Rom-less direct digital frequency synthesis using the 3rd-order parabolic approximation

This paper deals with the introduction of "the third-order parabolic approximation (PB3)" as a new method for sine computation in direct digital frequency synthesizers (DDSs). PB3 is, in fact, an improvement to the second-order parabolic approximation (PB2) [1] that leads to more accurately computing a sine function. The possibility of being implemented using standard logic gates (not even a bit of memory) is one of most important advantages of the third- order parabolic approximation. Another interesting property of the proposed digital implementation for PB3 is that the additional hardware needed for developing a. PB2-based DDS architecture to a PB3-based one is quite simple. This is because the hardware utilizes some internal signals that had already developed for PB2 computation.