A discrete time transmission model is proposed to characterize the response of fiber gratings, and the digital processing methods are used to analyze the phase response of fiber gratings. The inner band dispersion characteristics of apodized fiber gratings used for DWDM filtering is studied. It is shown that the amplitude and phase responses of symmetrical apodized fiber grating are related by means of the Hilbert transform, the closer to ideal rectangle the amplitude response is, the greater the inner band dispersion is. The coupled mode theory is used to calculate the reflection phase response and inner band dispersion of apodized fiber gratings, the above analysis is verified.