A frequency modulator includes a digitally-controlled oscillator (DCO) arranged for producing a frequency deviation in response to a modulation tuning word and a phase-locked loop (PLL) tuning word. In addition, another frequency modulator includes a DCO and a DCO interface circuit. The DCO is arranged for producing a frequency deviation in response to an integer tuning word and a fractional tuning word. The DCO interface circuit is arranged for generating the integer tuning word and the fractional tuning word to the DCO, wherein the fractional tuning word is obtained through asynchronous sampling of a fixed-point tuning word.