  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.
