Deriving the plucking point location along a guitar string from a least-square estimation of a comb filter delay

This paper focuses on the extraction of the excitation point location on a guitar string by an iterative estimation of the structural parameters of the spectral envelope. In a simple digital physical model of a plucked-string instrument, the resonant modes translate into an all-pole structure while the initial conditions (a triangular shape for the string and a zero-velocity at all points) result in a FIR comb filter structure. The delay D of the comb filter can be expressed as the product of the relative plucking position R and the fundamental period T_o. We propose a general method to estimate the plucking point location, working into two stages: starting from a measure related to the autocorrelation of the signal as a first approximation, a least-square estimation is used to refine the comb filter delay value to better fit the measured spectral envelope.