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.     

Normal Pulse Voltammetric Determination of Subnanomolar Concentrations of Chromium(VI) with Continuous Wavelet Transformation

The renewable mercury film‐modified silver solid amalgam annular band electrode (MF‐AgSAE) applied for quantitative determination of sub‐nanomolar concentrations of Cr(VI) using differential pulse (DP) and normal pulse (NP) catalytic adsorptive striping voltammetry (CAdSV) is presented. In this context a signal processing algorithm is described and applied for the transformation of sigmoidal shaped NP curves to peak shaped curves. The method utilizes continuous wavelet transform (CWT) and a specially constructed mother wavelet defined using the ideal wave‐shaped curve. It simplifies the interpretation of sigmoidal curves. In the effect the new strategy of Cr(VI) determination is 10 times more sensitive than differential pulse and square‐wave techniques. The reproducibility is below 3–5 % (n=3) for the 0.2–2.2 nM concentration range of Cr(VI). The detection limit for 30 s preconcentration is equal to 0.05 nM with sensitivity of 0.809±0.012 µA nM^?1 and is limited by the purity of the used reagents. The correlation coefficient is equal to 0.9993. For 2 nM of Cr(VI), in the tested range, 0≤t_acc≤60 s, the relation wave height? accumulation time (I_w–t_acc) is linear. The operation and effectiveness of the proposed procedures was confirmed by the quantitative determination of Cr(VI) in supporting electrolyte and CRM (surface water samples and urine) with known amounts of the analyte. The obtained results show substantial improvement of the performance of NP CAdSV technique.     

Comparison of spline wavelet and orthogonal wavelet in processing analytical chemistry signals

Spline wavelet and orthogonal wavelet are two widely used wavelet methods. In this paper, comparison of these two methodshas been made, including their algorithm, properties and results of signal processing in analytical chemistry signals. It is found that spline wavelet is more effective than orthogonal wavelet in processing high noise signals. The curves obtained from spline wavelet are closer to the theoretical ones than those obtained from orthogonal wavelet and the errors of spline wavelet are smaller than those of orthogonal wavelet.     

Dedicated mother wavelet in the determination of antimony in the presence of copper

In this paper, a new signal-processing procedure is applied to the optimization of voltammetric determination of antimony in the presence of copper and the parallel determination of these two elements. The proposed numerical algorithm for the separation of the overlapping peaks utilizes the continuous wavelet transform and the inverse continuous wavelet transform. As the base function, the specially defined dedicated mother wavelet is used. In its construction the ideal, simulated voltammetric peak is intensively exploited. This approach, corresponding to the wavelet theory, gives satisfactory signals separation, even in the cases when they constitute one peak. The possibility of Sb(III) determination is presented in the case of different distances between copper and antimony peaks and also in 10-, 20- and 50-fold excesses of Cu. The parallel determination of Cu(II) and Sb(III) is possible even in the case of a 10-fold excess of copper. The quality of the obtained results fulfills the requirements of validation.     

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%.     

样条小波和Fourier变换联用技术在分析化学中的应用

探讨了样条小波和Fourier变换方法的算法及应用特征,将两种方法联合使用,设计出了一种新型的数字滤波器,使两种方法互相取长补短,使各自的优势能得到充分发挥.优选了处理低信噪比分析化学信号的滤波参数.不仅能使结果峰形高度保真,克服样条小波分析方法的不足,而且可对高噪声信号进行处理.     

小波包分析用于重叠分析化学信号的处理

对小波包分析的算法进行了改进,并将此算法成功地应用于多组分重叠色谱信号的解析.结果表明,本文提出的算法解决了MRSD算法的不足,更适合处理分析化学信号,用于重叠信号的解析时不需重构(逆变换),简化了数据处理步骤,加快了数据解析速度,具有较强的解析能力.对于重叠色谱信号的解析,小波包分析比小波分析具有更强的解析能力.     

Spline wavelet in the resolution of overlapping voltammetric peaks

Spline wavelet transform is used to resolve overlapping voltammetric peaks. A suitable resolving factor is chosen to multiply the filters of spline wavelet and make it a peak resoluter. Simulated overlapping voltammetric peaks are processed by the peak resoluter and satisfactory results are obtained. Base-line separation can be achieved, the relative errors of peak position are less than 3.0%, and the relative errors of peak area are less than 5.0%. The effect of different resolving factors and spline wavelet basis are discussed. To test the procedure, two systems, cadmium (Ⅱ)-indium (Ⅲ) and lead (Ⅱ)-thallium (Ⅰ), are used.     

