Modulo Sampling and Recovery in Shift-Invariant Spaces

The recovery of high dynamic range shift-invariant (SI) signals presents a significant challenge in the realm of analog-to-digital converters (ADCs). A critical aspect in this context is that the dynamic range of the ADC, needs to surpass that of the input analog signal in order to prevent any loss of information. Modulo sampling, a technique recently studied primarily for bandlimited (BL) signals, has proven effective in mitigating dynamic range limitations. Here we extend recent results to more general SI signals. Our suggested method involves applying a low-pass filter (LPF) to obtain a BL signal, which can then be uniquely reconstructed from its modulo samples when sampled above the Nyquist rate. Subsequently, the original SI signal is successfully recovered from the reconstructed BL signal via appropriate filtering. The system’s performance under various noise levels is demonstrated. This method opens new possibilities for efficiently recovering SI signals using modulo sampling, extending its applicability beyond BL signals and leveraging a slightly higher sampling rate than the Nyquist rate.