On the frequency response of scalar discrete-time systems (Q1805807)

Gain and phase characteristics of real and complex discrete-time zeros and poles are considered. The frequency response of polynomials in \(z\) is obtained by varying \(z\) around the unit circle. The minimum and the maximum of the gain values are determined for different parameters. For conjugate complex discrete-time zeros, the behaviour of gain and phase strongly depends on the position of the zeros in the complex \(z\)-plane. The behaviour for different regions is investigated. The application of the results is illustrated by a controller design example.