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

概要

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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.
2004-10-01