Signal Processing in Normal Pulse Voltammetry by Means of Dedicated Mother Wavelet

In the work, a new signal processing algorithm is presented and applied for the transformation of the sigmoidal shaped curves, registered in normal pulse voltammetry (NPV), to the peak shaped curves. The method is based on the continuous wavelet transform (CWT) and specially constructed mother wavelet defined using the ideal wave‐shaped curve. Transformation of the signal, elimination of noises and separation of overlapping data can be achieved in one step by means of proposed procedure. The operation and effectiveness of the algorithm is presented using ideal, noised and overlapping simulated curves. The process of simultaneous determination of lead and indium as well as transformation of curves registered for elements' ions: lead, indium, thallium and cadmium is described. The obtained results show substantial improvement of the performance of NPV.     

基于小波变换平滑主成分分析

小波变换具有很强的信号分离能力,很容易把随机噪音从信号中分离出来,从而提高信号的信噪比。本文把小波变换引入到因子分析中,提出了基于小波变换平滑主成分分析,该算法既保留普通主成分分析的正交分解,又具备了小波变换的信号分离能力。模拟数据和实验数据的结果表明,该算法具有从低信噪比的数据中提取出有用信息,并提高信号的信噪比。迭代目标变换因子分析处理实验数据的结果表明,基于小波变换平滑主成分分析的处理结果优     

去卷积伏安法中离散数据处理的方法研究(Ⅰ)──正交小波变换平滑

一系列的离散数据处理方法已成为化学计量学的重要组成部分[1],去卷和伏安法就是结合计算机技术的新一代电分析方法,其激励信号与输出信号均为计算机发生和采集的数字信号,对采集到的信号一般采用移动平均法[2]和Fourier变换处理法[3]进行平滑处理．但是,Fourier变换在电分析化学领域的难度较大,运算复杂,为此,Aubarel等[4]提出了不用FFT的Fourier变换平滑算法,但是该法要先对信号进行预处理,并且对Fourier的和式要反复进行折叠,计算量较大．80年代末发展起来的小波变换引起了人们广泛的关注[5],被称为数学“显微镜”,具有…     

Daubechies小波主成分回归法机理及算法研究

将小波变换与主成分回归相结合,提出一种新型多元校正算法---小波基主成分回归法。理论分析和仿真实验表明,该法可更有效地去除噪声,提取有用信息。将其用于氯霉素及甲硝唑实际药物体系分析,与主成分回归法(PCR)相比,得到的回收率总平均相对误差由1.70%下降到0.90%。此外,通过将统计判据和小波多尺度分析相结合,发展了一种新的因子数判定方法。理论和实验研究表明,该法比传统因子数判定法具有更高的可靠性。     

二进小波变换极大模法用于分析化学信号的滤噪

实验数据的滤噪在分析化学领域中具有重要的意义。小波变换技术具有很强的信号分离能力，容易把随机噪声从信号中分离出来，从而提高信号的信噪比。本文使用滤噪方法不同于传统离散小波变换方法，而是通过引入二进小波变换和李氏指数的概念，根据噪声与有用信号的极大模截然不同的特征，实现信号滤噪。实验数据的仿真结果研究也证明该方法的可行性。     

基于导数直方图和神经网络的色谱基线提取算法

根据基线信号的变化特征,提出了一种新的色谱基线提取算法－基于一阶导数直方图和神经网络的色谱基线提取算法。鉴于信号总是存在着噪声,含噪声的基线信号一阶导数值也较大,并且分布无规律,而采用了多分辨率小波变换滤波技术。通过选择阈值门限,本算法可精确提取出信号的基线,尤其适用于非基线对称类的色谱信号的基线（趋势函数）提取。     

