Threshold distribution of equal states for quantitative amplitude fluctuations

Objective. The distribution of equal states (DES) quantifies amplitude fluctuations in biomedical signals. However, under certain conditions, such as a high resolution of data collection or special signal processing techniques, equal states may be very rare, whereupon the DES fails to measure the amplitude fluctuations.Approach. To address this problem, we develop a novel threshold DES (tDES) that measures the distribution of differential states within a threshold. To evaluate the proposed tDES, we first analyze five sets of synthetic signals generated in different frequency bands. We then analyze sleep electroencephalography (EEG) datasets taken from the public PhysioNet.Main results. Synthetic signals and detrend-filtered sleep EEGs have no neighboring equal values; however, tDES can effectively measure the amplitude fluctuations within these data. The tDES of EEG data increases significantly as the sleep stage increases, even with datasets covering very short periods, indicating decreased amplitude fluctuations in sleep EEGs. Generally speaking, the presence of more low-frequency components in a physiological series reflects smaller amplitude fluctuations and larger DES.Significance. The tDES provides a reliable computing method for quantifying amplitude fluctuations, exhibiting the characteristics of conceptual simplicity and computational robustness. Our findings broaden the application of quantitative amplitude fluctuations and contribute to the classification of sleep stages based on EEG data.