Second-order parabolic approximation: a new mathematical approximation dedicated to ROM-less DDFSs

An extended form of the parabolic approximation, which was previously introduced by the authors, is proposed. The proposed form of the approximation is so close to the sine function that satisfies the accuracy requirements for a typical sine-output direct digital frequency synthesizer (DDFS). However, the novel approximation presents a suitable formula for sine function in signal processing algorithms and software, and it is shown that it can be implemented using digital hardware.