Superluminal group velocity in dispersive media has long been controversial. A partial source of confusion seems to be the absence of high precision numerical results concerning the waveform of the transmitted signal. This paper gives the precise waveforms of a causal half-sine-modulated pulse and a triangle-modulated pulse propagating in the Lorentz medium. Thus, the effects of analyticity of signal are clarified, which the analysis using Gaussian pulse cannot. Further, to deepen understanding of the mechanism of superluminal group velocity, we give a network theoretic consideration.