ABSTRACT The spectrum of atmospheric motions is vast, encompassing phenomena having periods ranging from seconds to millennia. The motions of interest to the forecaster have timescales greater than a day, but the mathematical models used for numerical prediction describe a broader span of dynamical features than those of direct concern. For many purposes these higher frequency components can be regarded as {\it noise} contaminating the motions of meteorological interest. The elimination of this noise is achieved by adjustment of the initial fields, a process called {\it initialization}. In this chapter, the fundamental equations are examined and the causes of spurious oscillations are elucidated. The history of methods of eliminating high-frequency noise is recounted and various initialization methods are described. The normal mode initialization method is described, and illustrated by application to a simple mechanical system, the swinging spring.