A new method for decomposition of vibration signals measured on rotating machinery is presented in this paper. The method uses a signal measured from a number of sensors to decompose the spatial response according to the direction of the progression of motion, the frequency content and the various wavelengths. For the simple case of shaft vibration, two sensors, horizontal and vertical, are used to separate the vibration pattern into forward and backward progressing components. For the case of a rotating disc, more sensors are required to further decompose the response into different wavelengths. This allows one to monitor and to identify potentially dangerous vibration patterns exhibiting large backward components. The method is shown to provide better resolution in the time-frequency (speed of rotation) and spatial domains by separating several, usually overlapping patterns. Several analytical and experimental results demonstrate the usefulness of the proposed method.