Wavelet-Domain Respiratory-Cardiac Decoupling for Wi-Fi CSI Vital Sign Monitoring: A Multi-Resolution Analysis Framework

Wi-Fi Channel State Information (CSI) encodes superimposed respiratory and cardiac micro-movements, yet conventional band-pass filtering suffers from spectral leakage when heart rate harmonics overlap with respiratory frequencies during tachycardia or exercise. This paper proposes a wavelet-domain decoupling framework leveraging multi-resolution analysis (MRA) to separate respiratory (0.2–0.5 Hz) and cardiac (0.8–2.5 Hz) components with enhanced time-frequency localization. We formulate the separation problem as a constrained sparse decomposition over redundant Daubechies-8 and Symlet-6 wavelet dictionaries, and derive optimal reconstruction filters via ℓ1-regularized least squares. Theoretical analysis establishes cross-talk attenuation bounds (>28 dB) under worst case frequency overlap conditions using wavelet coherence metrics. Computational experiments on 50 synthetic CSI traces with physiologically realistic parameter variations (HR: 60–180 BPM, RR: 12–30 BrPM, SNR: 5–20 dB) demonstrate 41% reduction in respiratory-cardiac interference compared to Butterworth filtering, with mean absolute error of 1.2 BrPM for respiration rate and 2.8 BPM for heart rate. The algorithm achieves O(N logN) complexity via Fast Wavelet Transform, enabling real-time processing (<85 ms per 10-second window) on ESP32 microcontrollers without human subject data collection.