The parasympathetic nervous system is necessary to regulate both sleep and digestion. Investigating abnormalities during the controlled setting of sleep can shed light on digestion, specifically for patients with idiopathic gastroparesis. In this study, we specifically investigate heartbeat-derived parasympathetic activity during sleep at very low frequencies, relevant to sleep cycle regulation. To do this, we adapt a method that extracts both periodic and aperiodic information from the power spectral density and recognize that the aperiodic activity may contain information relevant to very low frequencies. After testing on both synthetic noise data (pink and white) and overnight data from seven healthy controls and idiopathic gastroparetics, we find that the healthy controls' low-frequency aperiodic activity reflects pink noise structure, while the majority of the patients' aperiodic activity reflects white noise structure. At these low frequencies, these differences suggest differences in autonomic sleep cycle regulation.Clinical Relevance- This methodology can be optimized to track the health of the parasympathetic nervous system and suggest whether individual disease etiology is autonomic-related.