Alentsev-Fok method of resolving complex spectra (original) (raw)
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Limits of mathematical methods of improving spectral resolution
Journal of Applied Spectroscopy, 1986
In many spectroscopic experiments (especially in molecular spectroscopy), even when using instruments with maximum resolution, marked superposition of lines and bands is observed, which complicates analytical procedures. To eliminate this deficiency, various mathematical methods of artificial improvement in the resolution have been developed [i]. In investigating these methods, it is natural to ask what the limits of their applicability are and whether still further improvement in resolution could be achieved by using more ingenious methods.
Communications in Nonlinear Science and Numerical Simulation, 2011
In this paper the authors suggest a new method of detection of possible differences between similar near infrared (NIR) spectra based on the self-similar (fractal) property. This property is a general characteristic that belongs to a wide class of the strongly-correlated systems. As an example we take a set of NIR spectra measured for three systems: (1) glassy carbon (GC) electrodes, (2) GC electrodes affected by azobenzene (AB) substance and finally (3) films (AB-FILM). Besides the physical model that should describe the intrinsic properties of these substances we found the fitting function that follow from the linear principle for the strongly-correlated variables. This function expressed in the form of linear combination of 4 power-law functions describes with the high accuracy the integrated curves that were obtained from the averaged values of the initially measured spectra. The nine fitting parameters can be considered as the quantitative “finger prints” for detection of the differences between similar spectra. Besides this result we established the self-similar behavior of the remnant functions. In other words, the difference between the initially integrated function and its fitting function can be expressed in the form of linear combinations of periodical functions having a set of frequencies following to relationship ω(k) = ω0ξk, where the initial frequency ω0 and scaling factor ξ are determined by the eigen-coordinates method. This behavior in the NIR spectra was discovered in the first time and physical reasons of such behavior merit an additional research.► A new method of detection of differences between similar spectra is proposed. ► The self-similar behavior identified. It belongs to a wide class of the strongly-correlated systems. ► The self-similar behavior for a certain class of remnant functions was found.
Mathematical Processing of Spectral Data in Analytical Chemistry
Cambridge Scholars Publishing , 2018
Mathematical Processing of Spectral Data in Analytical Chemistry: A Guide to Error Analysis By Joseph Dubrovkin Cambridge Scholars Publishing Release Date: Aug. 1, 2018 This book will appeal to both practitioners and researchers in industrial and university analytical laboratories, as well as students specializing in analytical spectroscopy and chemometrics. The subjects covered include the advanced principles of calibration (univariate and multivariate) and the estimation of the peak parameters in spectra with overlapping components. This book differs from existing studies on the subject in that it provides easily reproducible computer calculations illustrating its significant theoretical statements. As such, it can also serve as a practical guide to lecturers in analytical spectrometry and chemometrics. ABOUT THE AUTHOR Joseph Dubrovkin gained a degree in Automatics from the Aviation Institute, Russia, in 1968, and Doctoral degrees in Technical Sciences and Physics and Mathematics from Leningrad State University, Russia, in 1979 and 1989 respectively. He was a Lecturer at the Aviation Institute and the Pharmaceutical Institute, Russia, and Western Galilee College (department of Bar-Ilan University), Israel, before retiring. 20% discount on online orders using the discount code ERROR20 – purchase through www.cambridgescholars.com or email orders@cambridgescholars.com
A contribution to the derivative ratio spectrum method
Analytica Chimica Acta, 1995
The performance of two graphical methods (the derivative ratio spectrum method and its variant with normalized divisor) for the determination of the resolution of several binary mixtures of analytes is compared. This paper demonstrates that normalized spectra used as divisors facilitate optimization of the working conditions and diminishes quantitation errors. The additional use of diode array spectrophotometers allows quantitation of second order derivative ratio spectra. In order to validate the proposed approach to derivative ratio spectra, two binary mixtures, acetylsalicylic acid-salicylamide and imipramine-perphenazine, were assayed. The results obtained by using the proposed method in its conventional and modified variants are discussed. On the other hand, a multi-wavelength regression method is suggested for the determination of several metal ions by using an organic reagent as chelating agent. It was shown that it is possible to determine the analytes without any previous knowledge of stoichiometry of the complexes involved and how the contribution from excess of chelating agent can be eliminate. The method has been validated on several binary mixtures of Fe(U), Cu(II) and Z&I) by using 4-(1'H-1',2',4'-trizolyl-3'-azo)-2-methylresorcinol (TrAMeR) as chelating agent. Keywords: Multiwavelength regression; Derivative ratio spectrum method 0003-2670/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIOOO3-2670(95)00426-2
Statistical properties of AR spectral analysis
IEEE Transactions on Acoustics, Speech, and Signal Processing
Problem, an unnecessary waste of computer time, Fortunately, we can use these mappings in either order, and so we map Y onto 2 using (4) and (6) in a manneF exactly parallel to the output mapping of the direct transform. ~ REFERENCES S. Winograd, "On computing the discrete Fourier transform," Math. Cornput., vol. 32, pp. 178-199, Jan. 1978. H. F. Silverman, "An introduction to programming the Winograd Fourier transform algorithm (WFTA)," IEEE Z?ans. A~o u s t. ,
A general procedure for the derivation of principal domains of higher-order spectra
Faculty of Built Environment and Engineering School of Engineering Systems, 1994
An analysis of instantaneous frequency representation using time frequency distributions-Generalized Wigner distribution," IEEE Trans. on Signal Processing, to be published. LJ. StankoviC, "Wigner higher order spectra of multicomponent signals: A method for higher order time-frequency analysis," in Proc. Inr.
Error Propagation of Quantitative Analysis Based on Ratio Spectra
Error propagation of the quantitative analysis of binary and ternary mixtures based on the ratio spectra and the mean-centred ratio spectra has been studied. Gaussian doublets and triplets were used as models of the mixture pure-component spectra. The mixture spectra were disturbed by random constant and proportional noises and unknown background. The perturbations of the calibration matrix were modelled by systematic errors caused by the wavelength shifts. The least-squares estimation of the concentration vector and the estimation errors were obtained theoretically and numerically. The condition number of the matrix of the pure-component ratio spectra was theoretically evaluated for binary mixtures. The advantages and disadvantages of the ratio spectra methods are discussed.