Spurious signals in direct digital frequency synthesizers due to the phase truncation

One of the sources of spurious signals in DDFS is the use of smaller number, W, of the most significant bits (MSB) applied for the output sine wave reconstruction from all R bits stored in the accumulator. The result is a phase modulation of the output signal. The problem was first solved by Nicholas et al. [1987-8] in a rather complicated way with the result that the level of the largest spurious signal is about -6 W dB below the carrier with an increase of 3.9 dB in some instances. The present paper investigates the validity and correctness of these generally cited results.