ECG-TEM: Time-based sub-Nyquist sampling for ECG signal reconstruction and Hardware Prototype

Portable heart rate monitoring (HRM) systems based on electrocardiograms (ECGs) have become increasingly crucial for preventing lifestyle diseases. For such portable systems, minimizing power consumption and sampling rate is critical due to the substantial data generated during long-term ECG monitoring. The variable pulse-width finite rate of innovation (VPW-FRI) framework provides an effective solution for low-rate sampling and compression of ECG signals. We develop a time-based sub-Nyquist sampling and reconstruction method for ECG signals specifically designed for HRM applications. Our approach harnesses the integrate-and-fire time-encoding machine (IF-TEM) as a power-efficient, time-based, asynchronous sampler, generating a sequence of time instants without the need for a global clock. The ECG signal is represented as a linear combination of VPW-FRI pulses, which is then subjected to pre-filtering before being sampled by the IF-TEM sampler. A compactly supported robust filter with a frequency-domain alias cancellation condition is used to combat the effects of noise. Our reconstruction process involves consecutive partial summations of discrete representations of the input signal derived from the series of time encodings, further enhancing the accuracy of the reconstructed ECG signals. Additionally, we introduce an IF-TEM sampling hardware system for ECG signals, implemented using an analog filter device. The firing rate is 42-80Hz, equivalent to approximately 0.025-0.05 of the Nyquist rate. Our hardware validation bridges the gap between theory and practice and demonstrates the robust performance and practical applicability of our approach in accurately monitoring heart rates and reconstructing ECG signals.

Hardware Prototype of a Time-Encoding Sub-Nyquist ADC

Analog-to-digital converters (ADCs) are key components of digital signal processing. Classical samplers in this framework are controlled by a global clock. At high sampling rates, clocks are expensive and power-hungry, thus increasing the cost and energy consumption of ADCs. It is, therefore, desirable to sample using a clock-less ADC at the lowest possible rate. An integrate-and-fire time-encoding machine (IF-TEM) is a time-based power-efficient asynchronous design that is not synced to a global clock. Finite-rate-of-innovation (FRI) signals, ubiquitous in various applications, have fewer degrees of freedom than the signal's Nyquist rate, enabling sub-Nyquist sampling signal models. This work proposes a power-efficient IF-TEM ADC architecture and demonstrates sub-Nyquist sampling and FRI signal recovery. Using an IF-TEM, we implement in hardware the first sub-Nyquist time-based sampler. We offer a feasible approach for accurately estimating the FRI parameters from IF-TEM data. The suggested hardware and reconstruction approach retrieves FRI parameters with an error of up to -25dB while operating at rates approximately 10 times lower than the Nyquist rate, paving the way to low-power ADC architectures.