Integrate and fire is a resource efficient time-encoding mechanism that summarizes into a signed spike train those time intervals where a signal's charge exceeds a certain threshold. We analyze the IF encoder in terms of a very general notion of approximate bandwidth, which is shared by most commonly-used signal models. This complements results on exact encoding that may be overly adapted to a particular signal model. We take into account, possibly for the first time, the effect of uncertainty in the exact location of the spikes (as may arise by decimation), uncertainty of integration leakage (as may arise in realistic manufacturing), and boundary effects inherent to finite periods of exposure to the measurement device. The analysis is done by means of a concrete bandwidth-based Ansatz that can also be useful to initialize more sophisticated model specific reconstruction algorithms, and uses the earth mover's (Wassertein) distance to measure spike discrepancy.

翻译：积分与发放是一种资源高效的时间编码机制，其将信号电荷超过特定阈值的时间区间概括为带符号的脉冲序列。我们基于一种非常通用的近似带宽概念来分析IF编码器，该概念被大多数常用信号模型所共享。这补充了可能过度适应特定信号模型的精确编码结果。我们首次考虑了以下因素的综合影响：脉冲精确位置的不确定性（可能由降采样引起）、积分泄漏的不确定性（可能在实际制造中产生），以及有限测量周期固有的边界效应。分析通过一个具体的基于带宽的假设展开，该假设也可用于初始化更复杂的模型特定重建算法，并采用推土机（Wasserstein）距离来度量脉冲差异。