We propose an entirely redesigned framework of bandlimited signal reconstruction for the time encoding machine (TEM) introduced by Lazar and Tóth. As the encoding part of TEM consists in obtaining integral values of a bandlimited input over known time intervals, it theoretically amounts to applying a known linear operator on the input. We then approach the general question of signal reconstruction by pseudo-inversion of this operator. We perform this task numerically and iteratively using projections onto convex sets (POCS). The algorithm can be implemented exactly in discrete time with multiplications that are all reduced to scaling by signed powers of two, thanks to the use of relaxation coefficients. Meanwhile, the algorithm achieves a rate of convergence similar to that of Lazar and Tóth. For real-time processing, we propose an approximate time-varying FIR implementation, which avoids the splitting of the input into blocks. We finally propose some preliminary semi-convergence analysis of the algorithm under data noise.

中文翻译：

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带限信号的时间编码：通过伪反演和时变无乘法器 FIR 滤波重建

我们为 Lazar 和 Tóth 引入的时间编码机 (TEM) 提出了一个完全重新设计的带限信号重建框架。由于 TEM 的编码部分在于在已知时间间隔内获得带限输入的积分值，因此理论上它相当于在输入上应用已知的线性算子。然后我们通过这个算子的伪反演来解决信号重建的一般问题。我们使用凸集（POCS）上的投影以数值方式和迭代方式执行此任务。由于使用了松弛系数，该算法可以通过乘法精确地在离散时间内实现，这些乘法都被缩减为按 2 的有符号幂进行缩放。同时，该算法实现了类似于 Lazar 和 Tóth 的收敛速度。对于实时处理，我们提出了一种近似的时变 FIR 实现，它避免了将输入分成块。最后，我们对算法在数据噪声下的一些初步半收敛性分析提出了建议。