Interferometric optical fibre sensors have proved to be many orders of magnitude more sensitive than their electrical counterparts, but they suffer from limitations in signal demodulation caused by phase ambiguity and complex fringe counting when the output phase difference exceeds one fringe period and for multiple fringes. This paper presents a novel signal decoding technique based on the wavelet transform of optical data extracted from a non-contact vibration sensor using an extrinsic Fabry–Perot interferometer (EFPI) implemented using single-mode fibre. The EFPI cavity has been used to generate an optical interference signal between two parallel, highly reflective surfaces separated by a variable distance. Firstly, a few recorded experimental results of the interference fringe formation due to vibration are presented in this paper. Then the wavelet transform is used for decoding the vibration signature for three major purposes of the data analyses, namely elimination of noise from the optical signals collected in real time, identification of the frequency breakdown points of the signal efficiently and automatic counting of the interference fringes. In turn, the wavelet transform is successfully employed to decode the vibration signature from the non-stationary output signal of an EFPI sensor.