Abstract: For the sake of studying second-harmonic generation(SHG) and polarization gating(PG) frequency-resolved optical gating(FROG),both techniques measuring the intensity and phase of ultrashort laser pulses,SHG-FROG and PG-FROG traces of several types of common ultrashort pulses were numerically simulated using a matrix approach.Taking SHG-FROG as an example,the amplitude and the phase of these pulses were gleaned from these SHG-FROG traces by the principal component generalized projections algorithm and the SHG-FROG error was less than 10-4.The results show that FROG can accurately measure ultrashort laser pulses.