The gold standard for assessment of sleep quality is the polysomnography, where physiological signals are used to generate both quantitative and qualitative measurements. Despite the production of highly accurate results, polysomnography is a complex, uncomfortable, and expensive process, inaccessible to a large group of the population. Home monitoring devices were developed to address these issues, fitting the growing perspective of health care and focusing on prevention and wellness. The objective of this paper was to develop an algorithm capable of estimating the quality of sleep, by analyzing the cyclic alternating pattern rate. The algorithm uses a single-lead electrocardiogram to produce a spectrographic measure of the cardiopulmonary coupling that in turn was fed to a classifier to estimate the non-rapid eye movement sleep and the presence of the cyclic alternating pattern. Two classifiers were tested, a feedforward neural network and a deeply stacked autoencoder, with the second achieving better results, correctly classifying 77% of the subjects sleep quality (either good or bad). The developed method can be implemented in a home monitoring device to estimate the sleep quality in a non-invasive way and improve the detection of pathologies.