An equalizer for a multi carrier signal for carrying out equalization adapted to each carrier or group of carriers, Fourier transforms the multi carrier signal, and obtains difference terms of the multi carrier signal. Both are input to an adaptive filter, to output equalized signals, wherein decimation is applied to at least some of the difference terms input to the filter. This enables the complexity to be reduced for a given performance level. In particular since only non-zero filter taps need to be stored and updated, coefficient memory and coefficient calculation capacity can be reduced. Another way to reduce complexity involves measuring noise for at least some of the carriers, and dynamically adapting the size of the filter on a per carrier basis according to global optimizion heuristic algorithms which adapt this filter size based on the comparison between this noise and an optimal performance figure achieved in a previous ISI-ICI free measurement phase.