An up-sampled data stream, upsampled times a factor P, is generated by the input block providing signal samples having a frequency rate, while an intermediate data stream is generated by a Rate Adapting Stage providing signal samples adapted to an intermediate frequency rate. An output data stream is delivered by a final low pass filter, and includes M signal samples having a desired output sample frequency rate (fOUT=M/Ts). The method provides generation of a provisional stream in the Rate Adapting Stage, wherein this provisional stream is affected by aliases falling within the output Nyquist band [−fOUT/2, fOUT/2], although being adapted to the output frequency rate by a direct insertion of zero samples into the processed stream when L M. Then these aliases are suppressed in the Rate Adapting Stage by weighting the provisional stream via a set of weights.