Deterministic synthesis models

The analysis/synthesis system which corresponds to the deterministic/stochastic model is similar to the baseline sine-wave analysis/synthesis system. The primary differences he in the frequency matching stage for extraction of the deterministic component, in the subtraction operation to obtain the residual (stochastic component), and in the synthesis of the stochastic component. 

A deterministic mathematical model for simulating the biotechnological synthesis of acrylic acid was developed in a previous study [3] to explore an alternative process. The proposed... 

Intonation Synthesis with Deterministic Acoustic Models... 

Intonation synthesis with deterministic acoustic models... 

Serra and Smith, 1989] Serra, X. and Smith, J. (1989). Spectral modeling synthesis A sound analysis/synthesis system based on a deterministic plus stochastic decomposition. In Proc. oflnt. Computer Music Conf., pages 281-284, San Francisco, CA. 

A simplification of the glycolytic and respiratory routes considered in the deterministic model to represent bioethanol synthesis is shown below by stoichiometric expressions. More details of the kinetics can be found in Stremel [8]. 

The notion of sines plus noise modeling was posed and implemented by Xavier Serra and Julius Smith in the Spectral Modeling Synthesis (SMS) system. They called the sinusoidal components the deterministic component of the signal, and the leftover noise part the residual or stochastic component. Figure 6.12 shows the decomposition of a sung ahh sound into deterministic (harmonic sinusoidal) and stochastic (noise residue) components. 

Xavier Serra and Julius O. Smith. Spectral Modeling Synthesis A Sound Analysis/ Synthesis System Based on a Deterministic Plus Stochastic Decomposition. Computer Music Journal 14(4) 12-24 (1990). 

Laperriere L, Ghie W, Desrochers A (2002) Statistical and deterministic tolerance analysis and synthesis using a unified Jacobian-Torsor model. Ann CIRP 51(1) 417 20... 

Prominence prediction by deterministic means is actually one of the most successful uses of non-statistical methods in speech synthesis. This can be attributed to a number of factors, for example the fact that the rules often don t interact or the fact that many of the rules are base on semantic features (such that even if we did use a data driven technique we would still have to come up with the semantic taxonomy by hand). Sproat notes [410] that statistical approaches have had only limited success as the issue (especially in compound noun phrases) is really one of breadth and not modelling regardless of how the prominence algorithm actually works, what it requires is a broad and exhaustive list of examples of compound nouns. Few complex generalisations are present (what machine learning algorithms are good at) and once presented with an example, the rules are not difficult to write by hand. 

It is now common practice, for verification as well as for synthesis purposes, to take the deterministic Mealy finite state machine (FSM hereafter for short) as abstract model for clock-synchronized circuits described at the register transfer level. The model is based on the following hypotheses ... 

A main distinction has been made between deterministic and stochastic modeling techniques. A further distinction has been proposed based on the scale for which the mathematical model must be derived (eg, micro-, meso-, and/or macroscale). Notably, the complexity of the model approach depends on the desired model output. Detailed microstractural information is only accessible using advanced modeling tools but these are associated with an increase high in computational cost. The advanced models allow one to directly relate macroscopic properties to the polymer synthesis procedure and, thus, to broaden the application market for polymer products, based on a fundamental understanding of the polymerization kinetics and their link with polymer processing. 

The paper then focusses on 2 recent developments, namely response surface methods (RSM) and component mode synthesis (CMS). The former is a strategy to approximate the real structural behaviour as modelled by repeated finite element calculations by a response surface model that interpolates for structural response between well-chosen settings of uncertain parameters. The latter is an established theory for modelling structural dynamics using superelements. The paper extends the deterministic CMS to models with fuzzy uncertain parameters in the superelements. 

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