A linear discrete-time network (e.g. a digital filter) of the minimum-phase type is characterised by having a transfer function with poles and zeros all located outside the unit circle in the z−1plane. In the paper, the Cauchy integral formula is applied to this transfer function for values of z−1on the unit circle, and various sets of gain-phase relations are thereby obtained for the network. It is also shown that, when the sampling period approaches zero, these relations reduce to the well known gain-phase relations of a linear continuous-time network of the minimum-phase type.