A new application of continuous wavelet transform to overlapping chromatograms for the quantitative analysis of amiloride hydrochloride and hydrochlorothiazide in tablets by ultra-performance liquid chromatography

A new application of continuous wavelet transform (CWT) to overlapping peaks in a chromatogram was developed for the quantitative analysis of amiloride hydrochloride (AML) and hydrochlorothiazide (HCT) in tablets. Chromatographic analysis was done by using an ACQUITY ultra-performance LC (UPLC) BEH C18 column (50 x 2.1 mm id, 1.7 pm particle size) and a mobile phase consisting of methanol-0.1 M acetic acid (21 + 79, v/v) at a constant flow rate of 0.3 mL/min with diode array detection at 274 nm. The overlapping chromatographic peaks of the calibration set consisting of AML and HCT mixtures were recorded rapidly by using an ACQUITY UPLC H-Class system. The overlapping UPLC data vectors of AML and HCT drugs and their samples were processed by CWT signal processing methods. The calibration graphs for AML and HCT were computed from the relationship between concentration and areas of chromatographic CWT peaks. The applicability and validity of the improved UPLC-CWT approaches were confirmed by recovery studies and the standard addition technique. The proposed UPLC-CWT methods were applied to the determination of AML and HCT in tablets. The experimental results indicated that the suggested UPLC-CWT signal processing provides accurate and precise results for industrial QC and quantitative evaluation of AML-HCT tablets.     

Simultaneous spectrophotometric determination of metformin hydrochloride and glibenclamide in binary mixtures using combined discrete and continuous wavelet transforms

In this work, a combined discrete and continuous wavelet transform analysis was developed for simultaneous spectrophotometric determinations of metformin hydrochloride and glibenclamide, two antidiabetic drugs, in binary mixtures without any chemical pretreatment. Absorption spectra were subjected to the 4-level db4 discrete wavelet transform (DWT) for signal de-noising. Selected continuous wavelet transform (CWT) families (rbio3.1 with scaling factor, a = 80, and gaus2, a = 60) were applied on these de-noised signals. Finally, a zero-crossing technique was used for the construction of calibration curves for both drugs. The proposed method was validated by analyzing synthetic mixtures of the investigated drugs with various concentrations. The amount of metformin hydrochloride and glibenclamide were determined by using CWT amplitudes in zero-crossing points. The mean recovery values of metformin hydrochloride and glibenclamide were found between 98.6-102.0 and 97.9-102.4% for rbio3 and 98.3-101.2 and 97.1-101.4% for gaus2 families, respectively. The obtained results showed that the developed method is a simple, rapid and precise procedure for the simultaneous determination of metformin hydrochloride and glibenclamide in binary mixtures.     

Fractional wavelet analysis for the simultaneous quantitative analysis of lacidipine and its photodegradation product by continuous wavelet transform and multilinear regression calibration

Fractional wavelet transform (FWT) was applied to the original absorption spectra of lacidipine (LAC) and its photodegradation product (LACD), and the resulting FWT spectra were processed by continuous wavelet transform (CWT) and multilinear regression calibration (MLRC) for the simultaneous quantitative analysis of both products in their binary mixtures. These methods do not require any chemical separation step and chemical complex reaction to obtain a detectable signal for the degradation product. By using the Mexican hat function, 2 calibration functions for LAC and LACD were obtained by measuring the CWT transformed signals at 416.1 nm for LAC and 414.6 nm for LACD, after FWT processing of the original absorption spectra. The calibration graphs were linear in the concentration range of 5.08-40.64 microg/mL for LAC and 0.51-8.16 microg/mL for LACD. The limit of detection and the limit of quantitation were found to be 0.289 and 0.956 microg/mL for LAC and 0.036 and 0.118 microg/mL for LACD, respectively. For comparison, the MLRC algorithm was applied to the linear regression functions for the individual drug and its photoproduct. In this approach, a set of linear regression functions was obtained from the relationship between concentrations and FWT signals in the wavelength range 411.0-412.4 nm. Both methods were applied to the quantitative evaluation of LAC and LACD in laboratory and pharmaceutical samples, and produced very satisfactory results.     

A novel method to calculate the approximate derivative photoacoustic spectrum using continuous wavelet transform

A novel method based on continuous wavelet transform (CWT) using Haar wavelet function for approximate derivative calculation of analytical signals is proposed and successfully used in processing the photoacoustic signal. An approximate nth derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal. The results obtained from four other different methods--the conventional numerical differentiation, the Fourier transform method, the Savitzky-Golay method, and the discrete wavelet transform (DWT) method--were compared with the proposed CWT method; it was demonstrated that all the results are almost the same for signals without noise, but the proposed CWT method is superior to the former four methods for noisy signals. The approximate first and second derivative of the photoacoustic spectrum of Pr(Gly)3Cl3.3H2O and PrCl3.6H2O were obtained using the proposed CWT method; the results are satisfactory.     

