Abstract: A low-power digital communications transmitter (20) includes a programmable digital-processing circuit (22), which may be provided by a digital signal processor (DSP), a programmable direct digital synthesizer (DDS), and a constant-envelope, high power amplifier (32). The DDS (24) is programmed to provide pulse-shaping and IF/RF signal modulation functions. The digital-processing circuit (22) produces only one sample per unit interval (134) and is programmed so that the one sample per unit interval (134) is a frequency-profile index symbol (52?) produced from a I,Q baseband symbol (52?). The DDS (24) converts each frequency-profile index symbol (52?) into a frequency profile (130) that controls the frequency of a synthesizer (56) to induce modulation into a periodic output (68) of the synthesizer. Moreover, the frequency profile (130) is configured to confine spectral emissions within a spectral mask (140).