FRI-TEM: Time Encoding Sampling of Finite-Rate-of-Innovation Signals

Classical sampling is based on acquiring signal amplitudes at specific points in time, with the minimal sampling rate dictated by the degrees of freedom in the signal. The samplers in this framework are controlled by a global clock that operates at a rate greater than or equal to the minimal sampling rate. At high sampling rates, clocks are power-consuming and prone to electromagnetic interference. An integrate-and-fire time encoding machine (IF-TEM) is an alternative power-efficient sampling mechanism which does not require a global clock. Here, the samples are irregularly spaced threshold-based samples. In this paper, we investigate the problem of sampling FRI signals using an IF-TEM. We provide theoretical guarantees for a recently proposed recovery method to perfectly recover an FRI input. In addition, we propose a modified sampling approach in the presence of noise that is more robust than existing techniques. This method is also proven to ensure recovery in the noise-free setting. The modified approach requires twice the number of measurements compared to the existing method, however, it results in lower error in the presence of noise for the same number of measurements. Our results enable designing low-cost and energy-efficient analog-to-digital converters for FRI signals.