A novel stretched-compressed exponential low-pass filter and its application to electrocardiogram signal denoising

The study investigates a novel stretched-compressed exponential low-pass (SCELP) filter to denoise electrocardiogram (ECG) signals. As an extension of Gaussian filter and unlike other denoising filters, the SCELP filter utilizes the stretched-compressed exponential function (SCEF) in the convolution kernel, being the Gaussian function its particular case. A MATLAB implementation is provided with a single parameter (β), which allows to modify the filter strength, to increase the signal-to-noise ratio (SNR) and reduce the mean squared error (MSE). The SCELP filter’s advantages over traditional denoising filters (i.e., Gaussian, Mittag–Leffler, and Savitzky-Golay filters) were assessed on 100 ECG signals, 50 normal and 50 abnormal (affected by sleep apnea), provided by the PhysioNet dataset. The SCELP filter’s efficacy in rejecting noise was evaluated as the β parameter varies, quantifying the filters' performance in terms of mean SNR and MSE to determine the optimal β value. The obtained results showed that the SCELP filter's best performances are achieved for β equal to 1.6 (i.e., 16.9508 dB and 13.7574 dB SNR values, and 0.01025 and 0.01178 MSE values for normal and abnormal ECGs, respectively). Furthermore, the SCELP filter was tested on ECG signals with added white noise; compared to Gaussian, Mittag–Leffler, and Savitzky-Golay filters, the SCELP filter yields better performance regarding SNR (16.495 and 14.940 dB) and MSE (0.0106 and 0.0114) values, for normal and abnormal ECGs, respectively, suggesting its applicability for ECG signals' denoising.