Evaluation of spline functions for digital filtering problems

Abstract

Methods for the evaluation of spline functions for digital filtering in data processing systems are developed. Basis polynomials of general form and basis discrete orthogonal polynomials are considered. Computations are organized by solving constrained optimization problems. Recurrences for the system of normalized discrete orthogonal polynomials and their derivatives are obtained. The proposed spline functions on discrete orthogonal polynomials reduce the computational cost and approximation errors compared with the case of general polynomials. The results of the statistical simulation of the application of spline functions based on discrete orthogonal polynomials in digital filtering problems are presented.