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.     

示波信号能谱的傅里叶自去卷积法

以支持电解质溶液产生的示波计时电位信号作为线性函数、去极剂本身的示波信号作为去噪函数，提出了一种傅里叶自去卷积新方法--示波信号能谱的傅里叶自去卷积法。研究了噪音和切口重叠等对去卷积结果的影响。与其他傅里叶自去卷积法相比较：该方法具有操作简单、不会引起负的帝瓣效应、不用选择去噪函数等优点。     

Fourier自去卷积示波计时电位法的研究

经典的示波计时电位法一般用ｄＥ/ｄｔＥ曲线上的切口深度进行定量测定 .由于施加于电解池的极化电流频率较高 ,使方法灵敏度和分辨率大大降低 .通过选择适当的体系、改进方法等手段可改善示波图的分辨率和提高灵敏度[13],但二者常常不能同时兼备 .Ｆｏｕｒｉｅｒ自去卷积 (ＦＳＤ)是以Ｆｏｕｒｉｅｒ变换为基础、主要用于重叠峰解析的信号处理技术[4 ].它可使信号中峰形变窄、处理后峰的位置不发生变化 .然而 ,由于线性函数和滤噪函数的选择比较困难 ,使其应用受到了限制 .本文探讨了使用小波变换所得模糊项作为线性函数的可能性 ,并将改进…     

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…     

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.     

HREELS signal processing via wavelets

In spectroscopy, the recorded spectra can often be modelled as the noisy convolution product of an instrumental function with the ‘true’ signal to be estimated. Such models have often been used for high‐resolution electron energy‐loss spectroscopy (HREELS). In this article, a new method is suggested to estimate the ‘true’ HREELS signal, i.e. the original electronic diffusion function with ‘true’ peak intensities. Our method relies upon the use of wavelets that, because they exhibit simultaneous time and frequency localization, are well‐suited for signal analysis. Firstly, 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. This step mainly rests on the existing relation between the Lipschitz regularity of the signal and the decay with scale of its wavelet coefficients and on least squares. The efficiency of this technique is highlighted by comparing the results obtained with those provided by other published methods. This work is the second in a series of three papers in this issue. The first one presents background knowledge on the wavelets required to understand the estimation methods. The third paper explores the application of wavelet filtering and deconvolution techniques to x‐ray photoelectron spectroscopy. Copyright © 2004 John Wiley & Sons, Ltd.     

Introduction to wavelet applications in surface spectroscopies

In experimental sciences, recorded data are often modelled as the noisy convolution product of an instrumental response with the ‘true’ signal. High‐resolution electron energy‐loss spectroscopy (HREELS) and x‐ray photoelectron spectroscopy (XPS) constitute two examples of this. A series of three papers is proposed about an estimation method of this ‘true’ signal in the particular cases of HREELS and XPS. This method uses wavelets that, as functions well localized in time and frequency, are properly adapted to signal analysis. In this first article, the wavelet theory is introduced and its rapid expansion is justified by a comparison of the wavelet transform with the Fourier transform. Afterwards, in order to illustrate the efficiency of the wavelet approach, some wavelet‐based signal analysis tools are presented. These tools include: filtering of a noisy signal, localization of irregular signal structures such as singularities or peaks and deconvolution itself. Copyright © 2004 John Wiley & Sons, Ltd.     

The effect of apodization and finite resolution on Fourier transform Raman spectra

The effects that finite resolution and choice of apodization function have on Fourier transform (FT) Raman spectra are illustrated by the 839 cm⁻¹ (ν₁) and 914 cm⁻¹ bands of KMnO₄. FT-Raman spectra were recorded at 0.5, 1, 2, 4, 8, 16 and 32 cm⁻¹ resolution using boxcar, Norton—Beer (strong, medium and weak) and triangular apodization functions at each resolution. The results show the dramatic changes in bandshape that occur as the ratio (resolution/true full width at half height of band) increases. The changes were measured in terms of the full width at half height of the band, the height of the band, the area of the band and the bandshape (expressed as a sum of Lorentzian and Gaussian lines). At a given resolution the degree to which each of these characteristics is affected is strongly dependent on the choice of the apodization function.     

Wavelet transform as a new approach to the enhancement of signal-to-noise ratio in anodic stripping voltammetry

De-noising signals is a frequent aim achieved by signal processing in analytical chemistry. The purpose is to enable the detection of trace concentrations of analytes. The limit of detection is defined as the lowest amount of analyte that still causes signals greater than the background noise. Appropriate de-noising decreases only the noise and maintains the measurement signal, so that signal-to-noise ratios are enhanced. One adequate mean of signal processing for this purpose is wavelet transform, which still is not a common tool in analytical chemistry. In this paper, the ability of de-noising by wavelet transform is shown for measurements in anodic stripping voltammetry using a hanging mercury drop electrode. The calculation of limits of detection and signal-to-noise ratios on the basis of peak-to-peak noise is exercised to quantify the performance of de-noising. Furthermore, signal shape with regard of easing the application of base lines is discussed. Different wavelet functions are used, and the results are compared also to Fourier transform. Coiflet2 was found out to reduce noise by the factor of 330 and is proposed as the adequate wavelet function for voltammetric and similar signals.     

