Intuitive explanation for low roundoff noise in normal realizations of narrow-band digital filters

The low roundoff noise performance of narrow-band low-pass digital filters realized in normal form is explained in terms of the zeros of the internal transfer functions that control the dynamic range-roundoff noise interaction. For narrow-band filters that have pole pairs close to the real axis, the internal transfer functions of normal realizations have a zero between each of these pole pairs. The effect of this zero is to reduce the norm of the transfer function, and produce a more favorable tradeoff between dynamic range and roundoff noise.