Differentiation by integration using orthogonal polynomials, a survey (Q420766)

In the first part of the survey the authors give preliminaries on orthogonal polynomials and then a general approximation theorem. They present the contributions of Ciorănescu, Haslam-Jones and Lanczos to this theorem. In the main part, they search the least-squares approximation of this theory, analyzing the discrete case, applications to filters and special case of constant weights. In the last part, they discuss the \(R_\alpha\) and minimum \(R_\infty\) formulas with derivations of the characteristic functions and some examples for filter properties in the frequency domain.