Relationship between sampling rate and quantization noise

Few works have been done about the dependency of the quantization noise with the sampling rate for uniform quantizers. Some of these works have considered the problem from a deterministic point of view while others study it from a stochastic one, having explained the noise behavior in some specific cases. By using computer simulations with a sinusoidal input signal, we show that the quantization noise spectrum can show a discrete or complex structure depending on the sampling rate used. The results confirm that an integer ratio between the sampling rate (f_r) and the frequency of the input signal (f_s) produces quantization noise with the components in odd harmonics of the signal frequency. If there is not an integer ratio between f_r and f_s, then the quantization noise can present a stochastic structure for some rational ratios. An additional result is that the phase of the input signal can also modify the magnitude of the spectral components of the quantization noise. These results show that the quantization noise is clearly dependent on the input signal and the sampling rate.