Evaluation of the relationship between gain and phase using extrapolation techniques

The relationships between the magnitude and phase of the frequency response of a stable linear minimum phase system have been examined by several authors, including Bode, and they prove valuable in the design of a wide range of systems. It is shown that direct application of the expressions to estimate either the phase response from a known gain response, or the gain response from a known phase response, can lead to rather inaccurate results. It is also shown that the accuracy can be signiAcantly improved using appropriate extrapolation of the relevant expressions and functions at high and low frequencies. A range of numerical examples demonstrates the improved accuracy as the extrapolation process is refined, and provides a comparison with the situation where the initial given data are not limited in bandwidth.