Comparative spectral analysis of veterinary powder product by continuous wavelet and derivative transforms

Comparative simultaneous determination of chlortetracycline and benzocaine in the commercial veterinary powder product was carried out by continuous wavelet transform (CWT) and classical derivative transform (or classical derivative spectrophotometry). In this quantitative spectral analysis, two proposed analytical methods do not require any chemical separation process. In the first step, several wavelet families were tested to find an optimal CWT for the overlapping signal processing of the analyzed compounds. Subsequently, we observed that the coiflets (COIF-CWT) method with dilation parameter, a=400, gives suitable results for this analytical application. For a comparison, the classical derivative spectrophotometry (CDS) approach was also applied to the simultaneous quantitative resolution of the same analytical problem. Calibration functions were obtained by measuring the transform amplitudes corresponding to zero-crossing points for both CWT and CDS methods. The utility of these two analytical approaches were verified by analyzing various synthetic mixtures consisting of chlortetracycline and benzocaine and they were applied to the real samples consisting of veterinary powder formulation. The experimental results obtained from the COIF-CWT approach were statistically compared with those obtained by classical derivative spectrophotometry and successful results were reported.     

Multicomponent quantitative resolution of binary mixtures by using continuous wavelet transform

Continuous 1-dimensional wavelet transform (WT) was applied to the quantitative analysis of a vitamin 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 powerful tool for analysis of multicomponent mixtures. By measuring the amplitude signals corresponding to the selected zero-crossing points of the transformed signal, we obtained the calibration curve. The validation of the calibration graphs was confirmed 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 liquid chromatographic methods, and good agreement was found.     

Multidetermination of thiamine HCl and pyridoxine HCl in their mixture using continuous daubechies and biorthogonal wavelet analysis

A new graphical method based on the one-dimensional wavelet transform (WT) was proposed and tested on mixture of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) in the presence of strongly overlapping signals. We selected from the data of the UV-VIS absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg ml⁻¹ for each vitamin and we subjected it to Daubechies8 (DAUB8) and Biorthogonal6.8 (BIOR6.8) wavelet transforms. Since the peaks of the transformed signals were bigger than original ones a zero crossing method was applied to obtain the calibration graphs. In addition, the validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. Matlab 6.5 software was used for one-dimensional wavelet analysis and the basic concepts about wavelet method were given. The obtained results were successfully compared among each other as well as with those obtained by other literature methods. The method developed in this paper is rapid, easy to apply, not expensive and it is suitable for analyzing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment.     

基于小波-反向搜索及表面增强拉曼的食品中色素的光谱定性分析

使用金纳米粒子为增强因子的表面增强拉曼光谱技术,通过连续小波变换将拉曼光谱信号转化到小波空间(墨西哥帽小波作为小波基)。该步骤能够减轻信号中基线变化及随机噪音的影响并找到峰位置和最佳小波尺度系数。依据小波空间中的信息,对混合物光谱及标准谱光谱进行反向搜索得到反向搜索匹配系数(Reverse match quality,RMQ),作为判断混合物中目标成分是否存在的依据。该算法可对混合物中的目标物质进行准确定性,并已成功应用于多种食品中色素鉴定。食品中色素的检出率达到99%,且结果稳健,其效果明显优于传统的命中质量系数法(Hit quality index,HQI)。这证实了小波空间反向搜索方法是一种快速而准确的拉曼光谱定性算法。     

A novel method to calculate the approximate derivative photoacoustic spectrum using continuous wavelet transform

A novel method based on continuous wavelet transform (CWT) using Haar wavelet function for approximate derivative calculation of analytical signals is proposed and successfully used in processing the photoacoustic signal. An approximate nth derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal. The results obtained from four other different methods – the conventional numerical differentiation, the Fourier transform method, the Savitzky-Golay method, and the discrete wavelet transform (DWT) method – were compared with the proposed CWT method; it was demonstrated that all the results are almost the same for signals without noise, but the proposed CWT method is superior to the former four methods for noisy signals. The approximate first and second derivative of the photoacoustic spectrum of Pr(Gly)₃Cl₃· 3 H₂O and PrCl₃· 6 H₂O were obtained using the proposed CWT method; the results are satisfactory. Received: 21 December 1999 / Revised: 28 February 2000 / Accepted: 7 March 2000     

