Subtractive synthesis technique

In prior chapters we looked at subtractive synthesis techniques, such as modal synthesis (Chapter 4) and linear predictive coding (Chapter 8). In these methods a complex source is used to excite resonant fQters. The source usually has a flat spectnun, or exhibits a simple roll-off pattern like f or ip (6 dB or 12 dB per octave). The filters, possibly time-varying, shape the spectrum to model the desired sound. 

We can divide synthesis techniques into four basic categories Additive (Linear), Subtractive, Nonlinear and Physical modeling. Synthesis algorithms depend critically on the implementation of oscillators. For example, in the implementation of Frequency Modulation (F.M.), the output of one oscillator will serve as the input to another. Since the number of real time oscillators depends on the number of simple oscillators, it is important to efficiently and speedily implement the realizations. 

In prior chapters we found that spectral shape is important to our perception of sounds, such as vowel/consonant distinctions, the different timbres of the vowels eee and ahh, etc. We also discovered that sinusoids are not the only way to look at modeling the spectra of sounds (or soimd components), and that sometimes just capturing the spectral shape is the most important thing in parametric sound modeling. Chapters 5 and 6 both centered on the notion of additive synthesis, where sinusoids and other components are added to form a final wave that exhibits the desired spectral properties. In this chapter we will develop and refine the notion of subtractive synthesis and discuss techniques and tools for calibrating the parameters of subtractive synthesis to real sounds. The main technique we will use is called Linear Predictive Coding (LPC), which will allow us to automatically fit a low-order resonant filter to the spectral shape of a sound. 

Subtractive synthesis uses a complex source wave—such as an impulse, a periodic train of impulses, or white noise—to excite a spectral-shaping filter. Linear prediction, or linear predictive coding (LPC), gives us a mathematical technique for automatically decomposing a sound into a source and a filter. For low order LPC (6-20 poles or so), the filter is fit to the coarse spectral... 

The resynthesis process results from two simultaneous synthesis processes one for sinusoidal components and the other for the noisy components of the sound (Figure 3.15). The sinusoidal components are produced by generating sinewaves dictated by the amplitude and frequency trajectories of the harmonic analysis, as with additive resynthesis. Similarly, the stochastic components are produced by filtering a white noise signal, according to the envelope produced by the formant analysis, as with subtractive synthesis. Some implementations, such as the SMS system discussed below, generate artificial magnitude and phase information in order to use the Fourier analysis reversion technique to resynthesise the stochastic part. 

These techniques can be broadly split into two groups, the first of which can be represented by pooling methods, where deconvolution is obtained via various chemical steps, run in parallel or after the library synthesis. Pooling methods normally require multiple synthesis of many library members, including inactive individuals, in different pool formats. They are not single bead methods, so they are independent from analytical methods for structure determination. This group includes iterative deconvolution, recursive deconvolution, subtractive deconvolution, positional scanning and mutational... 

Petcavich et al. (1978) employed IR subtraction techniques to elucidate the mechanism of the oxidative degradation of polychloroprenes at 60 °C. The spectra were taken at 60 2°C. The results lead to the conclusion that 1,2- and 3,4-structural irregularities are involved in the initial stage of the thermal oxidation of these compounds at 60 °C. In addition, a simple free radical mechanism seems to be consistent with the experimental results. The observed results suggest that polychloroprenes may be stabilized towards oxidative degradation by eliminating the 1,2- and 3,4-structures by chemical modification of the polymer after synthesis. 

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