A Closed-Form Description for the Continuous Frequency Response of Lagrange Interpolators

In this letter, we present a closed formula for the continuous frequency response of Lagrange interpolators. The continuous frequency response is one of the most useful characterizations of an interpolation system. The proposed formula holds for arbitrary interpolation orders and enables efficient and numerically stable evaluation. Until now, several properties of Lagrange interpolators such as zero locations were described only empirically. Due the concise form of the proposed formula, these properties can now be characterized in an exact way.