ADDITIVE VS ADDITIVE–MULTIPLICATIVE MODELS FOR NONINVASIVE FETAL ELECTROCARDIOGRAPHY: CASCADE EXTRACTION METHODS AND NOISE ROBUSTNESS

Abstract

Transcutaneous fetal electrocardiogram (ECG) recording is considered a task of separating components in a mixed abdominal signal containing maternal ECG (MECG), fetal ECG (FECG), and noise. The article systematically compares two formulations – additive (linear superposition) and additive-multiplicative – in the time and frequency domains, including parameter identification and component separation procedures, as well as the assessment of resistance to typical interference and recording artifacts. It is shown that for most practical scenarios, an additive model with a processing cascade is adequate: zero-phase band filtering and amplitude normalization; adaptive suppression of the maternal component (LMS/RLS in the presence of a chest reference or ICA for multichannel recordings); local isolation of informative details using wavelet and multiresolution analysis (CWT/DWT, MRA); final refinement by weighted least squares. When cross-terms cause combinatorial frequencies, it is advisable to switch to an additive-multiplicative model, detecting nonlinearities through bispectral analysis and selectively suppressing them in the time-frequency representation.If spectral power estimates are available, a Wiener filter is effective. Quality is assessed by SNR, relative reproduction error (RRE), and QRS detection metrics (sensitivity, positive predictive value). The proposed cascade scheme minimizes overfiltering, preserves QRS morphology, and increases noise immunity to isoline drift, network interference, motion/ contact, and myogenic artifacts.