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Theory of the Optimum Interpolation Approximation in a ShiftInvariant Wavelet and Scaling Subspace
Yuichi KIDA Takuro KIDA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E90A
No.9
pp.18851903 Publication Date: 2007/09/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e90a.9.1885
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Digital Signal Processing Keyword: digital signal processing, the optimum interpolation, filter banks, wavelet subspace,
Full Text: PDF>>
Summary:
In the main part of this paper, we present a systematic discussion for the optimum interpolation approximation in a shiftinvariant 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 worstcase 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 socalled initial problem in wavelet theory.

