Approximate Hermite Interpolations for Compactly Supported Linear Canonical Transforms

Abstract

There has been several Lagrange and Hermite type interpolations of entire functions whose linear canonical transforms have compact supports in $ℝ$ . There interpolation representations are called sampling theorems for band-limited signals in signal analysis. The truncation, amplitude, and jitter errors associated with the Lagrange type interpolations are investigated rigorously. Nevertheless, the amplitude and jitter errors arising from perturbing samples and nodes are not studied before. The aim of this work is to establish rigorous analysis of their types of perturbation errors, which is important from both practical and theoretical points of view. We derive precise estimates for both types of errors and expose various numerical examples.