A method and apparatus for direct digital synthesis (DDS) of signals using Taylor series expansion is provided. The DDS may include a modified phase-to-amplitude converter that includes read-only-memories (ROMs), registers and, a single size, such as a coarse, intermediate, and fine ROM corresponding to respective higher resolution phase angles. The outputs of the ROMs when combined can form a digital output signal in the form of a Taylor series of a sinusoid function.