Design of a Low-Latency sEMG Real-Time Correction System Based on High CMRR and EMRMS Mathematical Modeling
Surface electromyography (sEMG) interfaces require interference-resistant acquisition, faithful preprocessing, and a responsive envelope for downstream control. This work presents a reproducible, analog-aware digital conditioning pipeline comprising an eighth-order Butterworth band-pass, a narrow static notch, a recursive-oscillator two-harmonic normalised least-mean-squares (NLMS) canceller, a rolling mains-frequency tracker, and an exponentially weighted RMS (EMRMS) envelope. The analog common-mode analysis is separated into a complex frequency-domain decomposition and a scalar CMRR sensitivity screen; the latter is explicitly treated as a pre-prototype approximation rather than a substitute for circuit simulation or bench measurement. A running-sum rectangular RMS requires O(1) arithmetic and O(L) memory, whereas EMRMS requires O(1) arithmetic and one dynamic power state. At fs = 2 kHz and{tau} = 25 ms, the EMRMS power smoother has a weight-centroid delay of 24.75 ms and a noise-equivalent rectangular length of 100.0 samples. In a controlled drifting-line experiment, the tracker achieved an RMSE of 0.118 Hz; tracked two-harmonic cancellation improved whole-record reconstruction SNR by approximately 19.3 dB relative to the static-notch baseline. In a separate 12-channel synthetic ablation, median reconstruction SNR was 11.5 dB for tracked harmonic cancellation, compared with 8.8 dB for fixed-frequency harmonic cancellation and -11.2 dB for the static-notch baseline. Delay-aligned EMRMS and length-200 running-RMS envelopes had correlation{rho} = 0.994. The host-Python fast path required a median of 13.0 {micro}s per sample and a 99th percentile of 24.9 {micro}s; accepted frequency updates required a median of 161 {micro}s and should be scheduled as a supervisory task on embedded hardware. All numerical performance results reported here are controlled synthetic experiments. The accompanying real-data workflow never substitutes generated data when recordings are absent; multi-subject and embedded-hardware validation remain future work.