A low complexity digital modulator, which is particularly useful for providing Gaussian frequency shift keying (GFSK) modulation, includes a filter, an integrator and a look-up table (LUT) stage. The filter is configured to receive a series of impulses and to generate a predetermined and fixed sequence of instantaneous frequency samples in response to each received impulse. The generated instantaneous frequency samples represent a predetermined type of filtering, such as Gaussian filtering, of the series of impulses. The integrator is configured to receive and integrate the instantaneous frequency samples to generate a sequence of phase samples. The LUT stage is configured to receive the phase samples and to generate sine and cosine samples of a complex baseband signal in response to each phase sample. The LUT stage stores only one quadrant of cosine samples and calculates the other cosine samples and all of the sine samples from the stored cosine samples. A controller generates and provides the series of impulses to the modulator. Transmitter digital-to-analog converters convert the sine and cosine samples of the complex baseband signal to analog form prior to transmission.