A Novel Residue Number System-Based Envelope for ECG Shannon Entropy Signals

Abstract

This study presents a novel, computationally efficient approach for ECG envelope extraction using the Residue Number System (RNS), a modular arithmetic framework. By decomposing ECG signals into residue components, the proposed method enables closed-form algebraic envelope estimation without relying on traditional transformations or filtering techniques. Comparative analysis with conventional methods - such as Hilbert, wavelet, and Shannon energy-based envelopes - demonstrates that the RNS approaches achieve superior accuracy and robustness in R-peak detection, particularly under noisy conditions. These results highlight the potential of modular arithmetic for efficient ECG analysis in embedded and wearable health monitoring systems.