Joint Source-Filter Estimation for Plucked-Guitar Tones

Motivation


Physical models for plucked string instruments can produce high-quality tones using a computationally efficient implementation, but the estimation of model parameters through the analysis of audio remains problematic. Moreover, an accurate representation of the expressive aspects of a performance requires a separation of the performer’s articulation (source) from the instrument’s response (filter). This research explores a physically-inspired signal model for plucked guitar sounds that facilitates the estimation of both string excitation and resonance parameters simultaneously. We present the application of the joint source-filter model in an analysis-synthesis framework to plucked-guitar recordings, and we demonstrate that our system is particularly adept at capturing and replicating the characteristic sounds resulting from various plucking styles. By explicitly modeling string articulations, we believe this system provides insight towards capturing the expressive intentions of a performer from the audio signal alone.

Model overview



There are many models capable of realistic synthesis of plucked guitar tones, however, we desire a model that is both computationally efficient for synthesis applications and has some correlation to the physical aspects of playing the guitar. We chose the so-called single delay-loop (SDL) structure shown in the figure below since it represents sound production on the guitar as a source-filter interaction. The source-filter model correlates well with actual guitar performance since the model excitation, p(n), represents the player string interaction while the feedback loop in the SDL represents the resonant behavior of the string. It is now our job to estimate the optimal source and filter parameters for accurate modeling.

Joint estimation


Existing techniques for extracting the model parameters from the figure above rely on offline calibration. We feel that accurate modeling of the expressive characteristics of a plucked string requires simultaneously accounting for the variation of source and filter parameters. Thus, we choose to jointly model the source by minimizing the "model error". The model error consists of the difference between an assumed "correct" model for the excitation and the residual obtained by inverse filtering the pluck sample with the filter.

Excitation modeling



By examining the residual signals obtained from previous model calibration techniques, we observe that the excitation signals contain well-defined contours due to the reflections of traveling waves along the string with smooth transitional regions. Our excitation model, therefore, consists of determining the appropriate boundaries so that we can fit polynomial functions to capture the contours of the various excitations. Thus, the excitation model consists of a piecewise polynomial function, where the order and number of segments must be determined.

Solving the convex optimization problem


We solve the joint estimation problem by forming a convex optimization based on the different between the excitation model and the residual obtained by inverse filtering. The parameters to be estimated consists of the polynomial coefficients for the excitation model and the coefficients of the SDL structure.

Results


Now, we present some preliminary results using our approach. The figures below were obtained by analyzing the the open, 3rd string of an electric guitar excited with a pick at medium strength.

In the panel to the right, we have a recorded, plucked string sample plotted with the residual obtained by inverse filtering with the estimated filter. The segment boundaries are also marked.
The re-synthesized plucked guitar tone and excitation signal using the estimated model parameters are shown in the panel to the right. We observe that the contours of the plucked-sample are well represented by our modeling approach.
The error between the original and re-synthesized input and output signals is shown in the right panel.

Sound Clips


Below are some selected sound clips produced using our joint analysis-synthesis method. Please check back as we will continue to update them as we refine our scheme.

String Fret Pluck Type Strength Original Clip Synthesized Clip
1 0 Pick Medium Listen Listen
1 0 Pick Soft Listen Listen
1 0 Thumb Medium Listen Listen
1 0 Thumb Soft Listen Listen
2 0 Pick Medium Listen Listen
2 0 Pick Soft Listen Listen
2 0 Thumb Medium Listen Listen
2 0 Thumb Soft Listen Listen
3 0 Pick Medium Listen Listen
3 0 Pick Soft Listen Listen
3 0 Thumb Medium Listen Listen
3 0 Thumb Soft Listen Listen
4 0 Pick Medium Listen Listen
4 0 Pick Soft Listen Listen
4 0 Thumb Medium Listen Listen
5 0 Pick Soft Listen Listen
5 0 Thumb Medium Listen Listen
5 0 Thumb Soft Listen Listen