A fixed-point quantization model in the statistical analysis of adaptive filters

In this paper, an improved fixed-point quantization model, suitable for statistical analysis of adaptive filters, is presented. The model considers that the input value to the quantizer can also be a previously quantized one and not only an infinite-precision value, as was the case in a very simple quantization model used in literature. For the fixed-point values obtained by the improved quantization model, the mean value and mean-squared value, used in the statistical analysis of adaptive filters, are obtained. It is also shown that the mean value for rounding is not zero if the input value to the quantizer is not an infinite-precision one, what is a very interesting and not well known result.