基于有限脉冲响应滤波器的实时小波算法及其在色谱信号解析中的应用

对色谱信号进行正确、实时地解析是利用色谱仪器系统进行过程检测的关键技术。小波分析方法能对色谱信号进行有效解析,但实时性一直是制约该方法在色谱信号处理中广泛应用的一个瓶颈。多分辨率分析与重构算法(MALLAT)是小波分析的一种快速算法,但是该算法的实时性仍然需要进一步提高。针对这一问题,以MALLAT算法原理为基础,利用在分解重组过程中两组滤波器系数之间的关系提出了一种基于有限脉冲响应滤波器的实时小波分析算法。仿真结果表明,与经典的MALLAT小波快速算法相比,该算法在保持信号有效分解与重构的基础上,运行耗时明显缩短,实时性得到较大提高。     

连续小波变换用于滴定终点的确定

针对基于二进小波变换奇异性检测方法的不足,提出基于连续小波变换奇异性检测方法,该方法具有较细致的局部奇异性刻画能力,能够对滴定曲线的滴定终点进行精确的定位。将这种方法应用于NaOH对HCl和H3PO4滴定曲线滴定终点的确定,取得了理想的结果。     

Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform

Spectral signals are often corrupted by noise during their acquisition and transmission. Signal processing refers to a variety of operations that can be carried out on measurements in order to enhance the quality of information. In this sense, signal denoising is used to reduce noise distortions while keeping alterations of the important signal features to a minimum. The minimization of noise is a highly critical task since, in many cases, there is no prior knowledge of the signal or of the noise. In the context of denoising, wavelet transformation has become a valuable tool. The present paper proposes a noise reduction technique for suppressing noise in laser-induced breakdown spectroscopy (LIBS) signals using wavelet transform. An extension of the Donoho's scheme, which uses a redundant form of wavelet transformation and an adaptive threshold estimation method, is suggested. Capabilities and results achieved on denoising processes of artificial signals and actual spectroscopic data, both corrupted by noise with changing intensities, are presented. In order to better consolidate the gains so far achieved by the proposed strategy, a comparison with alternative approaches, as well as with traditional techniques, is also made.     

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.     

Wavelet transforms in separation science for denoising and peak overlap detection

Wavelet transform is a versatile time‐frequency analysis technique, which allows localization of useful signals in time or space and separates them from noise. The detector output from any analytical instrument is mathematically equivalent to a digital image. Signals obtained in chemical separations that vary in time (e.g., high‐performance liquid chromatography) or space (e.g., planar chromatography) are amenable to wavelet analysis. This article gives an overview of wavelet analysis, and graphically explains all the relevant concepts. Continuous wavelet transform and discrete wavelet transform concepts are pictorially explained along with their chromatographic applications. An example is shown for qualitative peak overlap detection in a noisy chromatogram using continuous wavelet transform. The concept of signal decomposition, denoising, and then signal reconstruction is graphically discussed for discrete wavelet transform. All the digital filters in chromatographic instruments used today potentially broaden and distort narrow peaks. Finally, a low signal‐to‐noise ratio chromatogram is denoised using the procedure. Significant gains (>tenfold) in signal‐to‐noise ratio are shown with wavelet analysis. Peaks that were not initially visible were recovered with good accuracy. Since discrete wavelet transform denoising analysis applies to any detector used in separation science, researchers should strongly consider using wavelets for their research.     

Combined Wavelet Transform with Curve‐fitting for Objective Optimization of the Parameters in Fourier Self‐deconvolution

Fourier self‐deconvolution was the most effective technique in resolving overlapping bands, in which deconvolution function results in deconvolution and apodization smoothes the magnified noise. Yet, the choice of the original half‐width of each component and breaking point for truncation is often very subjective. In this paper, the method of combined wavelet transform with curve fitting was described with the advantages of an enhancement of signal to noise ratio as well as the improved fitting condition, and was applied to objective optimization of the original half‐widths of components in unresolved bands for Fourier self‐deconvolution. Again, a noise was separated from a noisy signal by wavelet transform, therefore, the breaking point of apodization function can be determined directly in frequency domain. Accordingly, some artifacts in Fourier self‐deconvolution were minimized significantly.     

