Residual minimization in a musical signal model based on a deterministic plus stochastic decomposition

Spectral modeling synthesis (SMS) is a spectrum modeling technique that models time‐varying spectra as (1) a collection of sinusoids controlled through time by piecewise linear amplitude and frequency envelopes (the ‘‘deterministic’’ part), and (2) a time‐varying filtered noise component (the ‘‘stochastic’’ part). This technique has proved to give general, high quality transformations for a wide variety of musical signals. As part of the analysis process of SMS the deterministic component is subtracted in the time domain from the original sound resulting into a residual signal. For a good deterministic‐stochastic decomposition this residual should be free of the partials of the analyzed sound and a minimization criteria of the residual can be establish to measure the quality of the decomposition. There are many control parameters in the analysis process and their impact in the synthesized sound can be measured numerically by studying their effect on the residual. This paper will discuss the effect that pa...