Sleep is one of the most important body mechanisms responsible for the proper functioning of human body. Cyclic alternating patterns (CAP) play an indispensable role in the analysis of sleep quality and related disorders like nocturnal front lobe epilepsy, insomnia, narcolepsy etc. The traditional manual segregation methods of CAP phases by the medical experts are prone to human fatigue and errors which may lead to inaccurate diagnosis of sleep stages. In this paper, we present an automated approach for the classification of CAP phases (A and B) using Wigner-Ville Distribution (WVD) and Rényi entropy (RE) features. The WVD provides a high-resolution time-frequency analysis of the signals whereas RE provides least time-frequency uncertainty with WVD. The classification is performed using medium Gaussian kernel-based support vector machine with 10-fold cross-validation technique. We have presented the results for randomly sampled balanced data sets. The proposed approach does not require any pre-processing or post-processing stages, making it simple as compared to the existing techniques. The proposed method is able to achieve an average classification accuracy of 72.35% and 87.45% for balanced and unbalanced data sets respectively. The proposed method can aid the medical experts to analyze the cerebral stability as well as the sleep quality of a person.Copyright © 2020 Elsevier Ltd. All rights reserved.