We have investigated the accuracy of wavelet analysis of spectral shearing inter ferometry signal with noisy data. Specifically, we have examined at the effects of additive noise, multiplicative noise, and quantization of the interferogram o n the reconstruction of the spectral phase, and revealed that the wavelet transf orm is a robust technique to retrieve spectral phase from the noise background. We also show that the phase of a femtosecond pulse can be identified from the tr ace of wavelet transform.