Wavelet transform applications in analytical chemistry

The wavelet transform has been established with the Fourier transform as a data-processing method in analytical chemistry. The main fields of application in analytical chemistry are related to denoising, compression, variable reduction, and signal suppression. Analytical applications were selected showing prospects and limitations of the wavelet transform. An important aspect consists in showing the advantage of wavelet transform over Fourier transform with respect to dual localization of a signal in both the original and the transformed domain enabling principal new application fields in comparison with Fourier transform.     

近红外漫反射光谱的小波变换滤波

利用小波变换对５２个烟草样品的近红外漫反射光谱进行滤波处理，并用ＰＬＳ法来计算烟草样品的总氮含量，结果表明小波变换滤波后，预测集的相对标准偏差由原来的９．２％降为７．４％，此结果也优于傅里叶变换和五点三次平滑。     

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...     

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.     

小波变换用于二次微分交流示波计时电位信号中有用信息的提取

小波分析是８０年代发展起来的一种新的数学分支。由于小波变换具有许多其它的信号处理手段所不具备的优良特性，如正交性，可变的时－频分辨率和可调节的局部支持等，使它成为信号处理的一种强有力的工具。     

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.     

付里叶变换红外光谱仪的操作参数对光谱的影响

本文以二苯基甲酮的ＫＢｒ压片为标样，在Ｂｒｕｋｅｒ ＩＦＳ １２０ＨＲ付里叶变换红外光谱仪上系统考察了该仪器折一些重要操作参数（光源光栏、切趾函数、扫描速度）对光谱质量（信噪比，分辨率）的影响。从而获得了测样时的优化操作条件。     

Synthesis and magnetic properties of organic multilayer films based on the layer‐by‐layer assembly

Two polymers containing pyridine rings were prepared by free‐radical polymerization and confirmed by Fourier transform infrared and ¹H NMR spectra. The preparation of four multilayer films that were obtained by self‐assembly of the polymer and the transition metal neutralized polyelectrolyte on PE substrate was described. UV–vis spectra and atomic force microscopy images were applied to characterize these films and indicate the uniform assembling process. The driving force for building up the multilayer films was identified by infrared spectroscopy to be the coordination interaction. The magnetic behavior was examined as a function of magnetic field strength at 30 kOe and as a function of temperature (5–300 K). All films display strong soft ferromagnetic properties and higher than those of the bulk materials. The magnetic results show that the layer‐by‐layer self‐assembling approach is beneficial to the ordered alignment of adjacent paramagnetic spins and induces better magnetic phenomena. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Inorganic–organic hybrids involving poly(ε‐caprolactone) and silica network: Hydrogen‐bonding interactions and isothermal crystallization kinetics

Inorganic–organic hybrids mediated by hydrogen‐bonding interactions involving silicon oxide network and poly(ε‐caprolactone) (PCL) were prepared via an in situ sol–gel process of tetraethoxysilane in the presence of PCL. Fourier transform infrared spectroscopy indicated that there were hydrogen‐bonding interactions between carbonyls of PCL and silanol hydroxyls that were formed by incomplete polycondensation in the sol–gel process. In terms of the frequency shift of the hydroxyl stretching vibration bands, it is concluded that the strength of the interassociation between PCL and silicon oxide networks is weaker than that of the self‐association in the control silica network. The phenomenon of equilibrium melting point depression was observed for the PCL/silica system. The hybridization of PCL with silica network causes a considerable increase in the overall crystallization rate and dramatically influences the mechanism of nucleation and growth of the PCL crystallization. The analysis of isothermal crystallization kinetic data according to the Hoffman‐Lauritzen theory shows that with increasing silica content in the hybrids, the surface energy of extremity surfaces increases dramatically for the hybrids. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2594–2603, 2005     

Self‐Healable Electrically Conducting Wires for Wearable Microelectronics

Electrically conducting wires play a critical role in the advancement of modern electronics and in particular are an important key to the development of next‐generation wearable microelectronics. However, the thin conducting wires can easily break during use, and the whole device fails to function as a result. Herein, a new family of high‐performance conducting wires that can self‐heal after breaking has been developed by wrapping sheets of aligned carbon nanotubes around polymer fibers. The aligned carbon nanotubes offer an effective strategy for the self‐healing of the electric conductivity, whereas the polymer fiber recovers its mechanical strength. A self‐healable wire‐shaped supercapacitor fabricated from a wire electrode of this type maintained a high capacitance after breaking and self‐healing.