The Experts below are selected from a list of 657 Experts worldwide ranked by ideXlab platform

Wataru Kase - One of the best experts on this subject based on the ideXlab platform.

  • A Simple Derivation of Lower Triangular Interactor Matrix
    2014
    Co-Authors: Wataru Kase
    Abstract:

    An interactor matrix plays several important roles in the control system theory. Recently, we presented a simple method to derive a special interactor matrix using Moore-Penrose Pseudoinverse. But, the structure of the proposed interactor was not specified. A triangular structure of interactor is useful for multivariable adaptive control. In this note, it will be shown a derivation of interactor with lower triangular structure. For this, a property of the interactor which we reported will play an important role. Key Words: interactor matrix, polynomial matrix, lower triangular structure, discrete-time systems, Pseudoinverse

  • a simple derivation of the interactor matrix and its applications
    International Journal of Systems Science, 2009
    Co-Authors: Wataru Kase, Yasuhiko Mutoh
    Abstract:

    An interactor matrix plays several important roles in the control system theory. In this article, we present a simple method to derive a special interactor matrix using Moore-Penrose Pseudoinverse. The interactor by the proposed method has all its zeros at the origin, and has the all-pass property in the discrete-time. A systematic procedure to obtain an identity interactor, which has an lower triangular structure or has arbitrarily prespecified zeros, is also shown.

  • a simple derivation of lower triangular interactor matrix
    International Conference on System Science and Simulation in Engineering, 2005
    Co-Authors: Wataru Kase
    Abstract:

    An interactor matrix plays several important roles in the control system theory. Recently, we presented a simple method to derive a special interactor matrix using Moore-Penrose Pseudoinverse. But, the structure of the proposed interactor was not specified. A triangular structure of interactor is useful for multivariable adaptive control. In this note, it will be shown a derivation of interactor with lower triangular structure. For this, a property of the interactor which we reported will play an important role.

Reza R Adhami - One of the best experts on this subject based on the ideXlab platform.

  • theoretical upperbound of the spurious free dynamic range in direct digital frequency synthesizers realized by polynomial interpolation methods
    IEEE Transactions on Circuits and Systems, 2007
    Co-Authors: Ashkan Ashrafi, Reza R Adhami
    Abstract:

    In this paper, a universal mathematical method is proposed to determine the upperbound of the spurious-free dynamic range (SFDR) in direct digital frequency synthesizers (DDFSs) realized by piecewise polynomial interpolation methods. The Fourier series is used to establish a linear matrix relationship between the frequency spectrum of the interpolated sinusoidal signal and the coefficients of the interpolating polynomials. This matrix relationship can be considered as a linear overdetermined system of equations, which can be solved for the ideal spectrum where the fundamental harmonic has an amplitude of one and the other harmonics are zero. It is shown that the Moore-Penrose Pseudoinverse and Chebyshev minimax methods find the coefficients corresponding to the largest signal-to-noise ratio and maximum SFDR designs, respectively. The proposed method is used to show that the maximum SFDR of a DDFS based on the even fourth-order polynomial interpolation is 74.35 dBc. A DDFS based on the aforementioned method is designed and its architecture is optimized to obtain an SFDR of 72.2 dBc. A VLSI implementation of the proposed DDFS is also reported.

  • Theoretical upperbound of the spuriousfree dynamic range in direct digital frequency synthesizers realized by polynomial interpolation methods
    2007
    Co-Authors: Ashkan Ashrafi, Reza R Adhami, Senior Member
    Abstract:

    Abstract—In this paper, a universal mathematical method is pro-posed to determine the upperbound of the spurious-free dynamic range (SFDR) in direct digital frequency synthesizers (DDFSs) re-alized by piecewise polynomial interpolation methods. The Fourier series is used to establish a linear matrix relationship between the frequency spectrum of the interpolated sinusoidal signal and the co-efficients of the interpolating polynomials. This matrix relationship can be considered as a linear overdetermined system of equations, which can be solved for the ideal spectrum where the fundamental harmonic has an amplitude of one and the other harmonics are zero. It is shown that the Moore–Penrose Pseudoinverse and Chebyshev minimax methods find the coefficients corresponding to the largest signal-to-noise ratio and maximum SFDR designs, respectively. The proposed method is used to show that the maximum SFDR of a DDFS based on the even fourth-order polynomial interpolation is 74.35 dBc. A DDFS based on the aforementioned method is designed and its architecture is optimized to obtain an SFDR of 72.2 dBc. A VLSI implementation of the proposed DDFS is also reported. Index Terms—Chebyshev minimax problem, direct digital frequency synthesizer (DDFS), polynomial interpolation, spurious harmonic analysis. I

Brian J. Mccartin - One of the best experts on this subject based on the ideXlab platform.

