An adaptive filter has a plurality of filter coefficients and a filter coefficients processing unit trains of the adaptive filter. The filter coefficients processing unit is operable to iterate to alter the plurality of filter coefficients of the communication system filter. Every Nth iteration, the filter coefficients processing unit is operable to identify a first group of filter coefficients of the plurality of filter coefficients that satisfy filter coefficient threshold rules and a second group of filter coefficients of the plurality of filter coefficients that do not satisfy the filter coefficient threshold rules. Every iteration, the filter coefficients processing unit is operable to: (1) update the first group of filter coefficients using a first step size and a first error signal; and (2) update the second group of filter coefficients using a second step size and a second error signal.