Quantization noise analysis of a general digital filter

A new, precise modeling technique is presented for the exact representation of digital filters, discrete systems, or computational algorithms. It leads to a method for the determination of the noise variance of the filter output due to quantization errors occurring at multipliers, summers, and the A/D converter. The noise formulae are in either infinite series or closed form and through their use a precise evaluation of an arbitrary filter structure may be obtained. The formulas can be easily computer implemented and require no filter analysis by the designer. The special case of state-space filters is examined in detail. Appropriate numerical examples are included.