When the input to a quantizer is a sampled time series represented by x1, x2, x3, …, the quantization noise is a time series represented by ν1, ν2, ν3, … Suppose that the input time series is stationary and that its statistics satisfy the conditions for multivariable QT II (it would be sufficient that two–variable QT II conditions were satisfied for x1 and x2, x1 and x3, x1 and x4, and so forth, because of stationarity). As such, the quantization noise will be uncorrelated with the quantizer input, and the quantization noise will be white, i.e. uncorrelated over time. The PQN model applies. The autocorrelation function of the quantizer output will be equal to the autocorrelation function of the input plus the autocorrelation function of the quantization noise.

Fig. 20.1(a) is a sketch of an autocorrelation function of a quantizer input signal. Fig. 20.1(b) shows the autocorrelation function of the quantization noise when the PQN model applies. Fig. 20.1(c) shows the corresponding autocorrelation function of the quantizer output.

Corresponding to the autocorrelation functions of Fig. 20.1, the power spectrum of the quantizer output is equal to the power spectrum of the input plus the power spectrum of the quantization noise. This spectrum is flat, with a total power of q2/12.