This paper studies approximation of possibly unstable linear time-invariant infinite-dimensional systems. The system transfer function is assumed to be continuous on the imaginary axis with finitely many poles in the open right half plane. A unified approach is proposed for rational approximations of such infinite-dimensional systems. A procedure is developed for constructing a sequence of finite-dimensional approximants, which converges to the given model in the L infinity norm under a mild frequency domain condition. It is noted that the proposed technique uses only the FFT and singular value decomposition algorithms for obtaining the approximations. Numerical examples are included to illustrate the proposed method.