An even better solution is to do the inversion, explicitly looking for a good set of phases. A better solution to this problem is to use an iterative algorithm proposed by Griffin and Lim many decades ago. Some people advocate starting with a random phase. Back in the time domain you get an answer, but there is a lot of destructive interference because the segments of adjacent frames do not have consistent phase. The easy solution is to just do the inversion assuming some phase (like 0). This code finds the waveform that has a magnitude spectrogram most like the input spectrogram. There are two big problems with spectrogram inversion: most importantly, one (generally) drops the phase when computing a spectrogram, and two not every (spectrogram) image corresponds to a valid waveform. It does not depend on any Mathworks toolboxes. This toolbox is provided as Matlab source code. This is useful because often one wants to think about, and modify sounds in the spectrogram domain. The Spectrogram Inversion Toolbox allows one to create spectrograms from audio, and, more importantly, estimate the audio that generates any given spectrogram.
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