The pole-zero map, invariably introduced on an ad hoc basis, gives a very good frequency domain approximation in the range 0 less-than-or-equal-to omega T < 1, where T is sampling period, to the unrealizable digital controller transfer function C(z) which would result from mapping the corresponding analogue transfer function G(c)(s) under z = e(sT), i.e., s = (1/T) ln z. A variation of the well known Tustin transformation emerges as a simple alternative.