A digital GMSK filter for use for frequency modulation of a carrier signal in a GMSK transmission system is described. The GMSK filter uses a large number of individual current sources, whose current values are individually weighted. The current sources are driven via a control logic module using a shift register with a thermometer code, such that this results in a total current with a Gaussian characteristic, which is converted across a resistor to a voltage and drives a voltage controlled oscillator (VCO). The filter provides exact implementation of the sample values, virtually without any quantization error, and requires only a small chip area for its implementation.