Digital Frequency Synthesizer Based on Two Coprime Moduli DDS

A new concept for direct digital synthesizer (DDS) design is presented in this brief. The originality of the method consists on the use of a traditional modulus $2^{L}$ DDS and a novel modulus $(2^{L}-1)$ DDS whose outputs are digitally mixed by means of a complex multiplier. This way, the number of different frequencies achievable equals $2^{L}(2^{L}-1)$ using two independent $L$-bits wide accumulators. No phase truncation is required resulting in extremely low spurs, while the size of the memories for the trigonometric look-up tables is only $2^{L}$ positions. The design has been implemented in a field-programmable gate array to demonstrate its performance and logic requirements.