Quantization Noise and Dithering

Abstract

While various circuit noise sources, such as thermal noise, shot noise or 1∕f noise, have a physical origin, other types of noise, like quantization or roundoff noise, occur as a consequence of computational operations performed by circuits. Specifically, the digitization of bandlimited signals with analog-to-digital converters (ADCs) involves not only signal sampling in time, but also amplitude quantization. The quantization operation introduces an error, which is called quantization noise. This noise plays an important role in analyzing the performance of DSP systems and in ADC design. Bennett observed in 1948 that for a sufficiently small discretization step, quantization noise can be viewed approximately as uniformly distributed and white. In a comprehensive study of quantization noise, Widrow was able to derive precise conditions for these properties to hold. Unfortunately, because it is a function of the input signal, the quantization noise is not independent from the input, which creates undesirable artifacts in audio systems. To overcome this problem, an independent dithering noise can be added to the input signal and removed after quantization. This chapter presents a comprehensive analysis of the properties of quantization noise and dithering.