Wavenumber spectra

Hughes BA, Grant GL, Chappell RW (1977) A fast response surface-wave slope meter and measured wind-wave moments. Deep-Sea Res 24 1211-1223 Hwang PA (1997) A study of the wavenumber spectra of short water waves in the ocean. Part II Spectral model and mean square slope. J Atm Oceanic Tech 14 1174-1186... 

Figure 2-17 Typical wavenumber spectra for a D = T/3 Rushton turbine with the blade passages removed. Parts (a) and (c) are taken at the tip of the impeller blades (r — 0.3T/2). Figures b) and (d) are in the discharge stream (0.7T/2). Parts a) and b) show only one component of the wavenumber spectrum, E x. Parts (c) and (d) show the transformation of the XX spectrum (smoother line) onto the measured yy and zz spectra. Local isotropy quickly penetrates to high wavenumbers. (From Michelet, 1998.)...

Seligson, 1970] Seligson, C. (1970). Comment on high-resolution frequency-wavenumber spectrum analysis . Proc. IEEE, 58 947-949. 

Theoretically, the function in Eq. 5.1-6 must be integrated between -oo and -l-oc. In practical IR spectroscopy, the integration can be carried out between i>o - 5 Ai>i/2 and zzo + 5 Ai>i/2. Here, Ai> is the halfwidth of the band. With modem equipment, the integrated intensities can be derived directly from the absorbance versus wavenumber spectrum. In general a peak area evaluation represents a summation of all absorbance values over the wavenumber range in which the band appears. Therefore the number of points in practical measurements depends on the wavenumber interval of the data and... 

The minimum number of data points for the created wavelength spectrum is equal to the number of data points found in the input wavenumber spectrum. The MCF defines the conversion properties in the high wavenumber end of the wavenumber spectrum, which is converted to the low wavelength end of the wavelength spectrum. 

Capon J (1969) High-Resolution Frequency-Wavenumber Spectrum Analysis. 

The appearance of an ATR spectrum is very subtly different to a transmission spectrum. Individual band shapes are slightly unsymmetric-al, but, more importantly, the intensity of the high-wavenumber spectrum (O-H and C-H stretches for instance) is significantly reduced. This cannot easily be avoided, as the ATR effect (equation (10.4)) shows that sampling depth is proportional to wavelength. However, this is not a... 

FIGURE 12.2B An NIR wavenumber spectrum of atactic poly(propylene) at low resolution (32 cm ). 

FIGURE 12.6B NIR wavenumber spectrum of poly(acrylic acid) at 32-cm resolution. 

FIGURE 12.8B NIR wavenumber spectrum of styrene-isoprene-styrene at (32-cm ) resolution. 

Turbulent blobs and their scalar counterparts are three dimensional, time-varying structures of arbitrary shape. They are represented by the wavenumber spectrum. Various portions of the spectrum, but not the whole spectrum, can be retained on scale-up. 

A continuum spectrum can be measured over a range of about 700 cm , the center frequency of which can be varied by changing the orientation of the crystal in the DFG. Single-beam spectra measured over two different ranges are shown in Figure 12.14b. (The fainter line above the higher wavenumber spectrum is the result of compensating for absorption by atmospheric water vapor.) Both the spatial resolution and the spectroscopic performance of this system were demonstrated in this paper. 

The equation of restriction can embody causality, lower boundedness of energies in the spectrum, positive wavenumber in the outgoing wave (all these in nonrelativistic physics) and interactions inside the light cone only, conditions of mass speciality, and so on in relativistic physics. In the case of interest in this... 

The principle of applying fuzzy logic to matching of spectra is that, given a sample spectrum and a collection of reference spectra, in a first step the reference spectra are unified and fuzzed, i.e., around each characteristic line at a certain wavenumber k, a certain fuzzy interval [/ o - Ak, + Afe] is laid. The resulting fuzzy set is then intersected with the crisp sample spectrum. A membership function analogous to the one in Figure 9-25 is applied. If a line of the sample spec-... 

In 1817, Josef Fraunhofer (1787-1826) studied the spectrum of solar radiation, observing a continuous spectrum with numerous dark lines. Fraunhofer labeled the most prominent of the dark lines with letters. In 1859, Gustav Kirchhoff (1824-1887) showed that the D line in the solar spectrum was due to the absorption of solar radiation by sodium atoms. The wavelength of the sodium D line is 589 nm. What are the frequency and the wavenumber for this line ... 

The detector must be sensitive to the radiation falling on it, and the spectrum is very often displayed on a chart recorder. The spectrum may be a plot of absorbance or percentage transmittance (IOO///0 see Equation 2.16) as a function of frequency or wavenumber displayed linearly along the chart paper. Wavelength is not normally used because, unlike frequency and wavenumber, it is not proportional to energy. Wavelength relates to the optics rather than the spectroscopy of the experiment. 

Figure 3.15 Wavenumber domain spectrum of a broad band source with a narrow absorption...

Make measurements of the transition wavenumbers in the rotational spectrum of silane from Figure 5.10 and hence determine the Si—H bond length. 

Because of fhe presence of heavy atoms in many inorganic molecules fhere may be several low-wavenumber vibrations. For tins reason if is generally more importanf fhan for organic molecules fo obfain fhe far-infrared or Raman spectrum. 

The Electromagnetic Spectrum. Electromagnetic radiation is characterized by its wavelength, L, frequency, v, or wavenumber, i), which are related by equation 2 ... 

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