Hearing beyond the spectrum

In this work we focus on the problem of acoustic signals modeling and analysis, with particular interest in models that can capture the timbre of musical sounds. Traditional methods usually relate to several “dimensions” which represent the spectral properties of the signal and their change in time. Here we confine ourselves to the stationary portion of the sound signal, the analysis of which is generalized by incorporating polyspectral techniques. We suggest that by looking at the higher order statistics of the signal we obtain additional information not present in the standard autocorrelation or its Fourier related power-spectra. It is shown that over the bispectral plane several acoustically meaningful measures could be devised, which are sensitive to properties such as harmonicity and phase coherence among the harmonics. Effects such as reverberation and chorusing are demonstrated to be clearly detected by the above measures. In the second part of the paper we perform an information theoretic analysis of the spectral and bispectral planes. We introduce the concept of statistical divergence which is used for measuring the “similarity” between signals. A comparative matrix is presented which shows the similarity measure between several instruments based on spectral and bispectral information. The instruments group into similarity classes with a good correspondence to the human acoustic perception. The last part of the paper is devoted to acoustical modelling of the above phenomena. We suggest a simple model which accounts for some of the polyspectral aspects of musical sound discussed above. One of the main results of our work is generalization of acoustic distortion measure based on our model and which takes into account higher order statistical properties of the signal.