A numerically controlled oscillator based on De Moivre´s identity and linear approximation: A ROMless NCO

Discrete sinusoidal quadrature signal generators whose output frequency is numerically and instantaneously controlled are in widespread use in digital communication systems. In this paper, a numerically controlled quadrature sinusoidal signal generator that uses De Moivre trigonometric identity is proposed. Fine samples between coarsely generated De Moivre oscillator outputs are obtained using linear approximation and some trigonometric identities. In the expense of 2 multipliers and limited fine frequency range, the method uses no look up table. Simulations and implementation proved excellent spectral characteristics, good controllability and low power requirements. Error analysis and simulation results provided in the paper show that the proposed method presents an adequate alternative to table based numerically controlled oscillators for VLSI/FPGA implementations.