Complex-Valued Transform Methods in ECG Signal Processing: A Review of Spectral Analysis, Filtering, and Arrhythmia Detection

Abstract

Electrocardiogram (ECG) signal processing is critical in biomedical engineering for monitoring cardiac health and diagnosing cardiovascular diseases. However, conventional real-valued methods often limit the representation of dynamic phase information, and most existing literature focuses narrowly on classification performance rather than the sequential mathematical workflow. To address this problem, this study provides a comprehensive, sequential analysis of complex-valued transform methods to enhance diagnostic representation. This study employed a focused narrative review method analyzing 12 primary studies published between 2019 and 2024, retrieved systematically from the Scopus, IEEE Xplore, and PubMed databases based on strict inclusion criteria. The findings indicate that complex numbers play a fundamental role in representing ECG signals through Fourier and wavelet transforms, enabling a comprehensive analysis of magnitude and phase. Analytical findings reveal that while the Fourier transform is highly effective for global spectral analysis and stationary noise filtering, the complex wavelet transform provides superior mathematical robustness in preserving non-stationary phase features during dynamic cardiac events. Furthermore, integrating complex-domain feature extraction with neural networks yields a quantitative accuracy improvement of 5–15% in automated arrhythmia identification. The main contribution of this review is bridging the gap between abstract mathematical concepts and practical engineering applications. Ultimately, this review establishes that complex numbers serve as a vital foundation for adaptive cardiac diagnosis systems, offering actionable insights for the development of future lightweight, real-time monitoring devices.