Partitioned block frequency domain adaptive filter device comprising: a frequency domain adaptive filter configured for filtering a frequency domain representation of a time domain input signal depending on a set of filter coefficients consisting of a plurality of blocks (FB.1, FB.2, FB.B) of filter coefficients in order to produce a filtered signal; a plurality of parallel arranged filter update blocks (3.1, 3.2, 3.B), each of the filter update blocks (3.1, 3.2, 3.B) being configured for updating one of the blocks (FB.1, FB.2, FB.B) of filter coefficients based on an update signal (US.1, US.2, US.B) gathered by a circular correlation of a block (BFDS.1, BFDS.2, BFDS.B) of the frequency domain representation signal and a frequency domain control signal comprising a representation of the filtered signal; wherein each of the filter update blocks (3.1, 3.2, 3.B) comprises an adaptation module (4.1, 4.2, 4.B) configured for executing an adaptation sequence comprising the step of calculating an approximation of a constrained gradient update (CU.1, CU.2, CU.B) for the filter coefficients of the respective block (FB.1, FB.2, FB.B) of filter coefficients by applying an approximated constraining matrix having a lesser complexity than a constraining matrix to an unconstrained gradient update for the filter coefficients of the respective block of filter coefficients, wherein the unconstrained gradient update is derived from the update signal (US.1, US.2, US.B); characterized in that the adaption sequence comprises the further step of calculating a cumulative error (CE.1, CE.2, CE.B) introduced on the unconstrained gradient update by applying the approximated constraining matrix to the unconstrained gradient update; wherein each of the filter update blocks (3.1, 3.2, 3.B) comprises a correction module (5.1, 5.2, 5.B) configured for executing a correction sequence comprising the steps of calculating a corrected constrained gradient update (CCU.1, CCU.2, CCU.B) for the filter coefficients of the respective block (FB.1, FB.2, FB.B) of filter coefficients by applying the constraining matrix to a sum of the approximation of the constrained gradient update (CU.1, CU.2, CU.B) and the cumulative error (CE.1, CE.2, CE.B). a frequency domain adaptive filter configured for filtering a frequency domain representation of a time domain input signal depending on a set of filter coefficients consisting of a plurality of blocks (FB.1, FB.2, FB.B) of filter coefficients in order to produce a filtered signal; a plurality of parallel arranged filter update blocks (3.1, 3.2, 3.B), each of the filter update blocks (3.1, 3.2, 3.B) being configured for updating one of the blocks (FB.1, FB.2, FB.B) of filter coefficients based on an update signal (US.1, US.2, US.B) gathered by a circular correlation of a block (BFDS.1, BFDS.2, BFDS.B) of the frequency domain representation signal and a frequency domain control signal comprising a representation of the filtered signal; wherein each of the filter update blocks (3.1, 3.2, 3.B) comprises an adaptation module (4.1, 4.2, 4.B) configured for executing an adaptation sequence comprising the step of calculating an approximation of a constrained gradient update (CU.1, CU.2, CU.B) for the filter coefficients of the respective block (FB.1, FB.2, FB.B) of filter coefficients by applying an approximated constraining matrix having a lesser complexity than a constraining matrix to an unconstrained gradient update for the filter coefficients of the respective block of filter coefficients, wherein the unconstrained gradient update is derived from the update signal (US.1, US.2, US.B); characterized in that the adaption sequence comprises the further step of calculating a cumulative error (CE.1, CE.2, CE.B) introduced on the unconstrained gradient update by applying the approximated constraining matrix to the unconstrained gradient update; wherein each of the filter update blocks (3.1, 3.2, 3.B) comprises a correction module (5.1, 5.2, 5.B) configured for executing a correction sequence comprising the steps of calculating a corrected constrained gradient update (CCU.1, CCU.2, CCU.B) for the filter coefficients of the respective block (FB.1, FB.2, FB.B) of filter coefficients by applying the constraining matrix to a sum of the approximation of the constrained gradient update (CU.1, CU.2, CU.B) and the cumulative error (CE.1, CE.2, CE.B).