13.3 Data quantization in iir filters

Finite-precision effects are much more of a concern with IIR filters than with FIR filters, since the effects are more difficult to analyze andminimize, coefficient quantization errors can cause the filters to become unstable, and disastrous things like large-scale limit cycles can occur.

Roundoff noise analysis in iir filters

Suppose there are several quantization points in an IIR filter structure. By our simplifying assumptions about quantization errorand Parseval's theorem, the quantization noise variance ${}_{\mathrm{y,i}}^2$ at the output of the filter from the $i$ th quantizer is

A general approach to find $H_i(w)$ is to write state equations for the equivalent structure as seen by $n_i$ , and to determine the transfer function according to $H(z)=CzI-A^{(-1)}B+d$ .

By making the assumption that each $Q_i$ represents a noise source that is white, independent of the other sources, and additive,