Audio Signal Processing and Coding

9.6 THE SINES + TRANSIENTS + NOISE (STN) MODEL

Although the basic sinusoidal model (Eq. (9.1)) can achieve very efficient representations of some signals (e.g., sustained vowels via harmonically related components), extensions to the basic model have also been proposed to deal with other signals containing significant nontonal energy that can lead to modeling inefficiencies. A viable model for many musical signals is one of a deterministic plus a stochastic component. The deterministic part corresponds to the pitched part of the sound, and the stochastic part accounts for intrinsically random musical characteristics such as breath noise or bow noise. The spectral modeling and synthesis system (SMS) [Serr89] [Serr90] treats audio as the sum of a collection of K sinusoids (“partials”) with time-varying parameters, (Eq. (9.1)), with the addition of a stochastic component, e(n), i.e.,

Figure 9.6. FM synthesis coding scheme (after [Wind98]).

where A_k represents the amplitude, ω_k(n) represents the instantaneous frequency, and ϕ_k(n) represents the instantaneous phase of the k-th sinusoid. Different parametric models for the stochastic component have been proposed, such as parametric noise spectral envelopes [Serr89] or parametric Bark-band noise [Good96]. Other investigators have constructed ...