The digital filter has a finite impulse response, whose length corresponds at most to the duration of N input values, with the filter emitting an output signal which is n-times oversampled in comparison to the input signal (I, Q). In this case, a device (38.1-38.5) for storage of a plurality of N look-up tables is provided in the filter. n data values are stored per value in each look-up table for a plurality of k possible values of the input signal. Each data value is in this case characteristic of the product of a coefficient of the impulse response and a value of the input signal (I, Q).