DRUGS, COSMETICS, FORENSIC SCIENCES Multicomponent Quantitative Resolution of Binary Mixtures by Using Continuous Wavelet Transform ERDAL DINÇ University of Ankara, Faculty of Pharmacy, Department of Analytical Chemistry, 06100, Tandoan, Ankara, Turkey DUMITRU BALEANU 1 University of Çankaya, Faculty of Arts and Sciences, Department of Mathematics and Computer Sciences, 06530, Ankara, Turkey Continuous 1-dimensional wavelet transform (WT) was applied to the quantitative analysis of a vita- min combination of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) with strongly overlapping signals. Absorbance data from the UV-Vis absorption spectrum of width 1150 were subjected to Gauss1 and Gauss2 WTs. Because of its flexibility, data processing, and its high signal amplitude, the continuous WT method is a power- ful tool for analysis of multicomponent mixtures. By measuring the amplitude signals corresponding to the selected zero-crossing points of the trans- formed signal, we obtained the calibration curve. The validation of the calibration graphs was con- firmed with different mixtures of THI and PYR at various concentration ratios. A brief explanation of the continuous wavelet method is given. MATLAB 6.5 software was used to perform the calculations. The results of our study were compared with those obtained by spectroscopic, chemometric, and liq- uid chromatographic methods, and good agree- ment was found. T he powerful wavelet transform (WT; 1–4) has been ap- plied in many areas, e.g., signal processing (5), de-nois- ing (6), spectral quantitative analysis (7), analysis of electrochemical noise data (8), photoacoustic signal process- ing (9), and resolution of simulated overlapping spectra (10). Mallat and Hwang (11) developed a fast implementation method for the discrete wavelet method and, as a result, they made the wavelet method an effective tool for processing chemical data. The basic idea of continuous wavelet transform (CWT) is to represent any arbitrary function as a superposi- tion of wavelets or "small waves." In early work, CWT and multiresolution analysis (MRA) were applied to remove noise and irrelevant information in absorption spectra. In the spectrophotometric studies, derivative spectrophotometry and ratio-spectra derivative spectropho- tometry were the basic tools for quantitative resolution of mixtures containing ³2 compounds. Unfortunately, in some cases these methods have a great disadvantage: the higher-de- rivative process reduces the peak amplitude, the process of finding zero-crossing points becomes difficult, and the sensi- tivity of the method decreases. The ratio-spectra derivative method gives, in some cases, an infinite value for the ratio spectra. Thiamine hydrochloride (THI) and pyridoxine hydrochlo- ride (PYR) in mixtures have been determined by spectropho- tometric (12), ratio-spectra derivative (13), liquid chromato- graphic (LC; 13), and chemometric methods (14). These methods have various disadvantages for the determinations due to the separation procedure in the LC method, the dimin- ished peak amplitude in the higher-derivative method, and the complex calculations in the chemometric method. In this con- text, the wavelet technique (1–4) is a promising tool for elimi- nating the above drawbacks. The simultaneous performance of data reduction and de-noising for signal analysis (4) is one of the main advantages of WT. The aim of this study was to apply Gauss continuous wave- let transform (GCWT) to the simultaneous determination of THI and PYR in a mixture. The first step was to obtain significant peak amplitude for the transformed signal. To reach this objective, we used 2 different Gauss mother wavelets, GCWT1 and GCWT2. In the second step, the transformed signal was subjected to a zero-crossing technique. METHOD Wavelet Transform Wavelets are an extension of Fourier analysis. The goal is to turn the information in a signal into numbers, which can be stored, transmitted, analyzed, or used to reconstruct the origi- nal signal. The coefficients tell in what way the analyzing function needs to be modified in order to reconstruct a signal. We can construct the signal by putting together wavelets of different sizes at different positions. The signal and the ana- lyzing function are multiplied together, and the integral of the product is calculated. Wavelets adapt immediately to the dif- 360 DINÇ &BALEANU:JOURNAL OF AOAC INTERNATIONAL VOL. 87, NO. 2, 2004 Received April 23, 2003. Accepted by JM July 18, 2003. Corresponding author's e-mail: dinc@pharmacy.ankara.edu.tr. 1 Present address: Institute of Space Sciences, National Institute for Laser, Plasma and Radiation Physics, Magurele-Bucharest, PO Box MG-23, R 76911, Romania. Downloaded from https://academic.oup.com/jaoac/article/87/2/360/5657263 by guest on 14 April 2024