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The authors present a review of phase to sine amplitude conversion (PSAC) techniques for direct digital frequency synthesis (DDFS). Principles of DDFS are first considered, then approaches for the reduction of system complexity are identified. It is shown that the basic problem for the design of the phase to sine amplitude converter, whether the system has single phase or quadrature outputs, is the reproduction of an approximated sine function for first quadrant angles. The state of the art in PSAC design is then reviewed following a systematic classification of techniques, namely angular decomposition, angular rotation, sine amplitude compression, polynomial approximation, and analogue approaches.