Improving performance of digital sinusoidal oscillators by means of error feedback circuits

A few structures for digital sinusoidal oscillators have been proposed, together with the design methods used for such structures. Because of the finite wordlength effects, these structures produce high roundoff errors which change both the amplitude and frequency of the generated sinusoidal signal. This makes it difficult to design an oscillator which generates a sinusoidal waveform with a particular frequency and amplitude. It is shown in this paper that if we add to the direct form digital oscillator a circuit which saves the quantization error and feeds it back for consideration at subsequent iterations, roundoff errors are considerably reduced, and the frequency and amplitude of the generated waveform are very close to those expected by theory. Formulas are derived for the resulting errors and simulation results are given, showing that a significant improvement is obtained by error feedback.