Spurious-free dynamic range of a uniform quantizer

Quantization plays an important role in many systems where analog-to-digital conversion and/or digital-to-analog conversion take place. If the quantization error is correlated with the input signal, then the spectrum of the quantization error will contain spurious peaks. Although analytical formulas describing this effect exist, numerical evaluation can take much effort. This brief provides approximations for the spurious-free dynamic range (SFDR) of a uniform quantizer with a single sinusoidal input, with and without additive Gaussian noise. It is shown that the SFDR increases by approximately 8 dB/bit, in case there is no noise. Generalizing this result to multitone inputs results in an additional 2 dB/bit per additional tone. Additive Gaussian noise decorrelates the sinusoid(s) and the quantization error, which results in a dramatic increase in SFDR.