Download Using the Distribution Derivative Method to Model Acoustic Musical Instrument Sounds with Polynomial AM-FM Sinusoids The oscillatory modes of musical instrument sounds are commonly modeled with time-varying sinusoids. Several estimation methods model quasi-stationary oscillations accurately, yielding a high-quality representation. However, nonstationary oscillations such as attack transients are still very challenging to model accurately. In this work, we propose to model musical instrument sounds with polynomial modulation sinusoids (PMS) estimated with the distribution derivative method (DDM). DDM gives accurate parameter estimations for PMS with arbitrary order, allowing great flexibility in modeling temporal changes inside analysis frames as amplitude and frequency modulations. We used 39 musical instrument sounds to compare DDM objectively against the standard (SM+) and an adaptive sinusoidal model (eaQHM) using time and frequency error measures. We showed that DDM captures more oscillatory energy than SM+ or eaQHM by modeling PMS more accurately. A MUSHRA listening test with 18 selected sounds confirmed that DDM has higher perceptual quality than both SM+ and eaQHM and that DDM is almost perceptually indistinguishable from the original sounds.