Automatic Partial Extraction from the Modal Distribution

The Modal Distribution (MD) is a time-frequency distribution specifically designed to model the quasi-harmonic, multi-sinusoidal, nature of music signals and belongs to the Cohen general class of time-frequency distributions. The problem of signal synthesis from bilinear time-frequency representations such as the Wigner distribution has been investigated [1,14] us-ing methods which exploit an outer-product interpretation of these distributions. Methods of synthesis from the MD based on a sinusoidal-analysis-synthesis procedure using estimates of in-stantaneous frequency and amplitude values have relied on a heuristic search ‘by eye’ for peaks in the time-frequency domain [2,7,8]. An approach to detection of sinusoidal components with the Wigner Distribution has been investigated in [15] based on a comparison of peak magnitudes with the DFT and STFT. In this paper we propose an improved frequency smoothing kernel for use in MD partial tracking and adapt the McCauley-Quatieri sinusoidal analysis procedure to enable a sum of sinusoids synthe-sis. We demonstrate that the improved kernel enhances automatic partial extraction and that the MD estimates of instantaneous amplitude and frequency are preserved. Suggestions for future extensions to the synthesis procedure are given