Effects of Tau and Sampling Frequency on the Regularity Analysis of ECG and EEG Signals Using ApEn and SampEn Entropy Estimators

Abstract

Electrocardiography (ECG) and electroencephalography (EEG) signals provide clinical information relevant to determine a patient’s health status. The nonlinear analysis of ECG and EEG signals allows for discovering characteristics that could not be found with traditional methods based on amplitude and frequency. Approximate entropy (ApEn) and sampling entropy (SampEn) are nonlinear data analysis algorithms that measure the data’s regularity, and these are used to classify different electrophysiological signals as normal or pathological. Entropy calculation requires setting the parameters r (tolerance threshold), m (immersion dimension), and τ (time delay), with the last one being related to how the time series is downsampled. In this study, we showed the dependence of ApEn and SampEn on different values of τ, for ECG and EEG signals with different sampling frequencies (Fs), extracted from a digital repository. We considered four values of Fs (128, 256, 384, and 512 Hz for the ECG signals, and 160, 320, 480, and 640 Hz for the EEG signals) and five values of τ (from 1 to 5). We performed parametric and nonparametric statistical tests to confirm that the groups of normal and pathological ECG and EEG signals were significantly different (p < 0.05) for each F and τ value. The separation between the entropy values of regular and irregular signals was variable, demonstrating the dependence of ApEn and SampEn with Fs and τ. For ECG signals, the separation between the conditions was more robust when using SampEn, the lowest value of Fs, and τ larger than 1. For EEG signals, the separation between the conditions was more robust when using SampEn with large values of Fs and τ larger than 1. Therefore, adjusting τ may be convenient for signals that were acquired with different Fs to ensure a reliable clinical classification. Furthermore, it is useful to set τ to values larger than 1 to reduce the computational cost.

On Quantization Errors in Approximate and Sample Entropy

“…In [ 31 ], SampEn was estimated from source signals (hip, knee, and jump angle in the sagittal plane), reporting that an increase in sampling frequency significantly reduced SampEn . Similar results are shown in [ 32 ] (box-plots), representing the SampEn of the original ECG and EEG signals. The tables in [ 33 ] show the same SampEn reduction with sampling frequency, where SampEn was applied to the main atrial wave (MAV) waveforms derived from the original ECG signal and then upsampled or downsampled to mimic different sampling frequencies.…”

Time Latency-Centric Signal Processing: A Perspective of Smart Manufacturing

“…The HHT acquires spindle power and vibration signals at a sampling frequency of 67 Hz and 10 kHz, respectively, and analyzes them. Espinosa et al [11] articulated that traditional frequency analysis is not effective for unfolding the characteristics of non-linear signals, compared to the alternative analytics such as Approximate Entropy (ApEn) and Sampling Entropy (SampEn). Bayma et al [29] proposed a Non-linear Output Frequency Response Functions (NOFRFs)-based approach for analyzing non-linear systems from the contexts of condition monitoring, fault diagnosis, and non-linear modal analysis.…”

“…The signals are generally processed in the time [5], frequency [6][7][8], and time-frequency [5,6,9] domains to extract the underlying features. In some cases, alternative processing methods, such as fractal-based [10], Approximate Entropy (ApEn)-based, and Sampling Entropy (SampEn)-based [11] methods, are used. Subsequently, the most relevant features are then selected using some computational arrangements (e.g., Principal Components Analysis (PCA) [12]).…”

“…These algorithms become the core of an intelligent monitoring system. However, the conventional signal processing methods (time, frequency, and timefrequency domain-based processing) require high data acquisition rates [13] and cannot mimic the dynamics underlying the signals [11]. Now, complex communication networks underlying smart manufacturing entail a phenomenon called time latency (also known as time delay) [14,15], which results in a low data acquisition rate.…”

“…Section 2 presents a literature review on sensor signal processing methods for machine-and process-condition monitoring. Section 3 presents the significances of the delay domain-based signal processing since the delay domain directly incorporates time latency associated However, the conventional signal processing methods (time, frequency, and timefrequency domain-based processing) require high data acquisition rates [13] and cannot mimic the dynamics underlying the signals [11]. Now, complex communication networks underlying smart manufacturing entail a phenomenon called time latency (also known as time delay) [14,15], which results in a low data acquisition rate.…”