Evaluating how well filtered white noise models the residual from sinusoidal modeling of musical instrument sounds

Nowadays, sinusoidal modeling commonly includes a residual obtained by the subtraction of the sinusoidal model from the original sound. This residual signal is often further modeled as filtered white noise. In this work, we evaluate how well filtered white noise models the residual from sinusoidal modeling of musical instrument sounds for several sinusoidal algorithms. We compare how well each sinusoidal model captures the oscillatory behavior of the partials by looking into how “noisy” their residuals are. We performed a listening test to evaluate the perceptual similarity between the original residual and the modeled counterpart. Then we further investigate whether the result of the listening test can be explained by the fine structure of the residual magnitude spectrum. The results presented here have the potential to subsidize improvements on residual modeling.