Data Interpolation, Causality Structure, and System Identification

Given a finite set {(x~, Yi)} of ordered pairs from X × Y where X, Y are Hilbert spaces over the same field, there are numerous techniques for constructing a function, f, on X to Y such that f(xi) = y¢ • However, when X, 2" have a causality structure and f must be causal then the data interpolation problem is much more complicated. In this paper two interpolation methods, namely linear interpolation and interpolation via generalized Lagrange poly-nomials are considered. It is shown that these techniques can be modified to accomodate the causality constraint. The development is indicative of the modifications that must be made in any existing data interpolation algorithm if causal interpolation is required.