Analysis of roughly quantized Gaussian signals

Experience shows that measurements on normally distributed signals are affected by a large uncertainty when the standard deviation of the signal is smaller than the quantization step. In this case, the so-called quantization noise model can not be assumed since the quantization error is correlated with the quantizer input. It is demonstrated that the correlation can be zeroed by slowly varying the mean value of the input signal within the quantization cell. This allows to obtain an accurate estimate of the input variance either when a low resolution quantizer is used. The above technique may be explained as a particular case of deterministic, narrow-band dithering. Finally, it will be shown that large-scale, random narrow-band dithering may be advantageously used when a deep knowledge of the input signal spectrum is necessary. The measurement of the different contributions to the internal noise of an A/D converter, represents a typical application of these techniques.