  • Pseudoinverse Formulation of Rayleigh-Schrödinger Perturbation Theory for the Symmetric Definite Generalized Eigenvalue Problem
    2015
    Co-Authors: Brian J. Mccartin
    Abstract:

    In this paper, a comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric definite generalized eigenvalue problem [1, 2] is fur-nished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose Pseudoinverse thus constituting the natural generalization of the procedure for the standard symmetric eigenvalue problem [3]. In addition to providing a concise matrix-theoretic formulation of this procedure, it also pro-vides for the explicit determination of that stage of the algorithm where each higher order eigenvector correction becomes fully determined. Along the way, we gen-eralize the Dalgarno-Stewart identities [15] from the standard to the generalized eigenvalue problem. The general procedure is illustrated by an extensive example

  • Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem
    Journal of Applied Mathematics, 2003
    Co-Authors: Brian J. Mccartin
    Abstract:

    A comprehensive treatment of Rayleigh-Schrodinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose Pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix-theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher-order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example.

  • Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem
    Hindawi Limited, 2003
    Co-Authors: Brian J. Mccartin
    Abstract:

    A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose Pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix-theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher-order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example

Ashkan Ashrafi - One of the best experts on this subject based on the ideXlab platform.

  • theoretical upperbound of the spurious free dynamic range in direct digital frequency synthesizers realized by polynomial interpolation methods
    IEEE Transactions on Circuits and Systems, 2007
    Co-Authors: Ashkan Ashrafi, Reza R Adhami
    Abstract:

    In this paper, a universal mathematical method is proposed to determine the upperbound of the spurious-free dynamic range (SFDR) in direct digital frequency synthesizers (DDFSs) realized by piecewise polynomial interpolation methods. The Fourier series is used to establish a linear matrix relationship between the frequency spectrum of the interpolated sinusoidal signal and the coefficients of the interpolating polynomials. This matrix relationship can be considered as a linear overdetermined system of equations, which can be solved for the ideal spectrum where the fundamental harmonic has an amplitude of one and the other harmonics are zero. It is shown that the Moore-Penrose Pseudoinverse and Chebyshev minimax methods find the coefficients corresponding to the largest signal-to-noise ratio and maximum SFDR designs, respectively. The proposed method is used to show that the maximum SFDR of a DDFS based on the even fourth-order polynomial interpolation is 74.35 dBc. A DDFS based on the aforementioned method is designed and its architecture is optimized to obtain an SFDR of 72.2 dBc. A VLSI implementation of the proposed DDFS is also reported.

  • Theoretical upperbound of the spuriousfree dynamic range in direct digital frequency synthesizers realized by polynomial interpolation methods
    2007
    Co-Authors: Ashkan Ashrafi, Reza R Adhami, Senior Member
    Abstract:

    Abstract—In this paper, a universal mathematical method is pro-posed to determine the upperbound of the spurious-free dynamic range (SFDR) in direct digital frequency synthesizers (DDFSs) re-alized by piecewise polynomial interpolation methods. The Fourier series is used to establish a linear matrix relationship between the frequency spectrum of the interpolated sinusoidal signal and the co-efficients of the interpolating polynomials. This matrix relationship can be considered as a linear overdetermined system of equations, which can be solved for the ideal spectrum where the fundamental harmonic has an amplitude of one and the other harmonics are zero. It is shown that the Moore–Penrose Pseudoinverse and Chebyshev minimax methods find the coefficients corresponding to the largest signal-to-noise ratio and maximum SFDR designs, respectively. The proposed method is used to show that the maximum SFDR of a DDFS based on the even fourth-order polynomial interpolation is 74.35 dBc. A DDFS based on the aforementioned method is designed and its architecture is optimized to obtain an SFDR of 72.2 dBc. A VLSI implementation of the proposed DDFS is also reported. Index Terms—Chebyshev minimax problem, direct digital frequency synthesizer (DDFS), polynomial interpolation, spurious harmonic analysis. I

Yasuhiko Mutoh - One of the best experts on this subject based on the ideXlab platform.

  • a simple derivation of the interactor matrix and its applications
    International Journal of Systems Science, 2009
    Co-Authors: Wataru Kase, Yasuhiko Mutoh
    Abstract:

    An interactor matrix plays several important roles in the control system theory. In this article, we present a simple method to derive a special interactor matrix using Moore-Penrose Pseudoinverse. The interactor by the proposed method has all its zeros at the origin, and has the all-pass property in the discrete-time. A systematic procedure to obtain an identity interactor, which has an lower triangular structure or has arbitrarily prespecified zeros, is also shown.