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.     

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     

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.     

Feature analysis of protein structure by using discrete Fourier transform and continuous wavelet transform

In this paper, discrete Fourier transform (DFT) and continuous wavelet transform (CWT) are used to predict the protein structure. Hydrophobicity plays a key role in the form of protein structure. The amino acid sequence is first mapped into hydrophobicity sequence, and then process it by DFT and CWT so that power spectral density is gained. The results show that continuous wavelet transform can extract the features of protein structure effectively and availably and has a tremendous development foreground.     

End-point detection in potentiometric titration by continuous wavelet transform

The aim of this work was construction of the new wavelet function and verification that a continuous wavelet transform with a specially defined dedicated mother wavelet is a useful tool for precise detection of end-point in a potentiometric titration. The proposed algorithm does not require any initial information about the nature or the type of analyte and/or the shape of the titration curve. The signal imperfection, as well as random noise or spikes has no influence on the operation of the procedure.The optimization of the new algorithm was done using simulated curves and next experimental data were considered. In the case of well-shaped and noise-free titration data, the proposed method gives the same accuracy and precision as commonly used algorithms. But, in the case of noisy or badly shaped curves, the presented approach works good (relative error mainly below 2% and coefficients of variability below 5%) while traditional procedures fail. Therefore, the proposed algorithm may be useful in interpretation of the experimental data and also in automation of the typical titration analysis, specially in the case when random noise interfere with analytical signal.     

A continuous wavelet transform algorithm for peak detection

Contactless conductivity detector technology has unique advantages for microfluidic applications. However, the low S/N and varying baseline makes the signal analysis difficult. In this paper, a continuous wavelet transform-based peak detection algorithm was developed for CE signals from microfluidic chips. The Ridger peak detection algorithm is based on the MassSpecWavelet algorithm by Du et al. [Bioinformatics 2006, 22, 2059-2065], and performs a continuous wavelet transform on data, using a wavelet proportional to the first derivative of a Gaussian function. It forms sequences of local maxima and minima in the continuous wavelet transform, before pairing sequences of maxima to minima to define peaks. The peak detection algorithm was tested against the Cromwell, MassSpecWavelet, and Linear Matrix-assisted laser desorption/ionization-time-of-flight-mass spectrometer Peak Indication and Classification algorithms using experimental data. Its sensitivity to false discovery rate curve is superior to other techniques tested.     

Determination of bismuth and copper using adsorptive stripping voltammetry couple with continuous wavelet transform

A new method is proposed for the determination of bismuth and copper in the presence of each other based on adsorptive stripping voltammetry of complexes of Bi(III)-chromazorul-S and Cu(II)-chromazorul-S at a hanging mercury drop electrode (HMDE). Copper is an interfering element for the determination of Bi(III) because, the voltammograms of Bi(III) and Cu(II) overlapped with each other. Continuous wavelet transform (CWT) was applied to separate the voltammograms. In this regards, wavelet filter, resolution of the peaks and the fitness were optimized to obtain minimum detection limit for the elements. Through continuous wavelet transform Symlet4 (Sym4) wavelet filter at dilation 6, quantitative and qualitative analysis the mixture solutions of bismuth and copper was performed. It was also realized that copper imposes a matrix effect on the determination of Bi(III) and the standard addition method was able to cope with this effect. Bismuth does not have matrix effect on copper determination, therefore, the calibration curve using wavelet coefficients of CWT was used for determination of Cu(II) in the presence of Bi(III). The detection limits were 0.10 and 0.05 ng ml⁻¹ for bismuth and copper, respectively. The linear dynamic range of 0.1-30.0 and 0.1-32.0 ng ml⁻¹ were obtained for determination of bismuth in the presence of 24.0 ng ml⁻¹ of copper and copper in the presence of 24.0 ng ml⁻¹ of bismuth, respectively. The method was used for determination of these two cations in water and human hair samples. The results indicate the ability of method for the determination of these two elements in real samples.     

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.     

Prediction of transmembrane proteins based on the continuous wavelet transform

A novel method based on continuous wavelet transform (CWT) for predicting the number and location of helices in membrane proteins is presented. Two bacteria proteins are chosen as examples to describe the prediction of transmembrane helices (HTM) by using this method. Selections of an appropriate dilation and hydrophobicity data types are discussed in the text. The results indicate that CWT is a promising approach for the prediction of HTM.     

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.     

Band shape determination with robust estimator based on continuous wavelet transform

The paper focuses on an alternative approach that allows one to identify overlapping band shapes with the help of the continuous wavelet transform (CWT). We show that less number of special points for determining a band shape is required unlike the fractional derivative spectrometry method [S.S. Kharintsev, M.Kh. Salakhov, Spectrochim. Acta Part A, 60 (2004) 2125]. Besides, the CWT-based derivative spectrometry can be successfully utilized in a case of complex spectra corrupted with a white and/or high-frequency noise. The power of this method is illustrated on model examples and experimental spectra of 1,2-diphenylethane in crystalline and melted phase.     

Improving detection power in trace analysis using wavelet transform

Environmental analysis most often is trace analysis. Therefore, the concentrations are commonly in the lower working range near the limit of detection of the corresponding analytical method. However, whenever the instrument's analytical noise is too large, it dominates the signal curves and analytes cannot be detected anymore. Furthermore, the evaluation of peaks with defined baselines is hindered very much. One possibility for de-noising is wavelet transform which is presented in this work. Different wavelet functions are applied and Symlet4 is suggested as the most powerful for analytical peaks that resemble Gaussian distribution curves, as it improves limits of detection by factors 6 to 7. The comparison of different wavelet functions has been carried out for two modern analytical scopes. At first, chromatograms are de-noised for the speciation of four arsenic compounds via the coupling of HPLC and ICP-MS. Secondly, the determination of cadmium is shown by HR-CS AAS, which is one of the most recently developed devices in atomic absorption spectrometry and allows the registration of three-dimensional spectra in order to investigate the spectral vicinity of analytical lines. On the basis of these investigations, we recommend using wavelet transform with Symlet4 for all analytical techniques which are resulting in similar signal curves.     

