Signal reconstruction from a given sequence of short-time Fourier transform magnitude spectra without phase information has been a challenging topic since many years. The key issue is how to invert a sequence of overlapping magnitude spectrum containing minimal phase data to generate a real-valued signal free of audible artifacts. Yet, practical implementations are still not able to accurately do that. Based on an implementation of the classical RTISI method for a variety of signal types including both monophonic and polyphonic audio signals such as speech and music, this study aims to determine the optimal conditions required to reconstruct a signal from magnitude spectrum, to understand the relevance of the contribution of each parameter and to take care of the recording conditions of the original signal. Results prove that an optimal selection of the frame length, the shift rate and the iterations number allows enhancing the quality of the reconstructed signals.