Pitch variations

Before attempting to develop any theory correlating molecular to cholesteric handedness, one must be completely sure of the experimental data. A cholesteric phase is fully described by its handedness and pitch, and often also knowledge of the pitch variations with temperature is fundamental. In particular, the determination of the handedness is quite a delicate matter. Before discussing the methods currently used to determine handedness and pitch, the principal textures of the cholesteric phase must be briefly reviewed The planar or Grandjean textures are obtained in thin cells by rubbing the cell walls (with... 

Another model which is a strong candidate for musical signals is the sinusoidal model, which has been used effectively for speech applications ([McAulay and Quatieri, 1986b] and chapter 9 of this book). A constrained form of the sinusoidal model is implicitly at the heart of short-time spectral attenuation (STSA) methods of noise reduction (see section 4.5.1). The model is also a fundamental assumption of the pitch variation algorithms presented in section 4.6. In its general form the signal can be expressed as ... 

Consider a fixed-frequency sinusoidal component (/) = sin(wojt + 00 ) from a musical signal, distorted by a pitch variation function p,v(t). The pitch-distorted component x,(t) can be written as (see [Godsill, 1993]) ... 

Figure 4.21 Estimated (full line) and true (dotted line) pitch variation curves generated for example Viola. (Reprinted with permission from [Godsill, 1994], 1994, IEEE)...

The second stage of processing involves extracting smooth pitch variation information from the time-frequency tracks. For the th block of data there will be Pn frequency estimates corresponding to the P tonal components which were being... 

In this procedure it is assumed that musical signals are made up as additive combinations of tones (sinusoids) which represent the fundamental and harmonics of all the musical notes which are playing. Since this is certainly not the case for most non-musical signals, we might expect the method to fail for, say, speech extracts or acoustical noises. Fortunately, it is for musical extracts that pitch variation defects are most critical. The pitch variation process is modelled as a smoothly varying waveform with no sharp discontinuities, which is reasonable for most wow generation mechanisms. 

Godsill, 1994] Godsill, S. J. (1994). Recursive restoration of pitch variation defects in musical recordings. In Proc. IEEE Int. Conf. Acoust., Speech and Signal Proc, volume 2, pages 233-236, Adelaide, Australia. 

A pair of screw elements is conveying if the flat profiles are extended into the third dimension by helical rotation. In this case, we speak of screw elements. The pitch T of the element is another important dimension here. In today s modular screws, individual elements each have a constant pitch and a pitch variation is achieved by using different types of element. 

A large k z/ki 1 ratio also permits a greater tolerance of pitch variations for a given cell gap. 

Figure 17.6 Pressure control by condensing medium flow variations, (a) Liquid coolant (5) refrigeration coolant, level control (c) refrigeration coolant, outlet flow control (d) air coolant, fan motor speed or fan pitch variation (e) turboexpander inlet guide vanes variation.

Many works deal with the variation of the helicoidal pitch in cholesteric phases as a function of temperature and composition. The best way to elucidate the origin of the twist seems to be to compare the pitch variations in lyotropic and in thermotropic systems. The first accurate work in this field is due to Robinson (1958-66) who studied PBLG (polybenzyl-L-glutamate) a synthetic polypeptide in organic solvents as dioxane, ethylic alcohol, chloroform etc. and Cano (1967) who made measurements of the pitches of nematic paraazoxyphenetol with different amounts of cholesterol benzoate. 

The frequency shift is usually in the audible range and can be detected by an audible pitch variation or can t plotted graphically. 

We notice that all the observed phase-matching peaks had widths greater than those predicted theoretically for a monochromatic laser and a perfect liquid-crystal sample. In the latter case, the full width at half-maximum of a phase-matching peak in terms of pitch variation would be given by... 

Figure 23 Sketch of the information recording on the pianariy oriented poiymeric LC fiims with the iocai pitch variation. and P2 are pitches of the heiix P2 > Pi is the axis of the heiix.

For electric fields which are not extreme, however, intermediate structures must exist between the spherical and planar solutions. The transition induced by the field has been observed to be continuous. In first approximation the helical structure of the cholesteric is considered to be unaltered, so new chiral surfaces have to be found that would then give the intermediate structure in a weak electric field. Flattened ellipsoids qualify as a natural generalization of the spheres (Figure 12.9(a)), but unfortunately such chiral surfaces are not equidistant, resulting in pitch variations. In first approxi-... 

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