The authors derive a recursive solution for a general time-variant interpolation problem of the Hermite-Fejer type, based on a fast algorithm for the recursive triangular factorization of time-variant structured matrices. The solution follows from studying the properties of an associated transmission-line. The line can be drawn as a cascade of first-order lattice sections, where each section is composed of a rotation matrix followed by a storage element and a tapped-delay filter. An application of the recursive algorithm to a so-called model validation (or Caratheodory-Fejer) problem is discussed.