Cyclic AFD algorithm for the best rational approximation

Qian, Tao

doi:10.1002/mma.2843

Cited by 49 publications

(58 citation statements)

References 16 publications

(55 reference statements)

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“…They proved the existence of the minimizer in cyclic AFD and proposed an algorithm for its construction. Applying the similar derivation as in , Theorem 5], we prove the existence of the minimizer in BAA. Theorem Let

F \in {boldH}^{2} (double-struckU)

and N be a fixed positive integer, and then there exist b * , c * ∈[−1,1] obeying | b * c * |≠1 such that Eq.…”

Section: Best Approximation Algorithm Based On Mono‐componentsmentioning

confidence: 96%

“…In , Qian et al studied the cyclic AFD, which is a practical algorithm of best rational approximation of a given order to a function in the Hardy space. They proved the existence of the minimizer in cyclic AFD and proposed an algorithm for its construction.…”

Section: Best Approximation Algorithm Based On Mono‐componentsmentioning

confidence: 99%

“…Fast convergence of adaptive Fourier decomposition (AFD), in both the energy and the pointwise sense, is verified by experiments. In , the authors proposed a practical algorithm of the best approximation to signals in the Hardy space by rational functions of degree less than a prescribed positive integer. The algorithm is called cyclic AFD as it adaptively selects one parameter during each cycle based on the maximal selection principle used in AFD.…”

Section: Introductionmentioning

confidence: 99%

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Best two‐parameter rational approximation algorithm of given order: a variation of adaptive Fourier decomposition

Huang

Tan

Yang

2014

Math Methods in App Sciences

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The concept of mono-component is widely used in nonstationary signal processing and time-frequency analysis. In this paper, we construct several classes of complete rational function systems in the Hardy space, whose boundary values are mono-components. Then, we propose a best approximation algorithm (BAA) based on optimal selections of two parameters in the orthonormal bases according to the approximation error. Effectiveness of BAA is evaluated by comparison experiments with the classical Fourier decomposition algorithm. It is also shown that BAA has promising results for filtering out noises and dealing with real-world signals.

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F \in {boldH}^{2} (double-struckU)

and N be a fixed positive integer, and then there exist b * , c * ∈[−1,1] obeying | b * c * |≠1 such that Eq.…”

Section: Best Approximation Algorithm Based On Mono‐componentsmentioning

confidence: 96%

Section: Best Approximation Algorithm Based On Mono‐componentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Best two‐parameter rational approximation algorithm of given order: a variation of adaptive Fourier decomposition

Huang

Tan

Yang

2014

Math Methods in App Sciences

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“…Not rigorously speaking, the set of all the IMFs can be regarded as the dictionary for EMD since signals can be decomposed into IMFs with EMD. As an important theoretic contribution in this field, several types of AFD (adaptive Fourier decomposition) were proposed recently, which employ the functions in the Takenaka-Malmquist system as the dictionary [25], [21], [22], [18]. Different frame or dictionary provides different decomposition, which characterizes the signal from different aspect.…”

Section: Applications To Time-frequency Analysismentioning

confidence: 99%

<formula formulatype="inline"><tex Notation="TeX">$\epsilon$</tex> </formula>-Mono-Component: Its Characterization and Construction

Huang

Yang

2015

IEEE Trans. Signal Process.

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This paper studies the consistency between the analytic amplitude and the physical amplitude for a mono-component of the form . A special class of mono-components, called -mono-components, are considered and a parameter is introduced to measure the consistency between these two kinds of amplitudes. It is shown that controls the number of zerocrossings of within each monotonic interval of , which means that the oscillation of the analytic amplitude is much slower than that of the phase part at any instant, provided that is sufficiently small. Some sufficient conditions, including the Fourier spectral characterization, for to be an -mono-component are given. Frames and Riesz bases composed of -mono-components are constructed. Finally, applications of -mono-components to signal decomposition and time-frequency analysis are discussed.Index Terms-Mono-component, analytic signal, analytic amplitude, instantaneous frequency, Hardy space.

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“…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

Qian

2019

Math Methods in App Sciences

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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.

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Cyclic AFD algorithm for the best rational approximation

Cited by 49 publications

References 16 publications

Best two‐parameter rational approximation algorithm of given order: a variation of adaptive Fourier decomposition

Best two‐parameter rational approximation algorithm of given order: a variation of adaptive Fourier decomposition

<formula formulatype="inline"><tex Notation="TeX">$\epsilon$</tex> </formula>-Mono-Component: Its Characterization and Construction

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

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