Numerical Methods and Computational Algorithms for ECG Signal Processing and Cardiac Abnormality Detection: A Review

Abstract

Electrocardiogram (ECG) signal processing plays a critical role in the early detection and diagnosis of cardiovascular diseases; however, reliable automated interpretation remains challenging due to noise contamination, inter-patient variability, and nonstationary signal characteristics. This review provides a critical and structured analysis of numerical methods and computational algorithms used in ECG signal processing and cardiac abnormality detection. Unlike conventional descriptive surveys, this work emphasizes the comparative evaluation of preprocessing techniques, feature extraction strategies, and machine learning and deep learning models under varying conditions such as noise intensity, dataset size, and realtime deployment constraints. The review systematically examines baseline correction, filtering, wavelet and decomposition-based denoising, fiducial point detection, and feature representation methods, highlighting their computational trade-offs, robustness, and clinical applicability. Furthermore, it critically contrasts classical machine learning approaches with modern deep learning and transformer-based models, identifying scenarios in which each paradigm is most effective. Key limitations of widely used datasets, particularly the MIT-BIH Arrhythmia Database, are analyzed in terms of generalization and evaluation bias. Emerging challenges, including domain shift, annotation inconsistency, interpretability, and deployment in wearable systems, are discussed with concrete research directions such as hybrid modeling, explainable AI, and federated learning. The review concludes that high-performance ECG analysis systems require an integrated pipeline combining numerically stable preprocessing with adaptive and interpretable learning frameworks, rather than reliance on standalone classification models.