April 2016
This project was completed for MUMT 622, Time-Frequency and Parametric Representations of Sounds, at McGill University. This project presents techniques for reconstructing a signal from the magnitude spectrum. An overview of the spectrogram is presented before a summary of the techniques. Implementations of the algorithms associated with each technique are explained, followed by results of their output. Finally, some conclusions about the appropriate uses of the spectrogram inversion algorithms are discussed.
Magnitude spectra modifications are common in many signal processing applications. For example in the elimination of noise from a signal, areas in the frequency domain contributing to the noise are reduced or eliminated. In this case, and many other applications, the phase information is disregarded. Sometimes, the original phase is combined with the modified magnitude spectra in order to transform the spectrum into the time domain. A lack of coherence between the two spectra will result in a reconstructed signal that contains artifacts or distortions.
Due to the commonality of magnitude-spectra-only modifications, the ability to reconstruct a signal without the phase spectrum is important. Spectrogram inversion proves a useful tool for many applications and has been researched for several decades.