Methods Based on Fourier Transform

Filter Diagonalization A Generalized Method Based on Fourier Transform. 

Finally, a quick, non-destructive method, based on Fourier transform near-infrared (FT-NIR) spectroscopy for egg content deteimination of dry pasta was presented by Fodor et al. (2011) with good results. 

Infrared spectroelectrochemical methods, particularly those based on Fourier transform infrared (FTIR) spectroscopy can provide structural information that UV-visible absorbance techniques do not. FTIR spectroelectrochemistry has thus been fruitful in the characterization of reactions occurring on electrode surfaces. The technique requires very thin cells to overcome solvent absorption problems. 

Infrared spectroelectrochemical methods, particularly those based on Fourier transform infrared (FTIR), can provide structural information that... 

In early work (8) we used infrared spectroscopy coupled with attenuated total reflection optics. This work was done before the availability of infrared equipment based on Fourier transform methods. Due to their relative speed these methods now permit in situ, real time measurements with a resolution of 1 sec or less (9), and continue to yield valuable data, particularly in the hands of the Battelle group in a series of studies dating from 1979 (10). In our early infrared work we had to be content to rinse and dry the surface before obtaining the infrared reflection spectrum Nevertheless the values of surface concentration were remarkably close to those determined more recently. Infrared studies of proteins suffer generally from the fact that the main features of protein spectra are similar for all proteins and therefore it is difficult to distinguish one from another. 

Recording of an IR spectrum of a sample based on Fourier Transform method has many advantages ... 

Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy. Attenuated total redectance (atr) ftir spectroscopy is based on the principle of total internal redection (40). Methods based on internal redection in the uv and visible regions of the spectmm are also common in addition to those in the ir region. The implementation of internal redection in the ir region of the spectmm provides a means of obtaining ir spectra of surfaces or interfaces, thus providing moleculady-specific vibrational information. 

A semiclassical description is well established when both the Hamilton operator of the system and the quantity to be calculated have a well-defined classical analog. For example, there exist several semiclassical methods for calculating the vibrational autocorrelation function on a single excited electronic surface, the Fourier transform of which yields the Franck-Condon spectmm [108, 109, 150, 244]. In particular, semiclassical methods based on the initial-value representation of the semiclassical propagator [104-111, 245-248], which circumvent the cumbersome root-search problem in boundary-value-based semiclassical methods, have been successfully applied to a variety of systems (see, for example, Refs. 110, 111, 161, and 249 and references therein). The mapping procedure introduced in Section VI results in a quantum-mechanical Hamiltonian with a well-defined classical limit, and therefore it... 

Apart from the methods based on Raman spectra and SHG, the Fourier transform coupled with infrared (IR) techniques (see e.g. Ref. 12), scanning tunneling microscopy (STM), and atomic force microscopy (AFM) have also been used. 

An analytical integration of an integrodifferential equation under a singular time boundary is always a complicated matter. The treatment of the method, based on a representation of the delta functional as a Fourier transform, and working in the complex plane, would be out of place in this report. It can be found in detail in Ref. 7) where also the solution obtained is discussed. It is shown that this solution is especially simple if the elution curves show a positive skewness, i.e. if they are tailed on the right-hand-side of their maximum (this is always true in PDC and GPC). A renormalization of the found concentration profile and a recalculation of the coordinates (z, t) to the elution volumina (V, V) then yield the spreading function of the considered column (Greschner 7))... 

Methods based on the short-time Fourier transform... 

The possibilities of application of far-UV circular dichroism (CD) and Fourier transform infrared (FTIR) spectroscopy in analysis of thermal stability of proteins and structural changes within protein molecules as well in explanation of cross reactivity between food allergens have been described in more detail in Section 3.4. Likewise nuclear magnetic resonance (NMR), especially 2D and multidimensional NMR as well as the method based on diffraction of monochromatic x-rays widely used in examination of tertiary structures of allergens have been described in Section 3.4 and by Neudecker et al. (2001) and Schirmer et al. (2005). 

Bayesian probability theory157 can also be applied to the problem of NMR parameter estimation this approach incorporates prior knowledge of the NMR parameters and is particularly useful at short aquisition times158 and when the FID contains few data points.159 Bayesian analysis gives more precise estimates of the NMR parameters than do methods based on the discrete Fourier transform (DFT).160 The amplitudes can be estimated independently of the phase, frequency and decay constants of the resonances.161 For the usual method of quadrature detection, it is appropriate to apply this technique to the two quadrature signals in the time domain.162-164... 

A rapid Fourier transform infrared spectroscopy (FTIR) method based on the stoichiometric reaction of triphenylphosphine (TPP) with hydroperoxides has been developed and successfully applied to determination of PV of edible oils (32). The hydroperoxides present in oil samples react stoichiometrically with TPP to produce triphenylphosphine oxide (TPPO), which has an intense absorption... 

Gangwall et al. [47] were the first to apply Fourier analysis for the evaluation of the transport parameters of the Kubin-Kucera model. Gunn et al. applied the frequency response [80] and the pulse response method [83] in order to determine the coefficients of axial dispersion and internal diffusion in packed beds from experiments performed at various Reynolds numbers. Bashi and Gunn [83] compared the methods based on the analytical properties of the Fourier and the Laplace transforms for the calculation of transport coefficients. MacDonnald et al. [84] discussed the applications of the method of moments to the analysis of the profiles of skewed chromatographic peaks. When more than two parameters have to be determined from one single run, the moment analysis method is less suitable, because only the first and second moments are reliable (see Figure 6.9). Therefore, only two parameters can be determined accurately. 

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