Construction of rational interpolations using Mamquist-Takenaka systems

Rational functions have deep system-theoretic significance. They represent the natural way of modeling linear dynamical systems in frequency (Laplace) domain. Using rational functions, goal this paper to compute models that match (interpolate) given data sets measurements. In paper, authors show using special orthonormal systems, Malmquist-Takenaka it is possible write interpolant $r_{(n, m)}$, for $n=N-1, m=N$ only $N$ sampling nodes (instead $2N$ nodes) if interpolating are complex unit circle or on upper half-plane. Moreover, prove convergence results related interpolant. give an efficient algorithm determination