  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 mean-squared 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.
