A digital filter with a pipeline structure includes processing structures timed by respective clock signals. Each processing structure in turn is formed by a number of processing modules for processing input samples. A phase generator aligns the processing modules with the input samples so that each input sample is processed by a respective one of the processing modules. An up-sampling buffer and a down-sampling buffer are used when the processing structures operate at different clock frequencies (thus implementing different clock domains) so as to convert signal samples between the clock domains for processing in the processing structures.