An Adaptive Nonlinear Differential Limiter (ANDL) is proposed in this paper to efficiently alleviate the impact of impulsive noise (IN) in a communication system. Unlike existing nonlinear methods, the ANDL is implemented in the analog domain where the broader acquisition bandwidth makes outliers more detectable and consequently it is easier to remove them. While the proposed ANDL behaves like a linear filter when there is no outlier, it exhibits intermittent nonlinearity in response to IN. Therefore, the structure of the matched filter in the receiver is modified to compensate the filtering effect of the ANDL in the linear regime. In this paper, we quantify the performance of the ANDL by deriving a closed-form analytical bound for the average signal-to-noise ratio (SNR) at the output of the filter. The calculation is based on the idea that the ANDL can be perceived as a time-variant linear filter whose bandwidth is modified based on the intensity of the IN. In addition, by linearizing the filter time parameter variations, we treat the ANDL as a set of linear filters where the exact operating filter at a given time depends upon the magnitude of the outliers. The theoretical average bit error rate (BER) is validated through simulations and the performance gains relative to classical methods such as blanking and clipping are quantified.