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Proceedings Paper

Extended discrete approximation minimizing many measures of error simultaneously
Author(s): Yuichi Kida; Takuro Kida
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Paper Abstract

In this paper, we will present the optimum interpolation functions minimizing various measures of approximation error simultaneously. For an ordinary interpolatory approximation using sample values of a band-limited signal and a FIR filterbank system having analysis filters Hm((omega) ) (m equals 0,1,...,M - 1), we outline necessary formulation for the time-limited interpolation functions (psi) m(t) realizing the optimum approximation in each limited block separately. Further, under some assumptions, we will present analytic or piece-wise analytic interpolation functions (phi) m(t) minimizing various measures of approximation error defined at discrete time samples tn equals n (n equals 0,+/- 1,+/- 2,...). In this discussion, (phi) m(n) are equal to (psi) m(n) (n equals 0,+/- 1,+/- 2,...). Since (phi) m(t) are time-limited, (phi) m(n) vanish outside of the finite set of n. Hence, one can use FIR filters if one wants to realize discrete synthesis filters which impulse responses are (phi) m(n).

Paper Details

Date Published: 30 September 1999
PDF: 12 pages
Proc. SPIE 3815, Digital Image Recovery and Synthesis IV, (30 September 1999); doi: 10.1117/12.364123
Show Author Affiliations
Yuichi Kida, Tokyo Institute of Technology (Japan)
Takuro Kida, Tokyo Institute of Technology (Japan)

Published in SPIE Proceedings Vol. 3815:
Digital Image Recovery and Synthesis IV
Timothy J. Schulz; Paul S. Idell, Editor(s)

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