Noise filtering and deconvolution of XPS data by wavelets and Fourier transform

In experimental sciences, the recorded data are often modelled as the noisy convolution product of an instrumental response with the ‘true’ signal to find. Different models have been used for interpreting x‐ray photoelectron spectroscopy (XPS) spectra. This article suggests a method of estimate the ‘true’ XPS signal that relies upon the use of wavelets, which, because they exhibit simultaneous time and frequency localization, are well suited to signal analysis. First, a wavelet shrinkage algorithm is used to filter the noise. This is achieved by decomposing the noisy signal into an appropriate wavelet basis and then thresholding the wavelet coefficients that contain noise. This algorithm has a particular threshold related to frequency and time. Secondly, the broadening due to the instrumental response is eliminated through a deconvolution process similar to that developed in the previous paper in this series for the analysis of HREELS data. This step mainly rests on least‐squares and on the existing relation between the Fourier transform, the wavelet transform and the convolution product. Copyright © 2004 John Wiley & Sons, Ltd.     

A Background and noise elimination method for quantitative calibration of near infrared spectra

A new hybrid algorithm is proposed to eliminate the varying background and noise simultaneously for multivariate calibration of near infrared (NIR) spectral signals. The method is based on the use of multi-resolution, which is one of the main advantages provided by wavelet transform. The signals are firstly split into different frequency components, which keep the same data points of the original signals. In conjunction with a modified uninformative variable elimination (mUVE) criterion, the new method can be used to remove the low-frequency varying background and the high-frequency noise simultaneously. The method is successfully applied to simulated spectral data set and experimental NIR spectral data, resulting in more parsimonious multivariate models with higher precision. In addition, the proposed strategy can be applied to other spectral signals as well.     

小波滤噪用于示波计时电位信号处理的研究

根据信号（Ｓ）和噪声（Ｎ）在小波变换下表现出的截然不同的性质,提出了一种新的滤噪方法,研究了噪音在不同细节的性质、滤噪阈值的确定及平滑与滤噪的特点。对不同Ｓ／Ｎ的示波计时电位信号进行了实验结果表明;小波滤噪在大大提高Ｓ／Ｎ的同时,信号强度基本不损失,优于传统的滤噪方法。     

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.     

Simplex optimization procedure for evaluating equivalence points in sigmoidal and segmented titration curves

The use of the simplex procedure as a non-linear least-squares curve-fitting method is proposed for evaluation of equivalence points in sigmoidal and segmented titration curves. The application of this procedure to theoretical curves affected by different amounts of random noise indicates its effectiveness and accuracy for locating the correct end-point in titrations characterized by very low reaction constants. The relevant results are compared with those obtained by other regression methods as well as by the first-derivative and Gran approaches.     

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.     

Sub-optimal wavelet denoising of coaveraged spectra employing statistics from individual scans

This paper proposes a novel wavelet denoising method, which exploits the statistics of individual scans acquired in the course of a coaveraging process. The proposed method consists of shrinking the wavelet coefficients of the noisy signal by a factor that minimizes the expected square error with respect to the true signal. Since the true signal is not known, a sub-optimal estimate of the shrinking factor is calculated by using the sample statistics of the acquired scans. It is shown that such an estimate can be generated as the limit value of a recursive formulation. In a simulated example, the performance of the proposed method is seen to be equivalent to the best choice between hard and soft thresholding for different signal-to-noise ratios. Such a conclusion is also supported by an experimental investigation involving near-infrared (NIR) scans of a diesel sample. It is worth emphasizing that this experimental example concerns the removal of actual instrumental noise, in contrast to other case studies in the denoising literature, which usually present simulations with artificial noise. The simulated and experimental cases indicate that, in classic denoising based on wavelet coefficient thresholding, choosing between the hard and soft options is not straightforward and may lead to considerably different outcomes. By resorting to the proposed method, the analyst is not required to make such a critical decision in order to achieve appropriate results.     

