We describe a method for the online classification of sleep/wake states based on cardiorespiratory signals produced by wearable sensors. The method was conceived in view of its applicability to a wearable sleepiness monitoring device. The method uses a fast Fourier transform as the main feature extraction tool and a feedforward artificial neural network as a classifier. We show that when the method is applied to data collected from a single young male adult, the system can correctly classify, on average, 95.4% of unseen data from the same user. When the method is applied to classify data from multiple users with the same age and gender, its accuracy is reduced to 85.3%. However, receiver operating characteristic analysis shows that compared to actigraphy, the proposed method produces a more balanced correct classification of sleep and wake periods. Additionally, by adjusting the classification threshold of the neural classifier, 86.7% of correct classification is obtained.