Extraction of Fetal ECG by Logarithmic Hyperbolic Secant Adaptive Algorithm in Alpha-Stable Noise

Direct fetal electrocardiogram (FECG) plays a crucial role in assessing fetal health and monitoring pregnancy conditions. Extracting high-quality FECG signals from maternal abdominal electrocardiogram (AECG) recordings remains a significant challenge due to the low amplitude of the FECG, its overlap with the maternal electrocardiogram (MECG), and the potential exposure to impulsive noise in the real world. Adaptive filtering (AF) is an essential method for FECG extraction, however, its performance tends to degrade in the presence of impulsive noise, such as instrument interference. To address this limitation, we propose a novel AF algorithm based on a nonlinear logarithmic hyperbolic secant (LHS) cost function. Alpha-stable distribution is adopted to model the realistic noises due to its high scalability. To further enhance extraction accuracy and optimize the preset parameters, we introduce a hyperbolic tangent-like transformation and develop the improved logarithmic hyperbolic secant adaptive filtering (ILHSAF) algorithm. The proposed approach leverages the approximate linear interval of the LHS function to maximize the preservation of original FECG information within the AECG. We use the synthetic dataset FECGSYN as well as two real datasets, Daisy and NI-FECG, to evaluate the performance and our methods outperform other existing AF algorithms. The ILHSAF algorithm exhibits commendable performance in R-peak detection and full-wave analysis on both real-world datasets, indicating its effective denoising capability and robustness in FECG extraction. This advancement establishes a foundation for long-term maternal and fetal monitoring using portable devices, as the proposed algorithms are capable of real-time operation.