Analog Phase Samples Approximation from Gain Samples by Discrete Hilbert Transform

The Hilbert transform has been recognized as an important method in circuit theory. One of its important applications is related to the gain–phase relationship. Many practical methods have been derived from the Hilbert transform to calculate the analog phase samples from the analog gain samples. However, the use of the discrete Hilbert transform is not so common in phase approximation through gain samples. One reason may be related to the possible presence of aliasing. In this paper, we show that yet another inconvenience can occur when it is desired to obtain some samples of the phase using the discrete Hilbert transform of the gain samples: the minimum-phase sequences of finite length allow only zero total net phase change. Thus, the computation of the analog phase samples using the discrete Hilbert transform is convenient only when its net phase change of the analog circuit is also zero.