In this work, we study the effects of noise present on spectral interferometry signals, for femtosecond pulse retrieval such as in the SPIDER technique (spectral phase interferometry for direct e-field reconstruction). Although previous works report SPIDER robustness, we have found that noisy signals with low signal-to-noise ratio (SNR), in the acquired spectral interferogram, could cause variations in the temporal pulse intensity retrieval. We demonstrate that even in a filtered SPIDER signal, following standard procedures, at some point the noise on the spectral interferogram could affect the spectral phase retrieval. As a novel alternative for spectral interferograms filtering, we have applied the wavelet transform and propose a target criterion to automatize the optimization algorithm. We apply this method on SPIDER signals and analyze its effectiveness on the spectral phase retrieval. We present numerical and experimental results to show the improvement in the phase retrieval and the temporal pulse reconstruction after applying this filtering method and compare the results with a standard method.