Quantization Noise as Superposition of Frequency-Modulated Sinusoids

A closed-form deterministic description of the quantization noise introduced by an infinite uniform quantizer as a function of an arbitrary input signal is given. The quantization noise can be regarded as a superposition of frequency-modulated (FM) sinusoids. For a band-limited Gaussian noise input signal, the power density spectrum of the quantization noise is derived. For a discrete-time system, conditions for the quantization noise being uniformly distributed and spectrally white are given. The analytic expressions are in excellent agreement with simulation results.