This study introduces a short-time Fourier transform-based method for reconstructing signals encoded using modulo analog-to-digital converters with 1-bit folding information. In contrast to existing Fourier-based reconstruction approaches that require complete access to the entire observation, the proposed technique performs reconstruction over short, overlapping segments, enabling significantly lower latency while preserving the recovery accuracy. We also address the spectral leakage introduced by the windowing operation by selecting window parameters that balance the leakage suppression and the computational complexity of the algorithm. In addition, we establish conditions under which the correct unfolding of the modulo samples is guaranteed, leading to a reconstruction error determined solely by the quantization noise at the output. The numerical results demonstrate that the proposed method enables modulo analog-to-digital converters to surpass the mean squared error performance of conventional analog-to-digital converters. Furthermore, the proposed recovery method offers improved reconstruction performance compared with higher-order difference-based recovery, particularly in low-resolution and low-sampling rate regimes.

翻译：本研究提出了一种基于短时傅里叶变换的方法，用于重建利用带1比特折叠信息的模数转换器编码的信号。与现有需要完整访问整个观测数据的傅里叶基重建方法不同，所提技术在短时、重叠的片段上执行重建，从而在保持恢复精度的同时显著降低延迟。我们还通过选择能平衡频谱泄漏抑制与算法计算复杂度的窗函数参数，解决了加窗操作引入的频谱泄漏问题。此外，我们建立了确保模数样本正确展开的条件，使得重建误差仅由输出端的量化噪声决定。数值结果表明，所提方法使模数转换器的均方误差性能超越了传统模数转换器。此外，与基于高阶差分的恢复方法相比，所提恢复方法在低分辨率和低采样率条件下提供了更优的重建性能。