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 finite-rate-of-innovation (FRI) signals using an IF-TEM. We provide theoretical recovery guarantees for an FRI signal with arbitrary pulse shape and without any constraint on the minimum separation between the pulses. In particular, we show how to design a sampling kernel, IF-TEM, and recovery method such that the FRI signals are perfectly reconstructed. We then propose a modification to the sampling kernel to improve noise robustness. Our results enable designing low-cost and energy-efficient analog-to-digital converters for FRI signals.

中文翻译：

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FRI-TEM：有限创新率信号的时间编码采样

经典采样基于在特定时间点获取信号幅度，最小采样率由信号的自由度决定。此框架中的采样器由全局时钟控制，该时钟以大于或等于最小采样率的速率运行。在高采样率下，时钟耗电且容易受到电磁干扰。积分触发时间编码机 (IF-TEM) 是一种替代的节能采样机制，不需要全局时钟。这里，样本是不规则间隔的基于阈值的样本。在本文中，我们研究了使用 IF-TEM 对有限创新率 (FRI) 信号进行采样的问题。我们为具有任意脉冲形状的 FRI 信号提供理论恢复保证，并且对脉冲之间的最小间隔没有任何限制。特别是，我们展示了如何设计采样内核、IF-TEM 和恢复方法，以便完美地重建 FRI 信号。然后我们建议修改采样内核以提高噪声鲁棒性。我们的结果能够为 FRI 信号设计低成本和高能效的模数转换器。