There are many methods for performing functional mapping from phase to sine amplitude (e.g., ROM look-up, coarse/fine segmentation into multiple ROM's, Taylor series, CORDIC algorithm). The spectral purity of the conventional direct digital synthesizer (DDS) is also determined by the resolution of the values stored in the sine table ROM. Therefore, it is desirable to increase the resolution of the ROM. Unfortunately, larger ROM storage means higher power consumption, lower reliability, lower speed, and greatly increased costs. Different memory compression and algorithmic techniques and their effect on distortion and trade-offs are investigated in detail. A computer program has been created to simulate the effects of the memory compression and algorithmic techniques on the output spectrum of the DDS. For each memory compression and algorithmic technique, the worst case spurious response is calculated using the computer program.