Innuence of Frequency Modulating Jitter on Higher Order Moments of Sound Residual with Applications to Synthesis and Classiication
In this paper we provide a simple model for musical sounds that accounts for timbre properties due to mi-croouctuations in the harmonics of the signal. When considering a sound model that consists of an excita-tion signal passing through a resonator lter, we nd, by means of higher order statistical analysis of the ex-citation, a grouping of sounds according to common instrumental families of string, woodwind and brass sounds. For resynthesis purposes we model the exci-tation by a family of stochastic, pulse train like functions whose statistical properties resemble those found in real signals. By introducing an idea of \eeective 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 4th moments of the residual. Musically speaking we suggest that microouctuations 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.