Fourier component analysis

Soon this concept was connected (234) with the magnitude of the Kj constant in a Fourier component analysis of internal rotation potential functions in molecules exhibiting the anomeric effect (see Section III.B.2). It was also used to account for bond lengths in methanediol (8) (235) and methoxymethanol (49) (244) (p. 196), but the authors claimed (235) that the shortening of the C—O bonds in the ap, ap conformers of 8 cannot be explained by the interaction pictured in Figure 26a. 

Principal component analysis has been used in combination with spectroscopy in other types of multicomponent analyses. For example, compatible and incompatible blends of polyphenzlene oxides and polystyrene were distinguished using Fourier-transform-infrared spectra (59). Raman spectra of sulfuric acid/water mixtures were used in conjunction with principal component analysis to identify different ions, compositions, and hydrates (60). The identity and number of species present in binary and tertiary mixtures of polycycHc aromatic hydrocarbons were deterrnined using fluorescence spectra (61). 

Fourier transform spectrum odd-harmonic components analysis... 

A special type of data pre-treatment is the transformation of data into a smaller number of new variables. Principal components analysis is a natural example and we have treated it in Section 36.2.3 as PCR. Another way to summarize a spectrum in a few terms is through Fourier analysis. McClure [29] has shown how a NIR... 

In contrast, SIMCA uses principal components analysis to model object classes in the reduced number of dimensions. It calculates multidimensional boxes of varying size and shape to represent the class categories. Unknown samples are classified according to their Euclidean space proximity to the nearest multidimensional box. Kansiz et al. used both KNN and SIMCA for classification of cyanobacteria based on Fourier transform infrared spectroscopy (FTIR).44... 

Luttinger-Tisza method is burdened by independent minimization variables, while analysis of the values of the Fourier components F k) makes it possible to immediately exclude no less than half of the variable set and to obtain a result much more quickly. Degeneracy of the ground state occurs either due to coincidence of minimal values of Vt (k) at two boundary points of the first Brillouin zone k = b]/2 and k = b2/2, or as a result of the equality Fj (k) = F2 (k) at the same point k = h/2. The natural consequence of the ground state degeneracy is the presence of a Goldstone mode in the spectrum of orientational vibrations.53... 

The Fourier components of a time signal can be displayed in the output file by enabling the Fourier option in the Transient Analysis dialog box. 

The molecular specificity of Fourier transform infrared (FTIR) lends itself quite well to applications in pharmaceutical development labs, as pointed out in a review article with some historical perspective.10 One of the more common applications of mid-IR in development is a real-time assessment of reaction completion when used in conjunction with standard multivariate statistical tools, such as partial least squares (PLS) and principal component analysis (PCA).18,19 Another clever use of FTIR is illustrated in Figure 9.1, where the real-time response of a probe-based spectroscopic analyzer afforded critical control in the charge of an activating agent (trifluoroacetic anhydride) to activate lactol. Due to stability and reactivity concerns, the in situ spectroscopic approach was... 

In general, there are two types of compression (1) individual spectra can be compressed and filtered and (2) the entire dataset can be compressed and filtered by representing each of the individual spectra as a linear combination of some smaller set of data, which is referred to as a basis set. In this section, we will address the processing of individual spectra by applying the fast fourier transform (FFT) algorithm and followed this discussion with one on processing sets of spectra with principal component analysis (PCA). 

Principal component analysis is most easily explained by showing its application on a familiar type of data. In this chapter we show the application of PCA to chromatographic-spectroscopic data. These data sets are the kind produced by so-called hyphenated methods such as gas chromatography (GC) or high-performance liquid chromatography (HPLC) coupled to a multivariate detector such as a mass spectrometer (MS), Fourier transform infrared spectrometer (FTIR), or UV/visible spectrometer. Examples of some common hyphenated methods include GC-MS, GC-FTIR, HPLC-UV/Vis, and HLPC-MS. In all these types of data sets, a response in one dimension (e.g., chromatographic separation) modulates the response of a detector (e.g., a spectrum) in a second dimension. 

One of the emerging biological and biomedical application areas for vibrational spectroscopy and chemometrics is the characterization and discrimination of different types of microorganisms [74]. A recent review of various FTIR (Fourier transform infrared spectrometry) techniques describes such chemometrics methods as hierarchical cluster analysis (HCA), principal component analysis (PCA), and artificial neural networks (ANN) for use in taxonomical classification, discrimination according to susceptibility to antibiotic agents, etc. [74],... 

Another important class of MVA is represented by cluster analysis methods and principal component analysis (PCA). The latter is a representative of data reduction methods that exploit linear algebra. We do not, however, believe all the important patterns can be captured by linear algebraic methods. Finear mathematical methods are ideal for data compression, because to recover the original data distortion is undesirable. Thus, data compression is essentially applied Fourier analysis [2], In contrast, data mining is a kind of pattern... 

---