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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