Theory for a wavelet analysis of electrochemical noise in the laplace space with use of two operational frequencies

The image of a random process in the Laplace space may be viewed as resulting from use of a oneway continuous wavelet transform with an exponential as the basic function, i.e. as resulting from the application of the Laplace wavelet. If the Laplace-wavelet variance of an electrochemical noise allows one to determine the Laplace transform of a time-correlation function, i.e. a factual operational spectral density of the noise, then the covariance of two Laplace waveletes of an electrochemical noise, each of which corresponds to its own operational frequency, allows one to verify a local consistency of the initial experimental noise data. The Laplace waveletes are applied rather widely. In fact, any stationary random process and stationary random time sequence can be described with operational noise spectra. Dedicated to the ninetieth anniversary of Ya.M. Kolotyrkin’s birth.     

Meixner Wavelet Transform: A Tool for Studying Stationary Discrete-Time Stochastic Processes

A general approach to analyzing discrete stochastic processes in the context of spectral analysis in the Laplace domain is considered. It is shown that a multichannel algorithm, which may be used for determining a discrete Laplace transform of the correlation function corresponding to a stationary discrete-time stochastic process, may be designed on the basis of Meixner wavelets.     

Software and Instrumentational Methods of Enhancing the Resolution in Electrochemical Noise Measurements

Several methods of enhancing the signal-to-noise ratio for instrumentation designed to measure electrochemical noise are practically tested. The experiments are carried out using model RC-circuits and lielectrolyte electrochemical cells. Strong limitations in the tested objects’ impedance values are found due to the input current noise of the instrumentation, especially during the parallel connection of several channels. The advantages of a two-channel scheme for automatically compensating the instrument’s self noise are demonstrated. Different methods of lowering the dispersion of the frequency dependences of the spectral power density of electrochemical noise are compared. It is shown that averaging over segments with an overlap is the most effective method but averaging over frequencies can lead to large distortions when investigating electrochemical systems.

     

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.     

Ensemble wavelet modelling for determination of wheat and gasoline properties by near and middle infrared spectroscopy

The wavelet transform has been shown to be a useful tool for multivariate calibration. However, the choice of wavelet transform settings (wavelet family, length and number of decomposition levels) for a given application is still an open problem. The present paper proposes an alternative approach, which consists of generating an ensemble model by combining individual models obtained with different wavelet transform settings. The advantages of the proposed method are demonstrated in two analytical problems, namely the determination of moisture and protein in wheat by near infrared spectroscopy and the determination of specific mass and three distillation temperatures (T10, T50, T90) in gasoline by middle infrared spectroscopy. In these problems, the results varied considerably among individual models, which underlines the risk associated to an inadequate choice of wavelet transform settings. In contrast, the ensemble model always provided adequate results in terms of prediction error and noise sensitivity. The proposed method can be seen as an advantageous alternative for multivariate calibration in the wavelet domain, as it frees the analyst from the need to choose a particular configuration for the wavelet transform.     

Photon correlation spectroscopy of polymers in the glassy state

Photon correlation spectroscopy has proven to be a very useful technique for studying slowly relaxing density and optical anisotropy fluctuations in bulk polymers near the glass transition. When some of the fluctuations achieve relaxation times much longer than the typical averaging time for the intensity autocorrelation function (10⁴ s), the result must be treated in the partially heterodyned limit. Also, when the sample is near the glass transition but not at equilibrium the correlation function is not stationary in time because the system is relaxing as a whole toward the equilibrium state. The above effects are discussed theoretically and demonstrated experimentally in polystyrene as a function of temperature and pressure. Light scattering with coherent excitation also fluctuates in space as well as in time (as shown in the accompanying paper). The consequences of this effect are discussed. When most of the intensity is associated with fluctuations whose relaxation times are very long in polystyrene, there is still a broad relaxation function evident. This is characteristic of a secondary relaxation process.     

