About sinusoidal models

The family of techniques known as sinusoidal models use this as their basic building block and performs speech modification by finding the sinusoidal components for a waveform and performing modification by altering the parameters of the above equation, namely the amplitudes, phases and frequencies. It has some advantages over models such as TD-PSOLA in is that it allows adjustments in the frequency domain. While frequency domain adjustments are possible in the linear prediction techniques, the sinusoidal techniques facilitate this with far fewer assumptions about the nature of the signal and in particular don t assume a source and all-pole filter model. 

Industrial experience with the three-phase MR is limited, since only few large-scale industrial plants are running in the world today. Very little has been published about these industrial reactors and reactor scale-up. Also, most modeling has been done on cylindrical channel geometry, while most industrial reactors use sinusoidal or square geometry. Hence this chapter mainly summarizes our own experience with three-phase monolith reactors, with limited reference to the literature. 

The result is exactly as expected from the vector model a pulse about the x-axis rotates z-magnctization towards the -> -axis, with a sinusoidal dependence on the flip angle, /. ... 

All carbon-carbon bonds in the skeleton have 50% double bond character. This fact was later confirmed by X-ray diffraction studies. A simple free-electron model calculation shows that there is no energy gap between the valence and conduction bands and that the limit of the first UV-visible transition for an infinite chain is zero. Thus a simple free-electron model correctly reproduces the first UV transition with a metallic extrapolation for the infinite system. Conversely, in the polyene series, CH2=CH-(CH=CH) -CH=CH2, he had to disturb the constant potential using a sinusoidal potential in order to cover the experimental trends. The role of the sinusoidal potential is to take into account the structural bond alternation between bond lengths of single- and double-bond character. When applied to the infinite system, in this type of disturbed free-electron model or Hiickel-type theory, a non-zero energy gap is obtained (about 1.90 eV in Kuhn s calculation), as illustrated in Fig. 36.9. 

In Chapter 4, we developed the notion that individual resonant filters can be used to model each vibrational mode of a system excited by an impulse. Thus, modal synthesis is a form of subtractive synthesis. For modeling the gross peaks in a spectrum, which could correspond to resonances (although these resonances are weaker than the sinusoidal modes we talked about in Chapter 4), we can exploit the resonance-factored form of a filter to perform our subtractive synthesis. The benefits of this are that we can control the resonances (and thus, spectral shape) independently. The filter can be implemented in series or cascade (chain of convolutions) as shown in Figure 8.4. The filter can also be implemented in parallel (separate subband sections of the spectrum added together), as shown in Figure 8.5. 

The cold crystallization starts at about 400 K at a supercooling not affected by modulation and registers as nonreversing. For separation of such nonreversing transitions, several modulation periods must occur across the transition, otherwise the pseudo-isothermal analysis would not develop the proper sinusoidal oscillations about , as can be seen from the modeling in Figs. 4.100-102 (loss of stationarity). 

The first term in the above equation represents the rate of osteoblast transformation into osteocjrtes, and the last term represents Ae rate of deaA of osteocytes. Reddy and Joshi (1987) simulated the stochastic compartmental model of bone cells in which Ae equation for the population means are the same as Ae above equations. In adAticm, the stochastic analysis provides information about the variations and covariences of cellular populations. Figure 1.5 shows the normalized number of osteoblasts plotted as a fimction of age of Ae mdividual when C, and are assumed to be sinusoidal... 

Impedance is an essential characterization of the current intensity response of the corrosion system to the sinusoidal perturbation of the potential applied to the metal. The results of impedance measurements made in a suitably wide range of frequencies provide valuable information about the system and electrochemical corrosion occurring therein. The majority of electrochemical as well as physical processes can be interpreted within the impedance spectroscopy method as elements of electrical circuits with appropriate time constants. Thus, to interpret the results of electrochemical impedance measurements surrogate models of electrical circuits, known as Randles models, can be used. 

Suppose flow rate W2 is varied sinusoidally about a constant value, while the other inlet conditions are kept constant at their nominal values that is, wi(t) = x[(t) = 0. Because wiit) is sinusoidal, the output composition deviation x t) eventually becomes sinusoidal according to Eq. 5-26. However, there is a phase shift in the output relative to the input, as shown in Fig. 14.1, owing to the material holdup of the. tank. If the flow rate W2 oscillates very slowly relative to the residence time t(co 1/t), the phase shift is very small, aiyroaching 0°, whereas the normalized amplitude ratio(A/KA) is very nearly unity. For the case of a low-frequency input, the output is in phase with the input, tracking the sinusoidal input as if the process model were G s) = K. 

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