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Analog to digital converters (ADCs) act as a bridge between the analog and digital domains. Two important attributes of any ADC are sampling rate and its dynamic range. For bandlimited signals, the sampling should be above the Nyquist rate. It is also desired that the signals' dynamic range should be within that of the ADC's; otherwise, the signal will be clipped. Nonlinear operators such as modulo or companding can be used prior to sampling to avoid clipping. To recover the true signal from the samples of the nonlinear operator, either high sampling rates are required or strict constraints on the nonlinear operations are imposed, both of which are not desirable in practice. In this paper, we propose a generalized flexible nonlinear operator which is sampling efficient. Moreover, by carefully choosing its parameters, clipping, modulo, and companding can be seen as special cases of it. We show that bandlimited signals are uniquely identified from the nonlinear samples of the proposed operator when sampled above the Nyquist rate. Furthermore, we propose a robust algorithm to recover the true signal from the nonlinear samples. We show that our algorithm has the lowest meansquared error while recovering the signal for a given sampling rate, noise level, and dynamic range of the compared to existing algorithms. Our results lead to less constrained hardware design to address the dynamic range issues while operating at the lowest rate possible.

Two important attributes of analog to digital converters (ADCs) are its sampling rate and dynamic range. The sampling rate should be greater than or equal to the Nyquist rate for bandlimited signals with bounded energy. It is also desired that the signals' dynamic range should be within that of the ADC's; otherwise, the signal will be clipped. A modulo operator has been recently suggested prior to sampling to restrict the dynamic range. Due to the nonlinearity of the modulo operation, the samples are distorted. Existing recovery algorithms to recover the signal from its modulo samples operate at a high sampling rate and are not robust in the presence of noise. In this paper, we propose a robust algorithm to recover the signal from the modulo samples which operates at lower sampling rate compared to existing techniques. We also show that our method has lower error compared to existing approaches for a given sampling rate, noise level, and dynamic range of the ADC. Our results lead to less constrained hardware design to address dynamic range issues while operating at the lowest rate possible.