Analysis and Resynthesis of Quasi-harmonic Sounds: an Iterative Filterbank Approach

We employ a hybrid state-space sinusoidal model for general use in analysis-synthesis based audio transformations. This model, which has appeared previously in altered forms (e.g. [5], [8], perhaps others) combines the advantages of a source-filter model with the flexible, time-frequency based transformations of the sinusoidal model. For this paper, we specialize the parameter identification task to a class of “quasi-harmonic” sounds. The latter represent a variety of acoustic sources in which multiple, closely spaced modes cluster about principal harmonics loosely following a harmonic structure (some inharmonicity is allowed.) To estimate the sinusoidal parameters, an iterative filterbank splits the signal into subbands, one per principal harmonic. Each filter is optimally designed by a linear programming approach to be concave in the passband, monotonic in transition regions, and to specifically null out sinusoids in other subband regions. Within each subband, the constant frequencies and exponential decay rates of each mode are estimated by a Steiglitz-McBride approach, then time-varying amplitudes and phases are tracked by a Kalman filter. The instantaneous phase estimate is used to derive an average instantaneous frequency estimate; the latter averaged over all modes in the subband region updates the filter’s center frequency for the next iteration. In this way, the filterbank structure progressively adapts to the specific inharmonicity structure of the source recording. Analysissynthesis applications are demonstrated with standard (time/pitchscaling) transformation protocols, as well as some possibly novel effects facilitated by the “source-filter” aspect.