The Relationship between the Group Delay and Envelope Delay of a Narrow-band Dispersive System

In this paper, the relationship between the group delay and correlation delay is discussed, and the influence of dispersion on the calibration of a system is analyzed, when a modulated signal passes through a dispersive narrow-band system. The envelope delay of a modulated signal is caused by the distortion of its rising and falling edges when it passes through a system. The researches on the modulated signals, including the rectangular pulse modulation, triangular pulse modulation, cosine pulse modulation and chirp modulation, show that the correlation delay is different from the group delay of the system at the point of the carrier frequency. The correlation delay is approximate to the weighted average of the group delay, and the weighting factor is the product of the spectrum of the signal and the amplitude response of the system. When the group delay is used to calibrate the correlation delay, the linearity of the phase response of the system becomes better, the calibration is higher.