Extended discrete approximation minimizing many measures of error simultaneously

Yuichi Kida; Takuro Kida

doi:10.1117/12.364123

30 September 1999 Extended discrete approximation minimizing many measures of error simultaneously

Yuichi Kida, Takuro Kida

Proceedings Volume 3815, Digital Image Recovery and Synthesis IV; (1999) https://doi.org/10.1117/12.364123
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

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 H_m((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 t_n 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).

Citation Download Citation

Yuichi Kida and Takuro Kida "Extended discrete approximation minimizing many measures of error simultaneously", Proc. SPIE 3815, Digital Image Recovery and Synthesis IV, (30 September 1999); https://doi.org/10.1117/12.364123

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