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.     

Maximum spectrum of continuous wavelet transform and its application in resolving an overlapped signal

To estimate the number of peaks and to find the individual peak positions in an overlapped signal, a new method called maximum spectrum of continuous wavelet transform (MSCWT) was developed by extracting the maximum coefficients of continuous wavelet transform (CWT). The peak position in MSCWT was the same as that in its original signal. In this process, CWT was performed not on a single dilation but on an appreciation dilation range. To obtain such a range, a new criterion was introduced to choose a center dilation, which was used to form the dilation range. If Cdilation denoted the center dilation, the proper dilation range was [Cdilation -6 +/- 2, Cdilation +1 +/- 1]. The Mexican Hat function was an analytical wavelet. Utilizing the information of the peak number and the position detected by MSCWT, a fitting route was performed to recover the original signal. One simulated and four true overlapped signals, including high performance liquid chromatography (HPLC), ultraviolet-visible (UV) spectrum, and differential pulse voltammetric (DPV), were processed, and the results indicated that MSCWT could detect an overlapped peak number and position, and the curve fitting based on information of MSCWT had a higher accuracy. The proposed method was an efficient one in resolving different types of overlapped signals.     

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.     

Determination of chlorogenic acid in plant samples by using near-infrared spectrum with wavelet transform preprocessing.

By theoretical analysis, it is found that wavelet transform (WT) with a wavelet function can be regarded as a smoothing and a differentiation process, and that the order of differentiation is determined by the vanishing moment, which is an important property of a wavelet function. Therefore, a method based on the continuous wavelet transform (CWT) for removing the background in the near-infrared (NIR) spectrum is proposed, and it is used in the determination of the chlorogenic acid in plant samples as a preprocessing tool for partial least square (PLS) modeling. It is shown that the benefit of the proposed method lies not only in its performance to improve the quality of PLS model and the prediction precision, but also in its simplicity and practicability. It may become a convenient and efficient tool for preprocessing NIR spectral data sets in multivariate calibration.     

Development of wavelet transform voltammetric analyzer

An on-line wavelet transform algorithm and development of voltammetric analyzer with the on-line wavelet transform (WT-voltammetric analyzer) are described. Because the on-line wavelet transform decomposes the sampled signal simultaneously with the progress of sampling, the WT-voltammetric analyzer gives all the components contained in the sampled voltammogram. Applications of the WT-voltammetric analyzer in linear sweep voltammetric analysis of mixtures of Pb(II) and Tl(I) and in square wave voltammetric analysis of mixture of Cd(II) and In(III) were investigated. Results showed that the overlapping peaks of Pb(II) and Tl(I) can be separated easily, and the peak position after the on-line wavelet transform does not change. The linearity of the calibration curves for Cd(II) and In(III) in the overlapping square wave voltammetric curves were kept after the on-line wavelet transform. Quantitative determination of Cd(II) and In(III) in mixture samples were investigated. The recoveries are between 92.5 and 107.1%.     

Modelling mutagenicity using properties calculated by computational chemistry

The recent advances in combinatorial chemistry and high throughput screening technologies have led to an explosion in the numbers of possible therapeutic candidates being produced at the early stages of drug discovery. This rapid increase in the number of chemicals to be classified results in a greater need for alternative methods for the prediction of toxicity. Most QSAR models for mutagenicity have been constructed for congeneric series. The prediction requirements of the pharmaceutical industry, however, cover quite diverse chemical structures. This paper reports a study of mutagenicity data for a diverse set of 90 compounds. Good discriminant models have been built for this data set using properties calculated by the techniques of computational chemistry. Jack-knifed (leave one out) predictions for these models are of the order of 85%.     

Modelling mutagenicity using properties calculated by computational chemistry

The recent advances in combinatorial chemistry and high throughput screening technologies have led to an explosion in the numbers of possible therapeutic candidates being produced at the early stages of drug discovery. This rapid increase in the number of chemicals to be classified results in a greater need for alternative methods for the prediction of toxicity. Most QSAR models for mutagenicity have been constructed for congeneric series. The prediction requirements of the pharmaceutical industry, however, cover quite diverse chemical structures. This paper reports a study of mutagenicity data for a diverse set of 90 compounds. Good discriminant models have been built for this data set using properties calculated by the techniques of computational chemistry. Jack-knifed (leave one out) predictions for these models are of the order of 85%.     

Preprocessing of ion mobility spectra by lognormal detailing and wavelet transform

This study has developed an efficient preprocessing strategy for ion mobility spectrometry (IMS) data allowing for improved peak clarity and comparability of different measurements. Using the discrete wavelet transform for data compression and denoising, and fitting a lognormal function to the strong tailing of the reactant ion peak (RIP), enables a data reduction to 25% or less, a significant increase of the signal-to-noise ratio, and the successful elimination of the RIP tailing. The preprocessing of breath measurements obtained by coupling an IMS to a gaschromatographic column, has resulted in the desired outcome of smooth peaks lying on a common base level. These results are transferable to other applications of one- and two-dimensional separations with IMS or instrumentations generating a similar data structure.