Single-Bit Digital Frequency Synthesis via Dithered Nyquist-Rate Sinewave Quantization

Single-Bit Nyquist-rate quantization of sinewaves with random dithering is studied as a means for all-digital frequency synthesis. Quantizer's output spectrum is analytically derived and related to the cumulative distribution function of the random dither formed by independent and identically distributed random variables. Necessary and sufficient conditions for spurs-free output are derived. The noise floor level due to random dithering is derived analytically and the output dynamic range is defined. The trade-off between selective frequency-spurs presence and dynamic range improvement is studied. Several MATLAB examples illustrate the theory and its applications.