## ISCA Tutorial and Research Workshop on Statistical and Perceptual Audition (SAPA2008)## Brisbane, Australia |

As many acoustic signal processing methods, for example for source separation or noise canceling, operate in the magnitude spectrogram domain, the problem of reconstructing a perceptually good sounding signal from a modified magnitude spectrogram, and more generally to understand what makes a spectrogram consistent, is very important. In this article, we derive the constraints which a set of complex numbers must verify to be a consistent STFT spectrogram, i.e. to be the STFT spectrogram of a real signal, and describe how they lead to an objective function measuring the consistency of a set of complex numbers as a spectrogram. We then present a flexible phase reconstruction algorithm based on a local approximation of the consistency constraints, explain its relation with phase-coherence conditions devised as necessary for a good perceptual sound quality, and derive a real-time time scale modification algorithm based on sliding-block analysis. Finally, we show how inconsistency can be used to develop a spectrogram-based audio encryption scheme.

__Bibliographic reference.__
Roux, Jonathan Le / Ono, Nobutaka / Sagayama, Shigeki (2008):
"Explicit consistency constraints for STFT spectrograms and their application to phase reconstruction",
In *SAPA-2008*, 23-28.