荧光光度法同时测定邻苯二酚、间苯二酚与对苯二酚

将一种直接信号校正(DOSC)-小波包变换(WPT)-偏最小二乘法(PLS)(DOSC-WPT-PLS)新方法用于解析荧光光谱严重重叠的邻苯二酚?间苯二酚和对苯二酚混合物,并对其进行测定。该法将DOSC、WPT及PLS 3种方法结合从而提高了获取特征信息的能力和回归质量。DOSC方法用于除去与浓度无关的结构噪音。利用WPT的时域和频域局部化的特点改进了除噪质量和数据压缩及信息提取能力。PLS方法用于多变量校准和噪音消除。处理该3种组分的荧光光谱数据,并实现了3种化合物的同时测定。设计了PDOSCWPTPLS程序执行相关计算,并对以上3种化学计量学方法进行了比较,其总体相对预测标准偏差分别为4.3%、7.7%、11.5%,结果表明DOSC-WPT-PLS法优于WPT-PLS法和PLS法。将该法用于测定自来水中邻苯二酚?间苯二酚和对苯二酚的含量,其回收率分别为99%~110%?95%~108%和98%~104%,结果满意。     

Analysis of Spontaneous Electrochemical Oscillations by the Wavelet Transformation Method

A new way of analyzing current oscillations that accompany anodic metal dissolution is presented. A wavelet transformation is used for separation and spectral analysis of singular courses—elementary components of electrochemical oscillation recordings. A method of obtaining oscillation energy distribution analogous to the spectral power density function is presented. It is shown that the chaotic component (Shil'nikov chaos) can be separated from the deterministic component of the described process.     

Resolving overlapping GC–MS signals with a multistep screening chemometric approach for the fast determination of pesticides

For the rapid analysis of multicomponent mixtures using GC–MS, a chemometric multistep screening approach was proposed to extract the signals of the components from the overlapping signals measured with a very fast temperature program. At first, independent component analysis was used to find all the possible mass spectra from the overlapping signal in the moving windows along the retention time, and iterative target transformation factor analysis was employed to validate the existence of the extracted spectra from each window. Then, identical signals in the validated spectra were excluded using match ratio as a criterion. Finally, the chromatographic profiles for each spectrum were calculated using non‐negative immune algorithm, and the spectra with a reasonable profile were taken as the identified components. A mixture of 53 pesticides was analyzed with a very fast temperature program of 7 min. A total of 48 pesticides and 16 interferences were identified from the overlapping GC–MS signal.     

Resolution of multicomponent NMR signals using wavelet compression and immune algorithm

A novel algorithm for fast resolution of multicomponent overlapping nuclear magnetic resonance (NMR) spectrum using the wavelet compression and the immune algorithm (IA) is proposed. Taking advantage of the linear property of the wavelet transform (WT), the overlapping NMR spectrum (antigen) can be compressed by WT before it is input into the immune network, the antibodies are also compressed to the same scheme. After extraction of the compressed information of each component, the resolved NMR spectra can be restored by the WT reconstruction. It was proven that the result is almost the same with the result from an IA, but the calculation speed is much faster.     

Simultaneous quantitative analysis of overlapping spectrophotometric signals using wavelet multiresolution analysis and partial least squares

The mathematical bases and program algorithms of discrete wavelet transform (DWT), multiresolution and Mallat’s pyramid algorithm were described. The multiresolution analysis (MRA) based on Daubechies orthogonal wavelet basis was studied as a tool for removing noise and irrelevant information from spectrophotometric spectra. After wavelet MRA pre-treatment, eight error functions were calculated for deducing the number of factors. A partial least squares based on wavelet MRA (WPLS) method was developed to perform simultaneous spectrophotometric determination of Fe(II) and Fe(III) with overlapping peaks. Data reduction was performed using wavelet MRA and principal component analysis (PCA) algorithm. Two programs, SPWMRA and SPWPLS, were designed to perform wavelet MRA and simultaneous multicomponent determination. Experimental results showed the WPLS method to be successful even where there was severe overlap of spectra.