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Bilinear Transformation

The Experts below are selected from a list of 264 Experts worldwide ranked by ideXlab platform

Li Xu – 1st expert on this subject based on the ideXlab platform

  • a general state space representation of n variable Bilinear Transformation
    Signal Processing, 2011
    Co-Authors: Natsuko Shiratori, Hsin-jang Shieh, Li Xu

    Abstract:

    This paper proposes a general formulation of the relationship between the state-space representations of a multidimensional (n-D) continuous system and an n-D discrete system which are related by the n-variable Bilinear Transformation such that the state-space representations of these two related systems can be directly calculated from each other. The new formulation is derived based on the theory of linear fractional Transformation (LFT) and the resultant form is simple and concise. Moreover, the relations among the proposed formulation and the existing 1-D and 2-D results are investigated and it turns out that the new formulation includes these existing results as special cases. A numerical example is presented to illustrate the effectiveness of the proposed formulation.

  • ISCAS – State-space formulation of n-variable Bilinear Transformation for n-D systems
    Proceedings of 2010 IEEE International Symposium on Circuits and Systems, 2010
    Co-Authors: Natsuko Shiratori, Hsin-jang Shieh, Li Xu

    Abstract:

    This paper establishes a general relationship between the state-space representations of an n-D continuous system and an n-D discrete system which are related by the n-variable Bilinear Transformation. In particular, a novel and simple formulation will be derived based on the theory of linear fractional Transformation (LFT), by which the state-space representations of an n-D continuous system and an n-D discrete system can be directly calculated from each other such that they are related by the n-variable Bilinear Transformation. Moreover, it will be shown that the obtained formulation includes the existing results for the 1-D and 2-D cases as special cases. A numerical example is presented to illustrate the effectiveness of the proposed formulation.

  • Simple state-space formulations of 2-D frequency Transformation and double Bilinear Transformation
    Multidimensional Systems and Signal Processing, 2010
    Co-Authors: Natsuko Shiratori, Li Xu

    Abstract:

    In this paper, an explicit relationship between the two-dimensional (2-D) frequency Transformation and the theory of linear fractional Transformation (LFT) representation is shown. Based on this relationship, a simple alternative state-space formulation of 2-D frequency Transformation for 2-D digital filters is derived by utilizing the well-known Redheffer star product of LFT representations. The proposed formulation is then utilized to establish a simple relationship between the state-space representations of a 2-D continuous system and a 2-D discrete system which are related by the double Bilinear Transformation. Moreover, the inherent relations among the proposed formulations and the existing results are discussed. It turns out that all the existing results given in the literature can be unified as special or equivalent cases by the new state-space formulation of 2-D frequency Transformation in a very concise and elegant form. Numerical examples are given to illustrate the effectiveness of the proposed formulations.

Natsuko Shiratori – 2nd expert on this subject based on the ideXlab platform

  • a general state space representation of n variable Bilinear Transformation
    Signal Processing, 2011
    Co-Authors: Natsuko Shiratori, Hsin-jang Shieh, Li Xu

    Abstract:

    This paper proposes a general formulation of the relationship between the state-space representations of a multidimensional (n-D) continuous system and an n-D discrete system which are related by the n-variable Bilinear Transformation such that the state-space representations of these two related systems can be directly calculated from each other. The new formulation is derived based on the theory of linear fractional Transformation (LFT) and the resultant form is simple and concise. Moreover, the relations among the proposed formulation and the existing 1-D and 2-D results are investigated and it turns out that the new formulation includes these existing results as special cases. A numerical example is presented to illustrate the effectiveness of the proposed formulation.

  • ISCAS – State-space formulation of n-variable Bilinear Transformation for n-D systems
    Proceedings of 2010 IEEE International Symposium on Circuits and Systems, 2010
    Co-Authors: Natsuko Shiratori, Hsin-jang Shieh, Li Xu

    Abstract:

    This paper establishes a general relationship between the state-space representations of an n-D continuous system and an n-D discrete system which are related by the n-variable Bilinear Transformation. In particular, a novel and simple formulation will be derived based on the theory of linear fractional Transformation (LFT), by which the state-space representations of an n-D continuous system and an n-D discrete system can be directly calculated from each other such that they are related by the n-variable Bilinear Transformation. Moreover, it will be shown that the obtained formulation includes the existing results for the 1-D and 2-D cases as special cases. A numerical example is presented to illustrate the effectiveness of the proposed formulation.

  • Simple state-space formulations of 2-D frequency Transformation and double Bilinear Transformation
    Multidimensional Systems and Signal Processing, 2010
    Co-Authors: Natsuko Shiratori, Li Xu

    Abstract:

    In this paper, an explicit relationship between the two-dimensional (2-D) frequency Transformation and the theory of linear fractional Transformation (LFT) representation is shown. Based on this relationship, a simple alternative state-space formulation of 2-D frequency Transformation for 2-D digital filters is derived by utilizing the well-known Redheffer star product of LFT representations. The proposed formulation is then utilized to establish a simple relationship between the state-space representations of a 2-D continuous system and a 2-D discrete system which are related by the double Bilinear Transformation. Moreover, the inherent relations among the proposed formulations and the existing results are discussed. It turns out that all the existing results given in the literature can be unified as special or equivalent cases by the new state-space formulation of 2-D frequency Transformation in a very concise and elegant form. Numerical examples are given to illustrate the effectiveness of the proposed formulations.

S V S Girija – 3rd expert on this subject based on the ideXlab platform

  • arc tan exponential type distribution induced by stereographic projection Bilinear Transformation on modified wrapped exponential distribution
    Journal of Applied Mathematics Statistics and Informatics, 2013
    Co-Authors: Y Phani, S V S Girija

    Abstract:

    In this paper we make an attempt to construct a new three parameter linear model, we call this new model as Arc Tan-Exponential Type distribution, by applying Stereographic Projection or equivalently Bilinear Transformation on Wrapped Exponential distribution, Probability density and cumulative distribution functions of this new model are presented and their graphs are plotted for various values of parameters. Mathematics Subject Classification 2000: 60E05, 62H11 Additional

  • Arc Tan- Exponential Type Distribution Induced By Stereographic Projection / Bilinear Transformation On Modified Wrapped Exponential Distribution
    Journal of Applied Mathematics Statistics and Informatics, 2013
    Co-Authors: Y Phani, S V S Girija

    Abstract:

    In this paper we make an attempt to construct a new three parameter linear model, we call this new model as Arc Tan-Exponential Type distribution, by applying Stereographic Projection or equivalently Bilinear Transformation on Wrapped Exponential distribution, Probability density and cumulative distribution functions of this new model are presented and their graphs are plotted for various values of parameters. Mathematics Subject Classification 2000: 60E05, 62H11 Additional