Algorithms for signal reconstruction from short-time Fourier transform magnitude

We have previously established a number of conditions under which a real signal can be uniquely reconstructed from its STFT magnitude. For the STFT magnitude to be a practical signal representation, we need robust reconstruction algorithms. In this paper, we discuss such a class of algorithms within the framework of sequential extrapolation techniques. Such techniques reconstruct the short-time sections of a signal in an order determined by their positions on the time axis. We find that compared to direct reconstruction, the robust algorithms are less sensitive to roundoff errors. To further test the robustness of these algorithms, we applied them to STFT magnitudes which were purposely modified for accomplishing signal processing tasks such as noise reduction and time-scale modification of speech.