Signal synthesis from the Modal Distribution using minimum phase

The Modal Distribution (MD) is a time-frequency distribution specifically designed to model the quasi-harmonic, multisinusoidal, nature of music signals and belongs to the Cohen general class of time-frequency distributions. Signal synthesis from bilinear time-frequency representations such as the Wigner distribution has been based on methods which exploit an outer-product interpretation of these distributions [1, 2]. Methods of synthesis from the MD based on a sinusoidal-analysis-synthesis procedure using estimates of instantaneous frequency and amplitude only have been investigated in [3, 4, 5]. However, the modal distribution is basically a subsampled version of the smoothed pseudo Wigner distribution and thus does not lend itself easily to direct inversion such as in the outer product methods mentioned above. Furthermore, the modal distribution is real, and the above sinusoidal-analysis-synthesis methods rely on phase estimated as the integral of instantaneous frequency. In this paper, we show that in some cases, this synthesis results in a roughness or phasiness in the synthesized signal and demonstrate that using minimum phase derived from the magnitude spectrum of the distribution produces a timbre closer to the original in the case of certain brass sounds. Suggestions for future work are also given.