A sine wave digital synthesizer based on a quadratic approximation

A sine evaluation architecture based on a quadratic interpolation is considered for the realization of direct digital frequency synthesizers (DDFS). In the proposed architecture the sine values are approximated with the output of a second order interpolator, whose coefficients are stored in a tiny look-up table (LUT). The memory and computation resources needed by this approach are compared with a solution where a first order interpolation is used, recently presented as the best LUT-based system for DDFS implementation. The comparison demonstrates that parabolic interpolation of the sine function asymptotically outperforms lower order approximations and that it could be considered as a better approach for frequency synthesizers with output resolution of practical interest. As a case example, a DDFS with a phase resolution of 20 b and an output resolution of 9 b has been designed. It is characterized by a maximum absolute error of 0.798 LSB, an output signal to noise ratio (SNR) of 55.60 dB and a spectral purity better than 74 dBc. The dimension of the LUT is only 104 b, and the parabolic interpolator has an estimated complexity equivalent to 175 full-adders. The structure of the evaluator is simple, easily pipelinable, and well suited to an integrated implementation.