Abstract: Modelling for dispersion of media is constructed by a set of infinite impulse(IIR) for the frequency dependent FDTD method(FD FDTD).Filter design methods,such as bilinear transform and impulse invariance procedure,are discussed in this paper.Based on the mature digital signal processing technology,the improved FD FDTD method can be applied to the instantaneous electromagnetic problems for the dispersive media.In order to demonstrate the effectiveness of this approach,some numerical examples are described.