Behavior of the Kramers-Kronig relation for measurement noise

In this paper the behavior of Kramers-Kronig relation is investigated. In practice measurements are used to calculate the Kramers-Kronig integral. Several integration procedures to solve this integral are discussed in the literature. However, the results of such procedures are often quite sensitive to the form of the measurement noise. It is the aim of this paper to clarify the influence of the measurement noise.