On the joint time-frequency characteristics of chemical oscillations

A method of time-frequency transformations of nonstationary signals has been discussed and applied to the analysis of oscillatory Belousov-Zhabotinsky (BZ) reaction. Selected registers of BZ reactions, that represent regular and complex dynamic behavior, have been submitted to the detailed spectral analysis using the short time Fourier transform (STFT). It has been demonstrated that the STFT is an accurate and suitable method for decomposition of chemical oscillations in the joint time and frequency domain. The energy distribution via STFT, presented in this article, revealed some specific characteristics of transitions between different regimes in the closed system of BZ reaction.     

Instrumental Broadening Correction in Size Exclusion Chromatography through Fast Fourier Transform Techniques

Abstract

This paper shows the practicability of the use of the fast Fourier transform (FFT), with appropriate filtering in the frequency domain, as a means of deconvoluting Tung's integral formula (1). The method is limited to uniform instrumental spreading functions, but presents several important advantages: it is numerically efficient, no assumptions about the shape of the spreading function are made, it eliminates the highfrequency measurement noise components from the corrected chromatogram without modifying the original data, and provides a means of physically interpreting the results.     

经验模态分解对瞬态电化学响应的滤波处理

用经验模态分解(EMD)对恒电量瞬态响应信号进行滤波处理. 通过计算机仿真实验评估EMD的滤波效果. 为了提高EMD滤波的实用性和减少滤波过程的主观性, 仿真实验主要针对混迭了白噪声、高频噪声和市电干扰以及上述混合噪声的恒电量瞬态响应. 在此基础上, 阐述了EMD滤波对多个时间常数恒电量瞬态响应的重要性, 并利用电化学阻抗谱结果验证了EMD滤波后的恒电量频谱. 结果表明, 经过EMD滤波的恒电量频谱和EIS有很好的相关性. 恒电量瞬态响应的EMD滤波, 采用前两项内在模函数(IMF)和IMF4的50 Hz成分置零的固定模式, 可以获得满意的滤波结果.     

快速傅立叶变换用于色谱噪声平滑及微弱信号的检测

应用快速傅立叶变换法（ＦＦＴ）对色谱噪声进行平滑处理及微弱信号检测,同时,也与其他数字滤波法进行了比较。结果表明,利用ＦＦＴ法可以很好地对噪声进行平滑处理,使信噪比提高１８倍,为更好地进行痕量组分的色谱微弱信号检测打下了基础。     

Artifacts in Fourier transform mass spectrometry

Recent work on a new, higher sensitivity preamplifier design for Fourier transform ion cyclotron resonance mass spectrometry (FTICRMS) revealed a number of artifact peaks (spectral features) which do not contain useful chemical information. In order to determine the cause of these artifacts and eliminate them, these severely distorted spectra were compared with similarly distorted signal models. The source of several common signal processing artifacts was thereby determined and correlated to radio‐frequency interference (RFI) noise and saturation of the amplifier and/or the digitizer. Under such conditions, the fast Fourier transform (FFT) generates spectral artifact peaks corresponding to harmonics and mixing frequencies of the real signal peaks and RFI frequencies. While this study was done using FTICRMS data, it is important to stress that these artifacts are inherent to the digitization and FFT process and thus are relevant to any FT‐based MS instrument, including the orbitrap and FT ion trap. Copyright © 2009 John Wiley & Sons, Ltd.     

Digital Harmonic Analysis of Cadmium Ion Reduction on a Dropping Mercury Electrode

The cadmium ions reduction on a mercury electrode is investigated. A sinusoidal voltage perturbation signal, superimposed on a linearly changing dc potential, is used. A total time–frequency analysis of the polarographic current of cadmium ions reduction on a dropping mercury electrode is performed. Classical Fourier transform leads to decomposition of the polarographic current into its harmonics. The current harmonics determined by Fourier transform are potential-independent. The STFT transform of the polarographic current also leads to its decomposition into harmonics. However, application of the STFT transform correctly reflects changes in the current harmonics as the function of potential.     

