Testing for Gaussianity and Non Linearity in the sustained portion of musical sounds
Higher order spectra of a signal contain information about the non Gaussian and non Linear properties of the system that created it. Since the non linearity in musical signal usually originate in the excitation signal while the linear spectral characteristics are attributed to the resonant chambers, we discard the spectral information by looking at the higher order statistical properties of the residual signal, i.e. the estimated input signal obtained by inverse ltering of the sound. In the current paper we show that the skewness and kurtosis values of the residual could be used for characterization of such important sound properties as belonging to families of strings, woodwind and brass instrumental timbres. The skewness parameter is shown to be closely related to the bicoherence function calculated over the original signal and as such it is succinct to an interpretation as statistical test for the signal conforming to a linear non Gaussian model. The above results are compared to the Hinich bispectral tests for Gaussianity and non Linearity of time series and exhibit a similar classiication results. Finally, regarding the higher order statistics of a signal as a feature vector, a statistical distance measure for the cumulant space is suggested.