1. An apparatus for compensating a nonlinear impairment of a signal traversing an optical communications system, the apparatus comprising: a parallel array of linear convolutional filters configured to process a selected set of samples of the signal to calculate an estimate of a nonlinear interference field, the selected set of samples comprising a first sample and a plurality of second samples; and a processor configured to apply the estimated nonlinear interference field to the first sample so as to at least partially compensate the nonlinear impairment, wherein each linear convolutional filter comprises a set of filter taps, each filter tap being configured to compute a product of a value provided by the processor and a complex coefficient representing an efficiency of nonlinear interaction, and wherein the complex coefficients are quantized to a predetermined number of levels, for each filter tap the value is either zero or a sum of doublets, a doublet being either a product obtained from two of the second samples or a product obtained from the first sample and one of the second samples, and the number of non-trivial complex multiplication operations that involve the complex coefficients and that are used to evaluate the output of each linear convolutional filter is less than the number of filter taps.