Bandpass signals are an important sub-class of bandlimited signals that naturally arise in a number of application areas but their high-frequency content poses an acquisition challenge. Consequently, "Bandpass Sampling Theory" has been investigated and applied in the literature. In this paper, we consider the problem of modulo sampling of bandpass signals with the main goal of sampling and recovery of high dynamic range inputs. Our work is inspired by the Unlimited Sensing Framework (USF). In the USF, the modulo operation folds high dynamic range inputs into low dynamic range, modulo samples. This fundamentally avoids signal clipping. Given that the output of the modulo nonlinearity is non-bandlimited, bandpass sampling conditions never hold true. Yet, we show that bandpass signals can be recovered from a modulo representation despite the inevitable aliasing. Our main contribution includes proof of sampling theorems for recovery of bandpass signals from an undersampled representation, reaching sub-Nyquist sampling rates. On the recovery front, by considering both time-and frequency-domain perspectives, we provide a holistic view of the modulo bandpass sampling problem. On the hardware front, we include ideal, non-ideal and generalized modulo folding architectures that arise in the hardware implementation of modulo analog-to-digital converters. Numerical simulations corroborate our theoretical results. Bridging the theory-practice gap, we validate our results using hardware experiments, thus demonstrating the practical effectiveness of our methods.

翻译：带通信号是一类重要的带限信号子集，在众多应用领域中自然出现，但其高频成分给采集带来了挑战。因此，“带通采样理论”已在文献中得到研究与应用。本文主要研究带通信号的模采样问题，目标是实现高动态范围输入信号的采样与恢复。我们的工作受到无限感知框架（USF）的启发。在USF中，模运算将高动态范围输入折叠为低动态范围的模采样值，从根本上避免了信号截断。由于模非线性输出是非带限的，带通采样条件从未成立。然而，我们证明尽管存在不可避免的混叠，带通信号仍可从模表示中恢复。我们的主要贡献包括：通过欠采样表示恢复带通信号的采样定理证明，实现亚奈奎斯特采样率。在恢复层面，通过时域与频域双视角分析，我们对模带通采样问题提供了全局性理解。在硬件层面，我们考虑了模模数转换器硬件实现中出现的理想、非理想及广义模折叠架构。数值模拟验证了理论结果。为弥合理论与实践差距，我们通过硬件实验验证了结果，从而证明了所提方法的实际有效性。