The Experts below are selected from a list of 3942 Experts worldwide ranked by ideXlab platform

Koichi Niijima - One of the best experts on this subject based on the ideXlab platform.

Thomas Trogdon - One of the best experts on this subject based on the ideXlab platform.

  • Rational Approximation, Oscillatory Cauchy Integrals, and Fourier Transforms
    Constructive Approximation, 2016
    Co-Authors: Thomas Trogdon
    Abstract:

    We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are derived using existing theory for trigonometric interpolants. Estimates on the Dirichlet Kernel are used to derive new bounds on the associated interpolation projection operator. Error estimates are desired partially due to a recent formula of the author for the Cauchy integral of a specific class of so-called oscillatory rational functions. Thus, error bounds for the approximation of the Fourier transform and Cauchy integral of oscillatory smooth functions are determined. Finally, the behavior of the differentiation operator is discussed. The analysis here can be seen as an extension of that of Weber (Numer Math 36(2):197–209, 1980 ) and Weideman (Math Comput 64(210):745–745, 1995 ) in a modified basis used by Olver ( 2011 ) that behaves well with respect to function multiplication and differentiation.

  • Rational approximation, oscillatory Cauchy integrals and Fourier transforms
    arXiv: Numerical Analysis, 2014
    Co-Authors: Thomas Trogdon
    Abstract:

    We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric interpolants. Estimates on the Dirichlet Kernel are used to derive new bounds on the associated interpolation projection operator. Error estimates are desired partially due to a recent formula of the author for the Cauchy integral of a specific class of so-called oscillatory rational functions. Thus, error bounds for the approximation of the Fourier transform and Cauchy integral of oscillatory smooth functions are determined. Finally, the behavior of the differentiation operator is discussed. The analysis here can be seen as an extension of that of Weber (1980) and Weideman (1995) in a modified basis used by Olver (2009) that behaves well with respect to function multiplication and differentiation.

Xiufang Feng - One of the best experts on this subject based on the ideXlab platform.

Sergey Tikhonov - One of the best experts on this subject based on the ideXlab platform.

  • Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds
    Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 2016
    Co-Authors: Erlan Nursultanov, Michael Ruzhansky, Sergey Tikhonov
    Abstract:

    In this paper we prove Nikolskii's inequality (also known as the reverse Holder inequality) on general compact Lie groups and on compact homogeneous spaces with the constant interpreted in terms of the eigenvalue counting function of the Laplacian on the space, giving the best constant for certain indices, attained on the Dirichlet Kernel. Consequently, we establish embedding theorems between Besov spaces on compact homogeneous spaces, as well as embeddings between Besov spaces and Wiener and Beurling spaces. We also analyse Triebel-Lizorkin spaces and beta-versions of Wiener and Beurling spaces and their embeddings, and interpolation properties of all these spaces.

  • Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds
    arXiv: Functional Analysis, 2014
    Co-Authors: Erlan Nursultanov, Michael Ruzhansky, Sergey Tikhonov
    Abstract:

    In this paper we prove Nikolskii's inequality on general compact Lie groups and on compact homogeneous spaces with the constant interpreted in terms of the eigenvalue counting function of the Laplacian on the space, giving the best constant for certain indices, attained on the Dirichlet Kernel. Consequently, we establish embedding theorems between Besov spaces on compact homogeneous spaces, as well as embeddings between Besov spaces and Wiener and Beurling spaces. We also analyse Triebel-Lizorkin spaces and $\beta$-versions of Wiener and Beurling spaces and their embeddings, and interpolation properties of all these spaces.

Songling Huang - One of the best experts on this subject based on the ideXlab platform.

  • new measurement algorithm for supraharmonics based on multiple measurement vectors model and orthogonal matching pursuit
    IEEE Transactions on Instrumentation and Measurement, 2019
    Co-Authors: Shuangyong Zhuang, Qing Wang, Wei Zhao, Ren Wang, Songling Huang
    Abstract:

    There are many cases of electromagnetic interference caused by supraharmonics emitted by power electronic equipment. However, there is currently no effective method for measuring supraharmonics. This paper proposes a new supraharmonics high-resolution measurement algorithm based on a multiple measurement vectors (MMVs) compressive sensing (CS) model and an orthogonal matching pursuit (OMP) recovery algorithm. First, by introducing an interpolation factor, based on a spectrum array of multiple discrete Fourier transform coefficient vectors and a Dirichlet Kernel matrix, an MMVs CS model is constructed. Then, by using the jointly sparse property of high-resolution spectrum array, the MMVs CS model is converted into a single-measurement vector CS model. Third, by using an OMP recovery algorithm, the support set of the high-resolution spectrum array is solved. Finally, by using least squares, the high-resolution spectrum array of supraharmonics is obtained. Simulation results and verification of the measured data show that the algorithm proposed in this paper can improve the frequency resolution by an order of magnitude without increasing the observation time, can shorten the calculation time by 100× compared with the single measurement vector compressive sensing-OMP algorithm, and can compute the amplitude and phase of supraharmonics accurately. Meanwhile, the amplitude fluctuation characteristics of supraharmonics can also be analyzed accurately. This algorithm shows a good application prospect in measuring supraharmonics accurately.

  • New Measurement Algorithm for Supraharmonics Based on Multiple Measurement Vectors Model and Orthogonal Matching Pursuit
    IEEE Transactions on Instrumentation and Measurement, 2019
    Co-Authors: Shuangyong Zhuang, Qing Wang, Wei Zhao, Ren Wang, Songling Huang
    Abstract:

    There are many cases of electromagnetic interference caused by supraharmonics emitted by power electronic equipment. However, there is currently no effective method for measuring supraharmonics. This paper proposes a new supraharmonics high-resolution measurement algorithm based on a multiple measurement vectors (MMVs) compressive sensing (CS) model and an orthogonal matching pursuit (OMP) recovery algorithm. First, by introducing an interpolation factor, based on a spectrum array of multiple discrete Fourier transform coefficient vectors and a Dirichlet Kernel matrix, an MMVs CS model is constructed. Then, by using the jointly sparse property of high-resolution spectrum array, the MMVs CS model is converted into a single-measurement vector CS model. Third, by using an OMP recovery algorithm, the support set of the high-resolution spectrum array is solved. Finally, by using least squares, the high-resolution spectrum array of supraharmonics is obtained. Simulation results and verification of the measured data show that the algorithm proposed in this paper can improve the frequency resolution by an order of magnitude without increasing the observation time, can shorten the calculation time by $100\times $ compared with the single measurement vector compressive sensing-OMP algorithm, and can compute the amplitude and phase of supraharmonics accurately. Meanwhile, the amplitude fluctuation characteristics of supraharmonics can also be analyzed accurately. This algorithm shows a good application prospect in measuring supraharmonics accurately.