Influence of Frequency Modulating Jitter on Higher Order Moments of Sound Residual with Applications to Synthesis and Classification

In this paper we provide a simple model for musical sounds that accounts for timbre properties due to microfluctuations in the harmonics of the signal. When considering a sound model that consists of an excitation signal passing through a resonator filter, we find, by means of higher order statistical analysis of the excitation, a grouping of sounds according to common instrumental families of string, woodwind and brass sounds. For resynthesis purposes we model the excitation by a family of stochastic, pulse train like functions whose statistical properties resemble those found in real signals. By introducing an idea of "effective number of harmonics" that represents the number of coupled, or statistically dependent harmonics among the complete set of partials present in the signal, we show that this number can be calculated directly form the 3rd and J^th moments of the residual. Musically speaking we suggest that microfluctuations administer a sense of texture within timbre and these texture properties depend upon the concurrence/non concurrence parameter of the random frequency deviations caused by the jitter.