Acoustic modeling

Some experiments outlined the frequency dependence of phonon scattering on surfaces [74]. Thus, Swartz made the hypothesis that a similar phenomenon could take place at the interface between solids and proposed the diffuse mismatch model [72]. The latter model represents the theoretic limit in which all phonons are heavily scattered at the interface, whereas the basic assumption in the acoustic mismatch model is that no scattering phenomenon takes place at the interface of the two materials. In the reality, phonons may be scattered at the interface with a clear reduction of the contact resistance value as calculated by the acoustic model. 

The two score plots in Figures 9.12 and 9.13 show similar trends for process data and acoustic data. A plot of score T1 for the acoustic model and T1 for the process data can be seen in Figure 9.14. 

In general, these traditional process monitoring data are more variable than their smoother acoustic chemo-metric counterparts. The latter are in general also more informative compare for example the score plot for the process data in Figure 9.16, in which the sudden drop in the airflow rate cannot be seen, to the score plot for the acoustic data (Figure 9.15). A plot of T2 for the acoustic model and T2 for the process data can be seen in Figure 9.17. 

Figure 9.17 Synoptic comparison of PC2 evoiution. T2 for acoustic model and T2 for process data 28 February 2001. The score vectors were normalized for easier interpretation.

Physical Modelling. The last method of synthesis, physical modeling, is the modeling of musical instruments by their simulating their acoustic models. One popular model is the acoustic transmission line (discussed by Smith in his chapter), where a non-linear source drives the transmission line model. Waves are propagated down the transmission line until discontinuities (represented by nodes of impedance mismatches) are found and reflected waves are introduced. The transmission lines can be implemented with lattice filters. 

Also, sampling and synthesis both can produce novel instrument sounds that have not been heard before, breaking away from traditional acoustical models. 

The mathematical formulation of seismic forward and inverse problems in the simplest case of an acoustic model in the frequency domain is given by equation (1.25), which we will repeat here for convenience ... 

Consider now a 3-D acoustic model with the arbitrary distribution of the wavespeed c (r) given by the formula... 

The torsional oscillation about axial C bonds in pol q5ropylene is predicted to occur at about 100 cm (/P). A weak peak, observed at 100 cm, decreased in intenaty rapidly with both increasing temperature and increasing tacticity, as would be expected for an acoustic model. The axial torsion is a cooperative vibration involving many monomer units it would be expected to be strongly affected by the 2 ... 

J. 0. Smith. Acoustic Modeling Using Digital Waveguides. In Musical Signal Processing, edited by Roads et al. Netherlands Swets and Zeitlinger, 1997. 

Furthermore, when we come to performing a bottom up analysis, where we wish to describe the continuous contour with a discrete set of linguistic units, we find the mapping even more complicated. Because of these problems, it is nearly universal to use some sort of acoustic model which acts as an interim representation between the abstract intonational form and the FO contour. This model has a fixed number of parameters per unit, and so we can use one of the standard mapping algorithms (such as CART) to generate these parameters from the intonational form ... 

While it is possible to build synthesis algorithms with any of the models outlined in Section 9.3.3, we will focus our attention on the most popular techniques, which divide into those based on AM models (described here) and those based on acoustic models (described next). 

Section 9.5. Intonation S5Tithesis with Deterministic Acoustic Models... 

While many of the AM models and deterministic acoustic models provide useful and adequate representations for intonation, the trend is clearly towards the data driven techniques described in Section 9.6. These have several advantages besides bypassing the thorny theoretical issues regarding the true nature of intonation, they have the ability to automatically analyse databases, and in doing are also inherently robust against any noise that can occur in the data, whether it be from errors in finding FO values or from other sources. 

The acoustic models, such as Tilt and Fujisaki, have synthesis algorithms built-in and hence S3mthesis is fairly trivial with these. 

Alwan, a., Narayanan, S., and Maker, K. Towards articulatory-acoustic models for liquid consonants based on MRl and EPG data, part 11 The rhotics. Journal of the Acoustical Society of America 10 f 2 (1997), 1078-1089. 

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