The Cascade Hilbert-Zero Decomposition: A Novel Method for Peaks Resolution and Its Application to Raman Spectra

Raman spectra of biological objects are sufficiently complex since they are comprised of wide diffusive spectral peaks over a noisy background. This makes the resolution of individual closely positioned components a complicated task. Here we propose a method for constructing an approximation of such systems by a series, respectively, to shifts of the Gaussian functions with different adjustable dispersions. It is based on the coordination of the Gaussian peaks’ location with the zeros of the signal’s Hilbert transform. The resolution of overlapping peaks is achieved by applying this procedure in a hierarchical cascade way, subsequently excluding peaks of each level of decomposition. Both the mathematical rationale for the localization of intervals, where the zero crossing of the Hilbert-transformed uni- and multimodal mixtures of Gaussians occurs, and the step-by-step outline of the numerical algorithm are provided and discussed. As a practical case study, we analyze results of the processing of a complicated Raman spectrum obtained from a strain of Mycobacterium tuberculosis. However, the proposed method can be applied to signals of different origins formed by overlapped localized pulses too.

DERIVATIVE UV SPECTROSCOPIC APPROACHES IN MULTICOMPONENT ANALYSIS–A REVIEW

The spectrophotometric multi-component analysis involves spectrum recording and mathematical equations. However, spectral interference poses a major limitation when mixture samples are encountered. To overcome this derivative spectrophotometry (DS) has been introduced for the resolution of overlapping peaks. In this review modified methods like derivative quotient spectra, double divisor ratio spectra derivative method, double divisor means centering of ratio spectra method, derivative subtraction coupled with the constant multiplication method (DS-CM), amplitude subtraction (AS), modified amplitude subtraction (MAS), amplitude factor method (P-Factor), amplitude modulation method (AM), amplitude summation method (A-Sum), simultaneous derivative ratio spectrophotometry (S1DD), derivative compensation ratio via regression equation, differential dual wavelength (D1 DWL), differential derivative ratio (D1DR), successive derivative subtraction method (SDS) and derivative transformation (DT) of derivative spectrophotometry theories and applications are reviewed. These methods were applied to solve different complex pharmaceuticals mixtures. These developed methods were simple and cost-effective.

Measurement of Voltammetric Peak Area and Resolution of Overlapping Peaks in the Simultaneous Determination of Copper, Lead, Cadmium, and Nickel in Environmental Matrix

Peak area was used for the simultaneous determination of copper(II), lead(II), cadmium(II), and nickel(II) in environmental matrixes by differential pulse voltammetry. The voltammetric measurements were performed with a conventional 3-electrode cell and an ammonia–ammonium chloride buffer, pH 9.1, as the supporting electrolyte. The analytical procedure was verified first in aqueous reference solutions and later by analysis of the standard reference materials Estuarine Sediment BCR-CRM 277 and River Sediment BCR-CRM 320. The precision and accuracy of the method, expressed as the relative standard deviation and the relative error, respectively, were <5% in all cases; the detection limit for each element under the experimental conditions used was in the range 1–5 μg/L. In the case of mutual interference between neighboring elements, an analytical procedure is proposed that is based on the standard additions technique, which allows the resolution of the overlapping voltammetric peaks.