On the effects of zero-pole pairs and individual zeros and poles on discrete-time transfer functions

This work presents analytical expressions as well as related curves to determine the maximum magnitude and phase deviations caused by a zero-pole pair, an individual pole or an individual zero on a discrete-time transfer function. The main motivation is to provide a clear link between the position of zeros and poles, considering their magnitudes and phases, and the effects of discarding them from a given transfer function, since evaluating these effects is crucial to attain the order reduction of physical system models.