Gain-phase relations for minimum-phase discrete-time networks

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¿1 plane. In the paper, the Cauchy integral formula is applied to this transfer function for values of z¿1 on 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.