Pre-filtering ECG signals using the parabolic moving average to boost denoising performance

Electrocardiogram (ECG) signals are frequently corrupted by different types of noise, including baseline wander, muscle artifacts, and additive Gaussian noise, particularly relevant in wearable and ambulatory monitoring systems. In this paper, we propose a simple and effective pre-smoothing step to enhance the robustness of classical ECG denoising techniques. Specifically, we introduce a Parabolic Moving Average (PMA), that is, a symmetric three-point weighted average with weights (1,4,1)/6, applied as a preliminary smoothing stage before standard filters such as Savitzky–Golay, Median, Butterworth and Second Order Smoothing. The PMA attenuates high-frequency fluctuations while preserving morphological features, with negligible computational cost. Unlike traditional moving averages, the PMA assigns nonuniform parabolic weights, yielding better smoothing with reduced distortion. We validate the approach on three noisy ECG signals, two synthetic and one real, measuring its effectiveness using standard metrics: Mean Squared Error, Signal-to-Noise Ratio, and Percentage Root-Mean-Square Difference. Results in all tested datasets demonstrate that the PMA improves the performance of all denoising filters considered without modifying their internal structure. These findings suggest that a simple pre-smoothing step can significantly improve traditional ECG denoising pipelines.