利用小波变换检测电化学噪声信号波形

简述了应用小波变换检测点蚀电化学噪声信号的基本原理,对在3.5％ NaCl溶液中工业纯铝发生点蚀的电化学噪声信号检测分析表明：小波变换能够提取发生点蚀的电化学噪声信号和测量系统噪声在多惊讶分辨空间中的波形特征,根据表征该特征的小波系数模极大值在不同尺度下的传播特性,可实现对点蚀电化学噪声信号波形的检测。     

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.     

电化学噪音数据小波分析法研究

电化学动力系统演化过程中 ,其状态参量 (如电极电位、电解池电流等 )的随机波动现象被称为“电化学噪音”(ECN) .小波变换是近年来数学与信号处理领域获得突破性进展的一种数据处理方法 .本文首次用连续小波变换的方法对混凝土中钢筋腐蚀产生的“电化学噪音”信号进行初步研究 ,通过将原始的时域信号变换至时_频相平面来观察其结构特征 ,并揭示出电化学腐蚀过程的混沌动力学行为 .     

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.     

Wavelet transform-based analysis for electrochemical noise

Wavelet transforms are presented as a useful tool to analyse electrochemical noise data. Various concepts developed in the framework of wavelet transforms have been adapted to study electrochemical noise measurements. The most relevant feature of this method of analysis is its capability of decomposing electrochemical noise records into different sets of wavelet coefficients, which contain information about corrosion events occurring at a determined time-scale. Thus, this mathematical approach could become an alternative tool which solves the limitations of other more established procedures for the analysis of electrochemical noise data, such as statistical or Fourier transform-based methods.     

小波变换用于近红外光谱性质分析

以汽油研究法辛烷值分析为例,研究了小波变换在近红外光谱分析中的应用。对近红外光谱的小波特性、小波变换参数以及变量提取方法进行了详细研究。研究结果表明：光谱噪音、有用信息和背景分别分布在小波高、中和低频区域;母小波函数对性质分析结果影响很大;小波变换可以同时扣除光谱背景、去除噪音和压缩变量,具有运算速度快、分析精度高以及无需去噪后处理等优点,在近红外光谱分析中具有很好的应用前景。     

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。     

Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry

Discrete wavelet transform (DWT) provides a well-established means for spectral denoising and baseline elimination to enhance resolution and improve the performance of calibration and classification models. However, the limitation of a fixed filter bank can prevent the optimal application of conventional DWT for the multiresolution analysis of spectra of arbitrarily varying noise and background. This paper presents a novel methodology based on an improved, second-generation adaptive wavelet transform (AWT) algorithm. This AWT methodology uses a spectrally adapted lifting scheme to generate an infinite basis of wavelet filters from a single conventional wavelet, and then finds the optimal one. Such pretreatment combined with a multivariate calibration approach such as partial least squares can greatly enhance the utility of Raman spectroscopy for quantitative analysis. The present work demonstrates this methodology using two dispersive Raman spectral data sets, incorporating lactic acid and melamine in pure water and in milk solutions. The results indicate that AWT can separate spectral background and noise from signals of interest more efficiently than conventional DWT, thus improving the effectiveness of Raman spectroscopy for quantitative analysis and classification.     

The fluorescence quenching rate constant for the distance-dependent quenching processes in the presence of diffusion

It is shown that the fluorescence quenching constant is given by the Laplace transform of the time-dependent bimolecular rate constant k(t). The dependence of the quenching rate constant on the transformation parameter can be obtained from measurements of the fluorescence decay functions and a Stern-Volmer-type analysis in the Laplace domain. The advantages of this type of investigation of the quenching rate function are demonstrated by a numerical calculation for the distance-dependentquenching process in     

小波变换用于示波信号中有用信息提取的研究

示波分析是近年来在我国发展起来的一个新的电化学分析研究领域［１～４］．它根据阴极射线示波器荧光屏上示波图及其变化进行分析测试,从原理上可以将其分为示波电位法和示波计时电位法;从测定方式上可以将其分为示波滴定和示波测定．关于示波电位法的一些理论问题（如...     

