A new time-domain model of precise-clock noise

According to the power-law model presented by J.A. Barnes et al. in 1971, it is known that the precise-clock noise can be regarded as the sum of five independent noise components. However, it is difficult to describe these noise components (especially flicker noise) clearly in time-domain, as the time-domain relationship between the noise component and other familiar random process such as white noise, is not known. In this paper, the concept of a half-integrating operator is defined. With this operator, the time-domain relationship between the noise part and white noise can be established. A new time-domain model of precise-clock noise, i.e., the half-integrating/half-differentiating operator model is described. This new time-domain model is equivalent to the power-law model, but it can be used to describe in time-domain all five noise components at their own layers. It can be also used as a strong mathematical tool to simulate, analyze, and process the precise-clock noise. A method for simulation of the precise-clock noise is presented and the time-domain property of the precise-clock noise is discussed. The separation (according to noise component) of the precise-clock noise is very important for optimal precise-clocks synthesis and optimal precise-clock prediction.