A Hybrid Recursive Trigonometric Technique for Direct Digital Frequency Synthesizer
Xing Xing, William Melek, Wilson Wang · Electronics · 2025
This paper proposes a Hybrid Recursive Trigonometric (HRT) technique for FPGA-based direct digital frequency synthesizers. The HRT technique integrates a recursive cosine generator with periodic reinitialization via a second-order Taylor polynomial to reduce cumulative errors without requiring ROMs or iterative CORDIC units. A resource-efficient combinational architecture is implemented and validated on the Lattice iCE40HX1K FPGA. The effectiveness of the proposed HRT technique is evaluated through simulation and FPGA-based experiments, with respect to spectral accuracy and resource efficiency, particularly for fixed-point cosine waveform synthesis in low-resource digital systems. Simulation results show that the system has a spurious-free dynamic range (SFDR) of −86.09 dBc and signal-to-noise ratio of 52.74 dB using 16-bit fixed-point arithmetic. Experimental measurements confirm the feasibility, achieving −58.86 dBc SFDR.