High and low frequency unfolded partial least squares regression based on empirical mode decomposition for quantitative analysis of fuel oil samples

Accurate prediction of the model is fundamental to the successful analysis of complex samples. To utilize abundant information embedded over frequency and time domains, a novel regression model is presented for quantitative analysis of hydrocarbon contents in the fuel oil samples. The proposed method named as high and low frequency unfolded PLSR (HLUPLSR), which integrates empirical mode decomposition (EMD) and unfolded strategy with partial least squares regression (PLSR). In the proposed method, the original signals are firstly decomposed into a finite number of intrinsic mode functions (IMFs) and a residue by EMD. Secondly, the former high frequency IMFs are summed as a high frequency matrix and the latter IMFs and residue are summed as a low frequency matrix. Finally, the two matrices are unfolded to an extended matrix in variable dimension, and then the PLSR model is built between the extended matrix and the target values. Coupled with Ultraviolet (UV) spectroscopy, HLUPLSR has been applied to determine hydrocarbon contents of light gas oil and diesel fuels samples. Comparing with single PLSR and other signal processing techniques, the proposed method shows superiority in prediction ability and better model interpretation. Therefore, HLUPLSR method provides a promising tool for quantitative analysis of complex samples.     

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.     

High-pass filters for spectral background suppression in airborne passive Fourier transform infrared spectrometry

High-pass (HP) digital filtering and second-derivative (SD) filtering are evaluated as methods of removing background contributions from spectra collected by passive Fourier transform infrared spectrometry. In measurements performed with a downward-looking spectrometer mounted on an aircraft platform, the effects of non-constant background radiance from the ground make it challenging to build automated classifiers for detecting an analyte of interest. Applying HP digital filtering to the spectra to remove background contributions is evaluated as a strategy to help improve classifier performance. This methodology is tested by building classifiers for detecting heated ethanol plumes released from a portable emission stack. The classifiers are trained with data collected on the ground with the spectrometer viewing the plumes against a synthetic backdrop designed to simulate a terrestrial radiance source. The resulting classifiers are tested with data collected by the same spectrometer mounted on an aircraft flying over the emission stack. Support vector machines are employed as a classification algorithm with HP filtered spectra used as input patterns. Butterworth filters are used to implement HP digital filtering, while Savitzky-Golay filters are used to implement SD filtering. Significant improvement in classification performance is achieved by use of the HP filters. Because of variation in backgrounds between the training and prediction data, the best classifier obtained with unfiltered spectra is unable to detect ethanol in 37% of the test cases. HP filtering of spectra with an optimized Butterworth filter (order 8, cutoff frequency 0.060) improves the prediction results, resulting in no missed ethanol detections and false positive rates of less than 0.4%.     

交流示波计时电位法中高次谐波电位的研究

用计算机模数转换和快速傅里叶变换技术，研究了微金电极上闰－时间曲线和频率响应关系，提出了利用高次谐波电位进行了交流示波计电位研究的新方法。扣除了交流示波极谱图中的充电电流和高频噪声，提高了示波极谱分析的信噪比。     

Improving liquid chromatography–tandem mass spectrometry determinations by modifying noise frequency spectrum between two consecutive wavelet-based low-pass filtering procedures

This paper employs one chemometric technique to modify the noise spectrum of liquid chromatography–tandem mass spectrometry (LC–MS/MS) chromatogram between two consecutive wavelet-based low-pass filter procedures to improve the peak signal-to-noise (S/N) ratio enhancement. Although similar techniques of using other sets of low-pass procedures such as matched filters have been published, the procedures developed in this work are able to avoid peak broadening disadvantages inherent in matched filters. In addition, unlike Fourier transform-based low-pass filters, wavelet-based filters efficiently reject noises in the chromatograms directly in the time domain without distorting the original signals. In this work, the low-pass filtering procedures sequentially convolve the original chromatograms against each set of low pass filters to result in approximation coefficients, representing the low-frequency wavelets, of the first five resolution levels. The tedious trials of setting threshold values to properly shrink each wavelet are therefore no longer required. This noise modification technique is to multiply one wavelet-based low-pass filtered LC–MS/MS chromatogram with another artificial chromatogram added with thermal noises prior to the other wavelet-based low-pass filter. Because low-pass filter cannot eliminate frequency components below its cut-off frequency, more efficient peak S/N ratio improvement cannot be accomplished using consecutive low-pass filter procedures to process LC–MS/MS chromatograms. In contrast, when the low-pass filtered LC–MS/MS chromatogram is conditioned with the multiplication alteration prior to the other low-pass filter, much better ratio improvement is achieved. The noise frequency spectrum of low-pass filtered chromatogram, which originally contains frequency components below the filter cut-off frequency, is altered to span a broader range with multiplication operation. When the frequency range of this modified noise spectrum shifts toward the high frequency regimes, the other low-pass filter is able to provide better filtering efficiency to obtain higher peak S/N ratios. Real LC–MS/MS chromatograms, of which typically less than 6-fold peak S/N ratio improvement achieved with two consecutive wavelet-based low-pass filters remains the same S/N ratio improvement using one-step wavelet-based low-pass filter, are improved to accomplish much better ratio enhancement 25-folds to 40-folds typically when the noise frequency spectrum is modified between two low-pass filters. The linear standard curves using the filtered LC–MS/MS signals are validated. The filtered LC–MS/MS signals are also reproducible. The more accurate determinations of very low concentration samples (S/N ratio about 7–9) are obtained using the filtered signals than the determinations using the original signals.     

