A new method using autoregressive modelling and pole tracking is proposed to detect cyclical activity within the oxygen saturation signal, SpO2, for subjects with obstructive sleep apnoea (OSA). OSA is a sleep condition whereby the upper airway is obstructed and a cessation in respiration (apnoea) occurs. The three types of detected activity include: apnoea, mix, and normal breathing, where mix, refers to breathing with a low-frequency component. Overall classifications produced by the analysis are in close agreement with expert scoring of the database. Furthermore, the pole-zero analysis method allows, for the first time, the mix sections to be identified automatically.