A proposed Optimized Spline Interpolation

TL;DR

This paper introduces optimized spline functions with compact support that approximate ideal filters by minimizing the least squares error, resulting in superior filtering properties validated through analysis and simulations.

Contribution

It presents a novel method to design compact support spline functions optimized for filter approximation using calculus of variation.

Findings

Optimized splines outperform traditional ones in filter approximation.

Mathematical analysis confirms the optimality of the proposed splines.

Simulation results demonstrate improved filtering performance.

Abstract

The goal of this paper is to design compact support basis spline functions that best approximate a given filter (e.g., an ideal Lowpass filter). The optimum function is found by minimizing the least square problem ($\ell$2 norm of the difference between the desired and the approximated filters) by means of the calculus of variation; more precisely, the introduced splines give optimal filtering properties with respect to their time support interval. Both mathematical analysis and simulation results confirm the superiority of these splines.