AI 中文总结
该研究针对模滞回模型的缺点，提出广义模编码器，推导带限信号由其广义模样本唯一确定的条件，给出带数学保证的恢复算法并通过数值实验验证理论结果。
AI 中文摘要
无限制传感及其通过模滞回的扩展，提供了一种高效的高动态范围信号编码方案，该方案在采样前将信号幅度折叠到模数转换器的范围内。受模滞回模型缺点的启发，本研究引入了广义模编码器，该编码器通过结合通用过渡函数并允许折叠次数依赖于折叠过渡的非理想性，灵活地设计折叠方式。我们严格研究了相应算子的数学性质，并推导了带限信号可由其广义模样本唯一确定的条件。最后，我们提出了一种带有数学保证的恢复算法，并通过数值实验说明了我们的理论结果。
英文摘要
Unlimited sensing and its extension via modulo hysteresis provide an efficient encoding scheme for high dynamic range signals by folding the signal's amplitude into the range of the analog-to-digital converter prior to sampling. Motivated by shortcomings of the modulo hysteresis model, in this work we introduce generalized modulo encoders that flexibly design the folding by incorporating a general transition function and allowing the folding times to depend on the nonideality of the folding transition. We rigorously study mathematical properties of the respective operators and derive conditions under which a bandlimited signal is uniquely determined by its generalized modulo samples. Finally, we propose a recovery algorithm backed by mathematical guarantees and illustrate our theoretical results through numerical experiments.
