Continuous positive airway pressure (CPAP) has a caricatural effect in reducing nocturnal respiratory abnormalities and improving the micro-and macrostructure of sleep. Studies characterizing the improvement of acute sleep parameters after the initiation of CPAP are limited to one or two nights of polysomnographic recording. This is related to the cost of performing these studies with repeated recordings in the laboratory and to the acceptability by patients to perform multiple nights of recordings. Investigators currently have powerful and reliable methods allowing us to carry out nights at home in the patient's ecosystem, in real-life conditions. The characterization of sleep parameters by these methods is equivalent to a polysomnographic recording. These technological innovations will allow us to characterize sleep before the initiation of CPAP treatment during several nights performed at home. Investigators will then be able to characterize the kinetics and stability of the improvement of sleep parameters in patients with obstructive sleep apnea syndrome in whom continuous positive airway pressure is initiated. These data will be original and will serve as exploratory data to judge whether the objective improvement of sleep parameters in the first weeks of treatment is associated with improvement in sleepiness, quality of life, and compliance with treatment.