In this thesis, a method of Direct Digital Frequency Synthesis, which uses a Non Linear DAC in place of a ROM look up table, is studied. The objective of this work is to explore the spurious performance of the ROM-less DDFS at high frequencies. Replacing the ROM by a non linear DAC has the potential to give similar performance with lower power dissipation and silicon area. An upper limit to this performance comes from the difficulty in designing an accurate high resolution DAC, and the spurious frequencies produced at the output due to quantization effects in the phase and amplitude word lengths. Various techniques at every level are described to reduce the output spurs by randomization, as well as analog matching performance of the DAC. Simulations indicate a spurious performance of over 77DB may be achieved for frequencies close to 125MHz.</p