Relation to Finite Difference Approximation

The Finite Difference Approximation (FDA) (§7.3.1) is a special case of the matched $z$ transformation applied to the point $s=0$ . To see this, simply set $a=0$ in Eq.(8.5) to obtain

$$s \;\to\; 1 - z^{-1} \protect$$ (9.7)

which is the FDA definition in the frequency domain given in Eq.(7.3).

Since the FDA equals the match z transformation for the point $s=0$ , it maps analog dc ($s=0$ ) to digital dc ($z=1$ ) exactly. However, that is the only point on the frequency axis that is perfectly mapped, as shown in Fig.7.15.