An adaptive nonrecursive digital filter includes a first filter unit having N controllable filter coefficients. A control unit controls the filter coefficients as a function of an input signal applied to the first filter unit at a given sampling rate and as a function of a difference between a reference signal and an output signal output by the first filter unit, in accordance with the least mean error square in each case. The first filter unit and the control unit sample the input signal and the reference signal continuously, with a cyclically varying delay, at a correspondingly increased sampling rate. A second filter unit is operated at the given sampling rate and has N controllable filter coefficients. The second filter unit receives the input signal, outputs a further output signal and has filter coefficients also being controlled by the control unit.