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

Direct digital frequency synthesizers (DDS or DDFS) are widely used in modern communications and measurement devices. Their advantages are small size and power consumption together with excellent frequency stability, high frequency resolution, and short switching times. The difficulties are rather low output frequencies (500 MHz at the present state of the art) and a large set of the spurious signals very often above the -80 dB level. One source of spurious signals in DDS 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 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. A simpler solution of the problem of spurious signal level due to the phase truncation in DDS was found earlier. However, no attention was paid to the validity of the corrections suggested. In this paper we will be concerned with this problem and investigate the validity and correctness of these generally cited results and provide a simple way for finding positions, levels, and numbers of these spurious signals generated by truncation to W bits of the phase information stored in the DDS accumulator memory of R bits (W