The performance and stability of an IIR filter depends
on the pole locations, so it is important to know how
quantization of the filter coefficients

How can we reduce this high sensitivity to IIR filter coefficient quantization?

**Solution**

Cascade
or parallel form
implementations! The numerator and denominator polynomials
can be factored off-line at very high precision and grouped into
second-order sections, which are then quantized section by
section. The sensitivity of the quantization is thus that
of second-order, rather than

Note that the numerator polynomial faces the same
sensitivity issues; the *cascade* form
also improves the sensitivity of the zeros, because they are
also factored into second-order terms. However, in the
*parallel* form, the zeros are globally
distributed across the sections, so they suffer from
quantization of all the blocks. Thus the
*cascade* form preserves zero locations
much better than the parallel form, which typically means
that the stopband behavior is better in the cascade
form, so it is most often used in practice.

### Note on FIR Filters:

### Exercise 1

What is the worst-case pole pair in an IIR digital filter?

#### Solution

The pole pair closest to the real axis in the z-plane, since the complex-conjugate poles will be closest together and thus have the highest sensitivity to quantization.