Finitely-Supported ${\rm L}_2$-Optimal Kernels for Digital Signal Interpolation

Interpolation is responsible for digital signal resampling and can significantly degrade the original signal quality if not done properly. For many years, optimal interpolation algorithms were sought within constrained classes of interpolation kernel functions. We derive a new family of unconstrained, finitely supported L
₂
-optimal interpolation kernels
H L
(
x
), and compare their properties to the previously known results. Our research demonstrates that L
₂
-optimal kernels provide superior interpolation quality, and can be efficiently applied to any digital signal, of arbitrary nature, bandwidth, and dimensionality.