This paper describes a computationally simple method to isolate transient vibration from rotating components whose frequency is tightly linked to rotation and to modes of vibration. The results can be viewed as an enhancement of computed order tracking or amplitude demodulation of multiple crossing frequency terms. By measuring the response with an array of sensors, one can compute the relative, instantaneous phase between different sensors and thus obtain information about the spatial behavior of different components with different wavelengths, frequencies, and traveling directions. An array of sensors would thus exploit spatial information to separate different vibration modes and thus gain deeper insight into the dynamical behavior. The proposed method is suitable for whirling shafts and rotating disk-like structures. It is computationally simple and fast while providing better separation of components than single sensor based approaches, in particular when ordinary methods fail to separate close frequencies. It is demonstrated that through the exploitation of cyclic symmetry of rotating structures and the angular periodicity of the vibration modes, the spectral contents of different modes can be separated. Simulated and measured data demonstrate the merits of the proposed algorithm.