通过反函数或者隐函数快速准确地绘制滴定曲线

滴定曲线是定量化学分析的重点之一,包含了大量有用信息。本文提出通过反函数或者隐函数的方式绘制滴定曲线。与传统绘制方式相比,反函数或者隐函数不仅容易推导,而且易于编程实现,因此能够快速获得大量数据点,从而显著提高滴定曲线的准确性。这种绘制方法适用于各种滴定体系,尤其是传统方法难以解决的一些复杂体系。此外,借助一些高级数据处理软件,非计算机专业人员能够快速掌握相关编程。得益于高效的绘制方案和简洁的编程,高精度滴定曲线得以发挥其应有功能,包括指示剂选择、准确滴定判别、终点误差计算以及直观地研究滴定体系的各种影响因素。本研究作为计算机技术高度发展背景下分析化学教学改革的一个尝试,对传统课程内容进行优化,去冗存精,使其简明凝练,重点突出,定量分析的主旨更加明晰。     

Spectrophotometric titration of ionisable groups in proteins: a theoretical study

A simple theoretical model is proposed for evaluation of the optical titration behaviour of tyrosyl and carboxyl residues in proteins. The pK values involved in the model are computed using the semi-empirical method. The titration curves are calculated using the values of the molar absorption differences for tyrosyl residues in the ultraviolet (UV) region at 245 and 295 nm, and for carboxyl residues in the infrared (IR) region at 1565 and 1707 cm(-1), respectively. The theoretical tyrosyl titration curves are compared with the experimental data for lysozyme, myoglobin and chymotrypsinogen (available in the literature). This approach provides a good tool for distinguishing between the ionisation and the conformational changes in the alkaline range. The quantitative evaluation of the change of molar extinction coefficients as a function of pH in the case of carboxyl titration for lysozyme, trypsin and cytochrome c shows a good agreement with the experimental titration data.     

毛细管电泳激光诱导荧光检测信号的小波滤噪

采用小波滤噪方法对毛细管电泳激光诱导荧光检测信号进行了处理，研究了小波变换中小波基的选择及噪声阈值的选择对滤噪的影响。结果表明，采用DB4小波基能有效消除毛细管电泳激光诱导荧光检测信号中存在的噪声，使信噪比得到较大改善。     

一种新的小波滤波方法在化学谱图信号滤噪中的应用

仪器分析测定中，噪声的存在往往影响分析的准确度和仪器的检出限。小波变换多分辨分析的特性使得它成为一种很好的滤噪方法。基于小波分解后信号与噪声的小波系数随尺度变化规律不同的特性，提出了一种新的滤波滤方法-空域相关法，即通过不同尺度上相关系数模值与小波系数模模值的比较，达到滤波滤的目的。本文提出的方法具有无需人为选定无需人为选定滤噪阈值和小波函数、方法简单、失真度小等优点，可以大在提高信号的信噪比。模拟数据和ICP-AES实验数据证明了该方法的有效性。     

Elucidation of aquatic humic partial structures by multistage ultrafiltration and two-dimensional nuclear magnetic resonance spectrometry

An on-line wavelet transform (WT) algorithm was proposed and successfully used in processing the photoacoustic (PA) signal. By investigating the spectra of three rare earth compounds, it was indicated that after on-line decomposition by WT, the noise in the PA spectra was cleanly removed, and the resolved information in the overlapping peaks was easily retrieved. The effect of different sampling rate on resolved results was also investigated. The experimental results showed that the position of peaks after decomposition agreed with the corresponding intramolecular energy transition bands, which demonstrated that WT is a useful and efficient tool for the study of energy bands of rare earth compounds using PA spectroscopy. Received: 7 July 1998 / Accepted: 14 September 1998     

Elucidation of aquatic humic partial structures by multistage ultrafiltration and two-dimensional nuclear magnetic resonance spectrometry

An on-line wavelet transform (WT) algorithm was proposed and successfully used in processing the photoacoustic (PA) signal. By investigating the spectra of three rare earth compounds, it was indicated that after on-line decomposition by WT, the noise in the PA spectra was cleanly removed, and the resolved information in the overlapping peaks was easily retrieved. The effect of different sampling rate on resolved results was also investigated. The experimental results showed that the position of peaks after decomposition agreed with the corresponding intramolecular energy transition bands, which demonstrated that WT is a useful and efficient tool for the study of energy bands of rare earth compounds using PA spectroscopy. Received: 7 July 1998 / Accepted: 14 September 1998