The Application of Complex Wavelet Transform to Spectral Signals Background Deduction

The accuracy of spectrograms may be affected by baseline excursion or drift when infrared spectrometers are used in the analyses of gases. Background deduction or baseline correction is one of the effective pretreatment methods that can improve measurement accuracy. This paper presents a novel methodology based on complex wavelet transform algorithm to perform background deduction. The complex wavelet transform methodology establishes a complex wavelet filter to decompose the spectral signals first, and set the decomposition coefficients in the high-frequency section to zero, and then reconstruct the background signals; finally, the background deduction can be realized by deducting the background signals. In this study, the complex wavelet established by Daubechies was selected to demonstrate background deduction aiming at simulative spectral signals with different backgrounds and the real spectral signal of SF6 decomposition gases. Compared with the results done by the real wavelet transform in the same conditions, the results indicate that complex wavelet transform methodology can perform background deduction more efficiently than real wavelet transform methodology, thus improving the effectiveness and precision of spectrogram measurements greatly, which is useful for SF6 gas decomposition compositions analysis     

Wavelet transform-based Fourier deconvolution for resolving oscillographic signals

Fourier self-deconvolution is an effective means of resolving overlapped bands, but this method requires a mathematical model to yield deconvolution and it is quite sensitive to noises in unresolved bands. Wavelet transform is a technique for noise reduction and deterministic feature capturing because its time-frequency localization or scale is not the same in the entire time-frequency domain. In this work, wavelet transform-based Fourier deconvolution was proposed, in which a discrete approximation (such as A(2)) obtained from performing wavelet transform on the original data was substituted for the original data to be deconvolved and another discrete appropriate approximation (such as A(5)) was used as a lineshape function to yield deconvolution. Again, instead of the apodization function, the B-spline wavelet was used to smooth the deconvolved data to enhance the signal-to-noise ratio. As a consequence, this method does not suffer as badly as Fourier self-deconvolution from noises in the original data. Thus, resolution enhancement can be increased significantly, especially for signals with higher noise level. Furthermore, this method does not require a mathematical model to yield deconvolution; it is very convenient to deconvolve electrochemical signals.     

On the use of wavelet filtering and correlation techniques in atmospheric condensed phase spectroscopy

The application of wavelet filtering and analysis in spectroscopy is discussed in relation to the analysis of complex atmospheric spectra, where contributions from condensed phase particles and gas phase molecules are present in the form of broad-band features and narrow lines, respectively. The broad-band contribution can be extracted as the 'smooth signal' component of the wavelet transform, with a large reduction in the size of the corresponding data files. This procedure is applied to an investigation of the H2SO4 aerosol content of a series of atmospheric spectra measured in the ATMOS missions. The sulfate content of the smooth signal is analysed by means of correlation techniques, using a set of laboratory reference spectra of varying sulfuric acid concentration and temperature. Correlation density maps and correlation curves are used to select the most appropriate spectral zones for sulfate analysis and to assess the sulfate aerosol content in the atmosphere subsequent to the eruption of the Mount Pinatubo volcano.     

Spatially adaptive stationary wavelet thresholding for the denoising of DNA capillary electrophoresis signal

The spatially adaptive thresholding based on the stationary wavelet transform was applied to the noise removal in the signal of DNA separated and determined by capillary electrophoresis. The threshold is derived in a Bayesian framework, and previously used on the wavelet coefficients is the generalized Gaussian distribution. The threshold is simple and closed form, which is adaptive to each subband because it depends on data-driven estimates of the parameters. Using this strategy, the noise in the signal of the DNA-separated analysis by capillary electrophoresis could be removed adequately. Experimental results show that the proposed denoising method is effective, and the spatially adaptive thresholding yields a lower root-mean-square error than the universal thresholding. The text was submitted by the authors in English.