Simultaneous determination and validation of some binary mixtures of antihypertensive drugs using ratio derivative spectrophotometric method

Ratio derivative spectrophotometric technique is presented for the rapid, accurate and precise simultaneous determination of olmesartan medoxomil (OLM), hydrochlorothiazide (HCT), and zofenopril (ZOF) as well as HCT binary mixtures in their dosage forms. First derivative of the ratio spectra (DD1) by measurements using different amplitudes was used and calibration graphs were established for 0.5–12 mg/mL HCT and 0.5–20 mg/mL OLM and ZOF. This method depends on first derivative of the ratio spectra by division of the absorption spectrum of the binary mixture by a standard spectrum of one of the components and then calculating the first derivative of the ratio spectrum. The first derivative of the ratio amplitudes at 250.4 and 291.5 nm for OLM, 250.4 and 298.1 nm for ZOF and 231.8, 332.2, 232.3 and 280.4 nm for HCT were selected for the determination. The proposed methods were successfully applied for determining of both drug combinations (ZOF-HCT and OLM-HCT) in their synthetic mixtures and in pharmaceutical dosage forms. The described procedures are extensively validated, non-destructive and do not require any separation steps.     

小波分析对奇异性检测用于滴定终点确定的研究

在分析化学领域中，利用数学判断法确定滴定终点，随着计算机的日益普及而备受关注。此文在介绍当前普遍采用的二进小波变换奇异性检测方法的基础上，提出基于多分辨率分析和连续小波变换两种奇异性检测方法，并应用于氢氧化钠对盐酸和磷酸滴定曲线判断终点的试验中，取得了良好的效果。     

Wavelet unfolded partial least squares for near-infrared spectral quantitative analysis of blood and tobacco powder samples

Continuous wavelet transform (CWT) has been shown to be a high-performance signal processing technique in multivariate calibration. However, the signal processed by CWT with a specific wavelet may account for only a part of the information. To effectively utilize more abundant information contained in analytical signals, a method, named as wavelet unfolded partial least squares (WUPLS), was proposed. In the approach, the measured dataset is firstly extended by CWT with different wavelets, and then partial least squares (PLS) is employed to develop the quantitative model between the extended dataset and the target values. In order to select the representative wavelets, principal component analysis (PCA) is used to investigate the distribution of the signals obtained by CWT with different wavelets. The performance of the method was tested with blood and tobacco powder samples. Compared with the results obtained by PLS methods, the WUPLS method combined with signal processing techniques is proven to be a promising tool for improving the near-infrared (NIR) spectral analysis of complex samples.     

Fractional-continuous wavelet transforms and ultra-performance liquid chromatography for the multicomponent analysis of a ternary mixture containing thiamine, pyridoxine, and lidocaine in ampules

New chemometric approaches based on the application of partial least squares (PLS) and principal component regression (PCR) algorithms with fractional wavelet transform (FWT) and continuous wavelet transform (CWT) are proposed for the spectrophotometric multicomponent determination of thiamine hydrochloride (B1), pyridoxine hydrochloride (B6), and lidocaine hydrochloride (LID) in ampules without any separation step. In this study PLS and PCR techniques were applied to the raw spectral data, FWT-coefficients, and FWT-CWT-coefficients. These calibration models were labeled as Raw-PLS and Raw-PCR, FWT-PLS and FWT-PCR, and FWT-CWT-PLS and FWT-CWT-PCR, respectively. A new ultra-performance liquid chromatographic (UPLC) method was developed for the comparison of the results obtained by applying the chemometric calibration methods. Chromatographic separation and determination of B1, B6, and LID in ampules were performed on an Acquity UPLC BEH C18 column (50x2.1 mm id, 1.7 pm particle size) using gradient elution with a mobile phase consisting of methanol and 0.01 M HCI at a constant flow rate of 0.6 mL/min. These combined chemometric calibrations and UPLC were validated by analyzing various ternary mixtures, B1, B6, and LID. The proposed chemometric approaches (signal processing-multivariate calibrations) and UPLC method were applied to the quantitative multicomponent analysis of marketed ampules containing the vitamins B1 and B6 with LID.     

