Abstract: A substantially pure sinusoidal carrier is produced by a digital-to-analog converter that repeatedly converts a sequence of N digital values provided by a digital sequencer to a stream of quantized analog samples. In certain embodiments, the N digital values comprise a time-domain function selected to substantially eliminate all odd harmonics between 1 and N-1 and all even harmonics from the stream of quantized analog samples. A filter may be used to eliminate additional unwanted harmonics. In some embodiments, the frequency of the carrier is selected by controlling the sequence rate of the digital sequencer via a programmable clock. The present invention synthesizes a harmonically pure and stable carrier of a selected frequency while enabling use of a low-resolution digital-to-analog converter.