Interpolation from Lagrange to Holberg
Abstract
As the order 2n tends to infinity Lagrange interpolators of periodically sampled 1D functions converge to the sinc function modulated by two exponentials. One is related to instabilities and the other to Gaussian apodizing. The Hermite interpolation of Lagrange interpolators gives convolutive C(kappa+1)-differentiable Lagrange-Hermite interpolators. Whereas their support has width of order 2n + 2, the active part of their impulse response is width of order square roots of 2n, instead of 2n for Holberg interpolators, which are optimal combinations of Lagrange-Hermite interpolators, and therefore much more efficient. Efficient filters can be derived from these differentiable interpolators, as well as numerical schemes of derivatives at any abscissa.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2000
- Accession Number
- ADP011996
Entities
People
- Michel Leger
Organizations
- French Institute of Petroleum