Proceedings Article | 30 September 1999

Proc. SPIE. 3815, Digital Image Recovery and Synthesis IV

KEYWORDS: Optical filters, Statistical analysis, Argon, Error analysis, Fourier transforms, Finite impulse response filters, Information technology, Thulium, Electronic filtering, Filtering (signal processing)

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<SUB>m</SUB>((omega) ) (m equals 0,1,...,M - 1), we outline necessary formulation for the time-limited interpolation functions (psi) <SUB>m</SUB>(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) <SUB>m</SUB>(t) minimizing various measures of approximation error defined at discrete time samples t<SUB>n</SUB> equals n (n equals 0,+/- 1,+/- 2,...). In this discussion, (phi) <SUB>m</SUB>(n) are equal to (psi) <SUB>m</SUB>(n) (n equals 0,+/- 1,+/- 2,...). Since (phi) <SUB>m</SUB>(t) are time-limited, (phi) <SUB>m</SUB>(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) <SUB>m</SUB>(n).