One-bit Unlimited Sampling

Conventional analog-to-digital converters (ADCs) are limited in dynamic range. If a signal exceeds some prefixed threshold, the ADC saturates and the resulting signal is clipped, thus becoming prone to aliasing artifacts. Recent developments in ADC design allow to overcome this limitation: using modulo operation, the so called self-reset ADCs fold amplitudes which exceed the dynamic range. A new (unlimited) sampling theory is currently being developed in the context of this novel class of ADCs. In this paper, we make a further step in this direction by coupling modulo sampling with one-bit ΣΔ quantization, or, in other words, consider one-bit unlimited sampling. We show that our scheme overcomes the dynamic range limitations of conventional one-bit quantizer, where no recovery guarantees are possible if the signal's dynamic range substantially exceeds the range of its one-bit output. We provide a constructive recovery algorithm for bandlimited signals from one-bit modulo samples complemented with a bound on the reconstruction error.