1. A method for reducing computational complexity of an m-stage adaptive filter, the method comprising: receiving an input signal-to be filtered; developing a set of filter coefficients for the received input signal; expanding a weighted sum of forward prediction error squares into a corresponding binomial expansion series; expanding a weighted sum of backward prediction error squares into a corresponding binomial expansion series; determining coefficient updates of the adaptive filter with the weighted sum of forward and backward prediction error squares approximated by a select number of terms of their corresponding binomial expansion series; filtering the received input signal in accordance with the updated coefficients to produce a filtered signal; and providing the filtered signal as an output signal.