This paper addresses the problem of identifying the class of all stable system transfer functions that interpolate the given partial impulse response sequence. In this context, classical Pade approximations that are also stable, are shown to be a special case of this general formulation. The theory developed in this connection is utilized to obtain a new criterion for determining the model order and system parameters for rational systems, and, further, to generate nonminimum phase optimal stable rational approximatinos of nonrational systems from its impulse response sequence.