Comments on "A 13-bit resolution ROM-less direct digital frequency synthesizer based on a trigonometric quadruple angle formula"

In this brief, the first- and second-order approximation of the quadruple angle formula (QAF) interpolation methods introduced in the paper by Wang et al. in 2004, are revisited. The limitations of those methods are completely overlooked in the paper. One of the limitations is maximum achievable spurious-free dynamic range (SFDR) of the generated sinusoidal signals, which are significantly overestimated. In this paper, it is mathematically proven that the best achievable spurious-free dynamic ranges using QAF interpolation methods are significantly less than the values given in the paper by Wang et al. Moreover, the corrected and complete digital implementation of the second-order approximation is introduced.