Viewing Eq. (7.2) in the frequency domain, the ideal differentiator transfer-function is , which can be viewed as the Laplace transform of the operator (left-hand side of Eq. (7.2)). Moving to the right-hand side, the z transform of the first-order difference operator is . Thus, in the frequency domain, the finite-difference approximation may be performed by making the substitution
The inverse of substitution Eq. (7.3) is
As discussed in §8.3.1, the FDA is a special case of the matched transformation applied to the point .
Note that the FDA does not alias, since the conformal mapping is one to one. However, it does warp the poles and zeros in a way which may not be desirable, as discussed further on p. below.