Theory of the Optimum Interpolation Approximation in a Shift-Invariant Wavelet and Scaling Subspace(Digital Signal Processing)

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概要

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• In the main part of this paper, we present a systematic discussion for the optimum interpolation approximation in a shift-invariant wavelet and/or scaling subspace. In this paper, we suppose that signals are expressed as linear combinations of a large number of base functions having unknown coefficients. Under this assumption, we consider a problem of approximating these linear combinations of higher degree by using a smaller number of sample values. Hence, error of approximation happens in most cases. The presented approximation minimizes various worst-case measures of approximation error at the same time among all the linear and the nonlinear approximations under the same conditions. The presented approximation is quite flexible in choosing the sampling interval. The presented approximation uses a finite number of sample values and satisfies two conditions for the optimum approximation presented in this paper. The optimum approximation presented in this paper uses sample values of signal directly. Hence, the presented result is independent from the so-called initial problem in wavelet theory.

• 社団法人電子情報通信学会の論文
• 2007-09-01

著者

• Kida Takuro

  Department of Electrical and Electronics Engineering Nihon University

• Kida Takuro

  Department Of Ee Nihon University

• Kida Yuichi

  School Of Pharmaceutical Sciences Ohu University

• Kida Takuro

  Department Of Ee Eng. Nihon University

• KIDA Yuichi

  School of Pharmaceutical Sciences, Ohu University

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