Effectiveness of representation of signals through group delay functions

The representation of signals in the group delay domain has been suggested in the literature recently. Because of some special properties of the group delay functions, this representation offers some advantages in several signal processing situations like digital filtering, pole-zero decomposition and deconvolution. In this paper, we study the effectiveness and limitations of the group delay representation of signal information. We show that most of the limitations arise from the discrete nature of handling the signals in the time and frequency domains. We also show that, as the number of DFT points is increased, the signal derived from the group delay functions, though our reconstruction algorithms, approaches the original signal. We discuss the limitations of the group delay functions in terms of location of the roots of the z-transform of the given discrete time signal. The group delay functions provide an accurate representation of the signal information, as long as the roots are not too close to the unit circle in the z-plane. The errors for the case of close roots are mostly due to reconstruction of phase from the group delay function