Design of High-Pass and Low-Pass Active Inverse Filters to Compensate for Distortions in RC-Filtered Electrocardiograms

Distortions of electrocardiograms (ECGs) caused by mandatory high-pass and low-pass analog RC filters in ECG devices are always present. The fidelity of the ECG waveform requires limiting the RC cutoff frequencies of the diagnostic (0.05–150 Hz) and monitoring systems (0.5–40 Hz). However, the use of fixed frequency bands is a compromise between enhanced noise immunity and ECG distortions. This study aims to propose active inverse high-pass and low-pass filters which are able to compensate for distortions in digital recordings of RC-filtered ECGs, thereby overcoming the limitations imposed by analog filtering. A new straightforward design of an inverse high-pass filter (IHPF) uses an integrator as the forward-path gain block, with a feedback loop containing an active digital filter equivalent to the analog RC high-pass filter. In contrast, the inverse low-pass filter (ILPF) employs a constant-gain block in the forward path to ensure stability and prevent phase delay, while its feedback path features an active digital counterpart of the RC low-pass filter. Second-order inverse filters are created by cascading two first-order stages. The proposed filters were validated according to essential performance requirements for electrocardiographs. The low-frequency (impulse) responses of IHPFs with cutoff frequencies of 0.05–5 Hz exhibit no overshoot and undershoot by magnitudes of 0.1–25 µV, well within the ±100 µV compliance limit defined for a test rectangular pulse (3 mV, 100 ms). The high-frequency responses of ILPFs with cutoff frequencies of 10–150 Hz present a relative amplitude drop of only 0.2–2.5%, far below the 10% limit for peak amplitude reduction of a triangular pulse (1.5 mV) with 20 ms vs. 200 ms widths. For any of the eight ECG leads (I, II, and V1–V6) available in the standard signal (ANE20000), the IHPF (0.05–5 Hz) presents ST-segment deviations <5 μV (within the ±25 μV limit) and R- and S-peak deviations <±3.5% (within the ±5% limit). The ILPF (10–150 Hz) preserves R- and S-peak amplitudes with deviations less than −1%. Diagnostic-level recovery of ECG waveforms distorted by first- and second-order analog RC filters in ECG devices is possible with the innovative and comprehensive inverse filter design presented in this study. This approach offers a significant advancement in ECG signal processing, effectively restoring essential waveform components even after aggressive, noise-robust analog filtering in ECG acquisition circuits. Although validated for ECG signals, the proposed inverse filters are also applicable to other biosignal front-end circuits employing RC coupling.