An efficient numerical algorithm is presented for the numerical modeling of the propagation of ultrashort pulses with arbitrary temporal and frequency characteristics through linear homogeneous dielectrics. The consequences of proper sampling of the spectral phase in pulse propagation and its influence on the efficiency of computation are discussed in detail. The numerical simulation presented here is capable of analyzing the pulse in the temporal-frequency domain. As an example, pulse propagation effects such as temporal and spectral shifts, pulse broadening effects, asymmetry and chirping in dispersive media are demonstrated for wavelet decomposition
