There have been many studies on analysis and control of time delay systems.Mapping or digitization methods have been a dominant approach for analyzing time delay systems.Recently.we proposed a continuous time approximation approach to develop a finite dimensional continuous time system to approximate the infinite dimensional time delay system.The continuous time approximation proposes to represent the delayed response by a set of differential operators, and can indeed predict the response of the time delay system accurately in time domain.However.it cannot capture the spectral properties of the time delay system in terms of poles and zeros.