A pipelined ROM-less architecture for sine-output direct digital frequency synthesizers using the second-order parabolic approximation

A mathematical approximation for the sine function is proposed which is so close to the sine function that it satisfies the accuracy requirements for sine computation in a typical sine-output direct digital frequency synthesizers (DDS). Then, it is shown that the proposed approximation is realizable by standard digital circuitry, so, a novel ROM-less architecture for sine-output DDS is developed, optimized, and implemented. Experimental results for the implemented ROM-less sine-output DDS are in complete agreement with simulation results in showing that the approximation error will cause harmonic levels below the spurious levels associated with the output quantization error. Another important advantage of the proposed architecture is that it dispenses with ROM, so it can be easily pipelined in order to be as fast as is required