30 September 1999 Extended discrete approximation minimizing many measures of error simultaneously
Author Affiliations +
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).
© (1999) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Yuichi Kida, Takuro Kida, "Extended discrete approximation minimizing many measures of error simultaneously", Proc. SPIE 3815, Digital Image Recovery and Synthesis IV, (30 September 1999); doi: 10.1117/12.364123; https://doi.org/10.1117/12.364123
PROCEEDINGS
12 PAGES


SHARE
Back to Top