Model Parameter Estimation

The important problem of parameter estimation for computational models can be considered to intersect with the field of system identification [103,151]. Some references pertaining to model parameter identification from measured acoustic data are summarized below, roughly in chronological order.

Applications of methods for digital filter design and system identification to violin modeling were developed in [151], and an expanded paper regarding filter design over a Bark scale is given in [163]. A review paper on frequency-warped signal processing for audio applications is given in [69].

An interesting combined linear and nonlinear approach to modeling woodwinds by Cook and Scavone [36,137] still appears promising today.

A method for estimating traveling-wave components from multiple non-uniformly spaced measurements of physical pressure in a bore was described in [167].

Methods for designing piano-string dispersion filters were reviewed and extended in [127], and recent relevant work includes [7,20,19,22,84,98].

In his 1996 thesis [148], Sharp describes his system for measuring horn reflectance via acoustic pulse reflectometry. This technique has been used to obtain data, e.g., for calibrating trumpet models [188].

Computational models of woodwind toneholes have been developed Scavone et al. [138,139,140,187,141,165] based on models from musical acoustics by Keefe [90,91]. More recent work on the musical acoustics of woodwind tone holes has been carried out by Dubos et al. [52] and Nederveen et al. [113], and experimental verifications have been conducted by Dalmont et al. [45,46]. A novel filter architecture and associated design procedure for acoustic tube loss modeling is described by Abel et al. [1].

Methods for the identification of control parameters for a trumpet model from the acoustic waveform (``model inversion'') have been developed by Hélie, D'haes, and Rodet, et al. [73,50,51].

In the Laboratory of Acoustics and Audio Signal Processing at the Helsinki University of Technology, many techniques have been developed for identifying the parameters of physical models of musical instruments. Most of these are available on their website (http://www.acoustics.hut.fi). Publications from this lab include [178,177] (calibration of a guitar synthesizer), [54] (acoustical analysis and model-based sound synthesis of the kantele), [12,13] (piano modeling, loss-filter design), [85] (bell-like sounds), [83] (audibility of string partial overtone tuning), and [175] (clavichord modeling).

It is generally very difficult to measure the dynamic frictional contact between a bow and string. However, it has recently been done indirectly by Woodhouse, Schumacher, and Garoff [204]. In this research, a digital waveguide model is inverted to estimate the friction force on the string by the bow, as well as the string velocity at the bowing point.

CCRMA Ph.D. student Krishnaswamy has recently developed an effective method for identifying selected control parameters in violin performance from measured audio spectra [95]. The idea of the method is to develop a forced classification scheme based on short-time power spectra indexed by pitch class. In other words, for each pitch class, a small linear-discriminant-analysis database is developed which returns the estimated playing parameters (bow position, which string was played, whether plucked or bowed) as a function of the measured power spectrum. Related work on estimating the plucking point along a guitar string based on recorded acoustic data was carried out by Traube et al. [173].

Derveaux and Chaigne have developed detailed time-domain simulations of the acoustic guitar [49], including finite element models of the guitar body as well as the surrounding air. Such detailed numerical simulations, while computationally demanding, can enable ``virtual acoustic experiments'' that can be used to calibrate simpler real-time methods along the lines discussed above. See also [199,200].