Physically Informed Subtraction of a String's Resonances from Monophonic, Discretely Attacked Tones : a Phase Vocoder Approach

A method for the subtraction of a string's oscillations from monophonic, plucked- or hit-string tones is presented. The remainder of the subtraction is the response of the instrument's body to the excitation, and potentially other sources, such as faint vibrations of other strings, background noises or recording artifacts. In some respects, this method is similar to a stochastic-deterministic decomposition based on Sinusoidal Modeling Synthesis [MQ86, IS87]. However, our method targets string partials expressly, according to a physical model of the string's vibrations described in this thesis. Also, the method sits on a Phase Vocoder scheme. This approach has the essential advantage that the subtraction of the partials can take place \instantly", on a frame-by-frame basis, avoiding the necessity of tracking the partials and therefore availing of the possibility of a real-time implementation. The subtraction takes place in the frequency domain, and a method is presented whereby the computational cost of this process can be reduced through the reduction of a partial's frequency-domain data to its main lobe. In each frame of the Phase Vocoder, the string is encoded as a set of partials, completely described by four constants of frequency, phase, magnitude and exponential decay. These parameters are obtained with a novel method, the Complex Exponential Phase Magnitude Evolution (CSPME), which is a generalisation of the CSPE [SG06] to signals with exponential envelopes and which surpasses the nite resolution of the Discrete Fourier Transform. The encoding obtained is an intuitive representation of the string, suitable to musical processing