Sinusoidal modeling stands out among the techniques used to represent and transform musical instrument sounds and speech due to the fidelity and flexibility of the representation. In essence, sinusoidal analysis models each partial with a time-varying sinusoid, capturing temporal variations in amplitude, frequency and phase. However, the sounds of musical instruments and speech also contain transients and noise, which are important in musical instrument sound and speech perception. Transients are poorly represented as stationary oscillations (i.e., by slowly-varying
sinusoids) and noise commonly requires a separate model. We have been investigating the representation of the oscillatory modes of musical instruments with adaptive (nonstationary) sinudoids. Adaptation of the sinusoids inside the analysis window allows representation of both transients and stationary oscillations preserving sharp onsets and presenting very little residual.