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In this paper, bearing fault vibrations are modelled as a series of impulse responses of a single-degree-of-freedom system. The model incorporates slight random variations in the time between pulses so as to resemble actual vibration signals. Although the bearing fault harmonics in the raw spectrum are caused by the random fluctuations to smear over one another, they remain quite clear in the spectrum of the envelope. However, the envelope spectrum is still prone to masking by discrete and random noise. Therefore, the simulated bearing fault signals were used to investigate the efficient application of self-adaptive noise cancellation (SANC) in conjunction with envelope analysis in order to remove discrete frequency masking signals. Two ways of combining these techniques have been suggested, both of which require the original signal to be band-pass filtered and frequency-shifted in order to reduce the …