Abstract Varying speed machinery monitoring is fraught with difficulties due to non-stationary machine dynamics and vibrations. Most conventional signal processing methods based on digital sampling carried out in equal time intervals become inappropriate when monitoring the vibrations of varying speed machinery. Parts I and II of this paper present a new data acquisition technique which pre-processes varying speed signals so that conventional signal processing methods can be applied. It is based on the application of recursive filtering and angle domain analysis to non-stationary vibration analysis. The present paper, Part I, is primarily concerned with the recursive filtering technique. It is shown that the recursive filtering can be used as an effective and reliable method of pre-conditioning the original vibration signals. The theoretical background and some basic properties of the non-stationary recursive filtering approach are described. The approach is implemented and validated using computer simulation and experiments.