 12 14 May 2015 as well as from matching pursuit. AFD has found applications in control theory ( [11,12]), as well as theoretical impacts to approximation theory and operator theory. In AFD, the maximal selection principle is performed as | f, B {a 1 ,...,a n } | = sup b∈D | f, B {a 1 ,...,a n−1 ,b} |.…”

Section: Introductionmentioning

confidence: 99%

Approximation of functions by higher order Szegö kernels I. Complex variable cases

Wang

Complex Variables and Elliptic Equations

2014

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We study the adaptive decomposition of functions in the complex Hardy spaces H 2 by higher order Szegö kernels. The purpose is to treat signals that are essentially of high frequencies. We show that each kernel function (basic function) we use is either a mono-component (as an analytic signal, its instantaneous frequency is positive everywhere), or a sum of two orthogonal mono-components. The proposed decomposition thus belongs to the category of adaptive mono-component decomposition.

“…Recently, 1D unwinding adaptive Fourier decomposition (1D‐UAFD) was proposed, which combines maximal selection and Nevanlinna factorization. Among different kinds of rational approximation algorithms,() 1D‐UAFD outperforms the other types in fast signal reconstruction …”

Section: Introductionmentioning

confidence: 99%

A novel 2D partial unwinding adaptive Fourier decomposition method with application to frequency domain system identification

Math Methods in App Sciences

2019

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This paper proposes a two‐dimensional (2D) partial unwinding adaptive Fourier decomposition method to identify 2D system functions. Starting from Coifman in 2000, one‐dimensional (1D) unwinding adaptive Fourier decomposition and later a type called unwinding AFD have been being studied. They are based on the Nevanlinna factorization and a maximal selection. This method provides fast‐converging rational approximations to 1D system functions. However, in the 2D case, there is no genuine unwinding decomposition. This paper proposes a 2D partial unwinding adaptive Fourier decomposition algorithm that is based on algebraic transforms reducing a 2D case to the 1D case. The proposed algorithm enables rational approximations of real coefficients to 2D system functions of real coefficients. Its fast convergence offers efficient system identification. Numerical experiments are provided, and the advantages of the proposed method are demonstrated.