Computation method of Sampling Bases for the State Functional Spaces with Input Signals Composed of Spline Functions

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  • Nakamura Koji
    Center for Tsukuba Advanced Research Alliance, University of Tsukuba
  • Kawabe Tohru
    Graduate School of System and Information Engineering, University of Tsukuba
  • Toraichi Kazuo
    Center for Tsukuba Advanced Research Alliance, University of Tsukuba
  • Katagishi Kazuki
    Graduate School of System and Information Engineering, University of Tsukuba
  • Sha Guangyi
    Doctoral Program in System and Infromation Engineering, University of Tsukuba

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  • スプライン関数で表される入力信号をもつ状態関数空間の標本化基底の導出
  • スプライン カンスウ デ アラワサレル ニュウリョク シンゴウ オ モツ ジョウタイ カンスウ クウカン ノ ヒョウホンカ キテイ ノ ドウシュツ

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Abstract

A continuous-time signal in the real world must be approximated within a discrete-time signal space for processing in digital devices in many actual engineering applications. One of the effective discrete approximation methods is to employ signals composed of the spline functions. In order to use such signals effectively, however, the sampling bases of such signal spaces play an important role in signal processing. On the other hand, recently, it becomes commonplace to use digital controllers in control engineering field. Therefore, it is important to assume input signals be composed of piecewise polynomials in the state functional spaces. The existence of sampling bases in the state functional spaces had been shown in previous research conducted by the authors. Therefore, in this paper, a computation method of sampling bases in the state functional spaces by using spline functions of general degrees is proposed. Furthermore, the sampling bases composed by spline functions of 2nd and 3rd degrees are concretely calculated as practical examples.

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