Abstract There are many defects in rotating machines which, when analysed by means of the Fourier spectrum of transversal vibration, show several harmonics of the rotational speed, more specifically the first and the second, although higher harmonics may also be present. Misalignments, looseness, the breakage of fastening screws, broken mechanical seals, are just some of the problems. Nevertheless, the effects of some of these defects differ when the angular vibration is measured using an incremental rotating encoder, which offers an additional aid for diagnosing the problem. In this paper, we analyse the characteristics measurements made of the angular vibrations by means of an incremental rotating encoder, in cases of a parallel misalignment between coupled shafts. The spectral frequency lines obtained from the pulse signal generated by the encoder show a series of equidistant lateral bands around the main frequency, which reveals the existence of a specific angular vibration and, therefore, the frequency modulation produced. The phenomenon is explained using the Bessel functions, which establishes a relationship between the frequency spectrum of the angular vibration and the modulated signal from the encoder. The spectral analysis of the pulsating signal of the encoder displays a set of main lines, which are multiples of the main frequency of the pulses, and a set of sidebands around each one of these spectral lines. The method proposed is verified by means of measurements made on laboratory test benches and on industrial equipment, comparing and analysing the angular vibrations, which are measured using a laser interferometer and incremental encoders.