Use of the filter diagonalization method in the study of space charge related frequency modulation in Fourier transform ion cyclotron resonance mass spectrometry

The filter diagonalization method (FDM) is a recently developed computational technique capable of extracting resonance frequencies and amplitudes from very short transient signals. Although it requires stable resonance frequencies and is slower than the fast Fourier transform (FFT), FDM has a resolution and accuracy that is unmatched by the FFT or any other comparable techniques. This unique feature of FDM makes it an ideal tool for tracing space charge induced frequency modulations in Fourier transform ion cyclotron resonance (FT-ICR) cells, which are shown to reach +/-400 ppm even for such simple spectra as Substance P.     

Comparison of methods to enhance flame ionization detector (FID) signals in gas chromatography

The performances of some numerical methods to improve the signal to noise ratio are compared and applied to enhance noisy signals obtained in gas chromatography with capillary columns and a flame Ionization detector. Several methods have been considered: cutoffs In the Fourier transform of the recorded signal; real time numerical filtering; theoretical model curve fitting; and the correlation of a chromatogram recorded from a pseudorandomly injected sample with the pseudorandom injection function. Numerical real time filtering is shown to be the most convenient method when the main periodic component of the noise has been determined by Fourier analysis.     

Automatic analysis of hydrogen/deuterium exchange mass spectra of peptides and proteins using calculations of isotopic distributions

High mass-resolving power has been shown to be useful for studying the conformational dynamics of proteins by hydrogen/deuterium (H/D) exchange. A computer algorithm was developed that automatically identifies peptides and their extent of deuterium incorporation from H/D exchange mass spectra of enzymatic digests or fragment ions produced by collisionally induced dissociation (CID) or electron capture dissociation (ECD). The computer algorithm compares measured and calculated isotopic distributions and uses a fast calculation of isotopic distributions using the fast Fourier transform (FFT). The algorithm facilitates rapid and automated analysis of H/D exchange mass spectra suitable for high-throughput approaches to the study of peptide and protein structures. The algorithm also makes the identification independent on comparisons with undeuterated control samples. The applicability of the algorithm was demonstrated on simulated isotopic distributions as well as on experimental data, such as Fourier transform ion cyclotron resonance (FTICR) mass spectra of myoglobin peptic digests, and CID and ECD spectra of substance P.     

Practical aspects of Fourier transform and correlation based processing of spectrochemical data

Fourier transform based signal processing methods are beginning to be widely used for the treatment of spectrochemical data. The most common approach to Fourier transformation is through the utilization of the so called Fast Fourier Transform algorithm or FFT as it is usually designated. However, several versions of the FFT abound in the literature and in program libraries and many subtleties exist with respect to data pre-treatment, data post-treatment, inverse Fourier transformation and manipulation of real and imaginary arrays that can cause considerable grief to the uninitiated. In this presentation numerous examples will be presented illustrating several practical aspects of implementing FFT's and cross-correlations (Fourier transform route) on spectrochemical data sets. Particular attention is paid to the manipulation to the input and output real and imaginary arrays.     

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。     

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.     

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 power spectra of the inductively coupled plasma

Noise power spectra for the ICP were determined under various conditions, by Fast Fourier Transform (FFT) digital techniques. The major noise types observed were white noise, low frequency noise, and high frequency proportional noise. The high frequency proportional noise increased with concentration of analyte and radio frequency input power. The high frequency proportional noise decreased with increasing nebulizer flow rate and coolant gas flow rate.. The low frequency noise components extended to higher frequencies as the resonance wavelengths of the measured transitions increased. Changing the observation height in the plasma determined which noise types were present in the noise power spectrum. At observation heights near the power coils, all three noise types were present, whereas, low frequency noise predominated at significantly greater heights. Changing the torch design changed the relative amplitudes of the different high frequency proportional noise components, but did not greatly change their respective peak frequencies.