Elimination of interference information by a new hybrid algorithm for quantitative calibration of near infrared spectra

A new hybrid algorithm is proposed to eliminate the interference information for multivariate calibration of near-infrared (NIR) spectra that includes noise, background and systemic spectral variation irrelevant to concentration. The method consists of two parts: approximate derivative based on continuous wavelet transform (CWT) and orthogonal signal correction (OSC). After the approximate derivative calculated by CWT, OSC was performed. It was successfully applied to real complex NIR spectral data to eliminate the interference information. Correction for the interference of NIR spectra resulted in a substantial improvement in the predicted precision, and a more concise calibration model was obtained. The proposed procedure also compared favourably with several pretreatment methods, and the new method appears to provide a high-performance pretreatment tool for multivariate calibration of NIR spectra. In addition, the strategy proposed here can be applied to various other spectral data for quantitative purposes as well.     

Quantification of components in overlapping peaks from capillary electrophoresis by using continues wavelet transform method

The application of continues wavelet transform (CWT) for resolving overlapping peaks from capillary electrophoresis (CE) is described. Overlapping peaks can be resolved easily by transforming experimental signals into their wavelet coefficients. The proposed method was applied for the determination of benzoic acid and salicylic acid in overlapping peaks from CE. The composition of the two acids in Zuguangsan, a traditional Chinese patent medicine, was determined. The quantification results are satisfactory. CWT has been shown to be a practicable approach for resolving overlapping peaks and for quantitative determining coeluted compounds in overlapping peaks from CE. The quantification results obtained from CWT were compared with those obtained from numerical differentiation method. CWT has been shown prior to numerical differentiation method for processing experimental signals which contain noise.     

连续小波变换-独立成分回归算法及其在多组分分析中的应用

采用连续小波变换（CWT）对光谱数据进行处理，用独立成分分析（ICA）进行特征提取，再用回归分析方法对被测组分进行测定，建立了连续小波变换一独立成分回归（CWT-ICR）方法。方法用于肉样品中水分、脂肪和蛋白质多组分的同时测定，所得结果与化学法测得结果相符。     

Wavelet frequency spectrum and its application in analyzing an oscillating chemical system

Based on the continuous wavelet transform (CWT), three types frequency spectra, wavelet frequency spectrum (WFS), point frequency spectrum (PFS) and time frequency spectrum (TFS), were developed. Two data sets were simulated and treated with the proposed spectra, the results indicated that WFS could extract the frequency information, which was like Fourier analysis but more accurate, PFS could obtain the frequency at any moment, TFS could show frequency change with time. These abilities of PFS and TFS were impossible for Fourier analysis. An oscillating chemical signal was processed with WFS and TFS. From the processed results, two points could be learned about the oscillating chemical reaction: one was the oscillating chemical reaction was a mixture one including two or more complex kinetics processes, the velocity of the switch from the reduced state (RS) to the oxidized state (OS) was faster than the reverse switch (from OS to RS); the other was increase of KBrO₃ could decrease the velocities of both switches, which led to the oscillating period became longer.     

Prediction of protein secondary structure based on continuous wavelet transform

In this paper, continuous wavelet transform (CWT) is used to extract the number and the relevant positions of the α-helices and short peptides connecting α-helices and β-strands (connecting peptides) from the amino acid sequences of proteins. The amino acid sequence is first mapped into hydrophobicity sequence, and then transformed into CWT value of sequence domain in appropriate scale via CWT. The number and the relevant positions of the α-helices and connecting peptides can be extracted easily and accurately according to the minima of wavelet coefficient in corresponding CWT plot of hydrophobic value sequences with appropriate scale. The analytical results demonstrate that α-helices and connecting peptides can be predicted conveniently and rapidly when this method is used in the processing of 100 non-homologous sequences. However, this method is not suitable for predicting the length of α-helices and connecting peptides.     

比值导数波谱法用于极谱及伏安法多组分分析

叙述了比值导数波谱法在电化学波谱解析中应用的原理。首先以混合物的极谱波（或伏安波）除以干扰组分的标准波谱得到比值波谱，再以比值波谱对电位求导得到比值导数波谱，藉此可消除干扰组分的影响。采用该法可对二组分体系进行分析，如选择合适的零交点便可对三组分体系进行分析。利用本法对苋菜红－日落黄的伏安波及铜－镉－镍的极谱波进行了解析及定量分析，获较好的结果。     

Continuous wavelet transform and its application to resolving and quantifying the overlapped voltammetric peaks

In order to resolve and quantify the overlapped peaks of voltammetry that can be described by sech²-function, continuous wavelet transform (CWT) is employed. Through CWT by using Marr wavelet, qualitative and quantitative analysis for the mixed solution of Cd(II) and In(III) can be performed from unresolved square wave voltammogram (SWV) and relevant theoretical basis is provided. A new method to construct the baseline for quantitative determination is also proposed. The results of analysis indicate that the overlapped voltammogram can be resolved and quantified effectively, conveniently and satisfactorily via CWT.