Modern rotating machines rotate faster than before in an attempt to produce more power while reducing weight. Rotating machines are coupled to fluids, electromagnetic forces and varying pressure fields, as a result, complicated vibration patterns can develop. In order to diagnose and understand the physical behavior of such machines, the measured vibrations need to be separated into components that indicate distinct physical phenomena. This paper deals with the separation of several types of vibrations in an attempt to diagnose and decompose the individual phenomena. The simplest decomposition isolates forward and backward whirl of shafts. Instead of performing this task in the frequency domain, in an off-line manner, a real-time decomposition that exploits a phase shifting filter is introduced here. This separation is a valuable tool to determine the isotropy of the supports and blade mistuning. An additional decomposition of the measured response isolates synchronous and non-synchronous vibrations thus highlighting the induced rotating vibrations and those coming from other sources. Yet decomposition adds the spatial dimension to the temporal, sense of whirl and frequency (or order) domains. This is accomplished by measuring along a spatial coordinate. Spatial decomposition can be achieved with an array of sensors or by continuously moving sensors.