The modification of magnitude spectrograms is at the core of many audio signal processing methods, from source separation to sound modification or noise canceling, and reconstructing a natural sounding signal in such situations is thus a very important issue. This article presents recent theoretical and experimental developments on the application to signal reconstruction from a modified magnitude spectrogram of the constraints that an array of complex numbers must verify to be a consistent short-time Fourier transform (STFT) spectrogram, i.e., to be the STFT spectrogram of an actual real-valued signal. We give here further theoretical insights, present several potential variations on our previously introduced algorithm, investigate various techniques to speed up the signal reconstruction process, and present a thorough experimental comparison of the performance of all the considered algorithms.

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The continuous wavelet transform (CWT) can be seen as a filterbank having logarithmic frequency subbands spacing similar to the human auditory system. Thus, to make computers imitate the significant functions of the human auditory system, one promising approach would be to model, analyze and process magnitude spectrograms given by the CWT. To realize this approach, we must be able to convert a processed or modified magnitude CWT spectrogram, which contains no information about the phase, into a time domain signal specifically for those applications in which the aim is to generate audio signals. To this end, this paper proposes a fast algorithm for estimating the phase from a given magnitude CWT spectrogram to reconstruct an audio signal. The experimental results revealed that the proposed algorithm was around 100 times faster than a conventional algorithm, while the reconstructed signals obtained with the proposed algorithm had almost the same audio quality as those obtained with the previous study.

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