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.     

Long time wave packet dynamics from energy eigenfunctions: nonuniform energy resolution via adaptive bisection fast Fourier transformation

This article presents a new approach to long time wave packet propagation. The methodology relies on energy domain calculations and an on-the-surface straightforward energy to time transformation to provide wave packet time evolution. The adaptive bisection fast Fourier transform method employs selective bisection to create a multiresolution energy grid, dense near resonances. To implement fast Fourier transforms on the nonuniform grid, the uniform grid corresponding to the finest resolution is reconstructed using an iterative interpolation process. By proper choice of the energy grid points, we are able to produce results equivalent to grids of the finest resolution, with far fewer grid points. We have seen savings 20-fold in the number of eigenfunction calculations. Since the method requires computation of energy eigenfunctions, it is best suited for situations where many wave packet propagations are of interest at a fixed small set of points--as in time dependent flux computations. The fast Fourier transform (FFT) algorithm used is an adaptation of the Danielson-Lanczos FFT algorithm to sparse input data. A specific advantage of the adaptive bisection FFT is the possibility of long time wave packet propagations showing slow resonant decay. A method is discussed for obtaining resonance parameters by least squares fitting of energy domain data. The key innovation presented is the means of separating out the smooth background from the sharp resonance structure.     

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.     

Application of a microcomputer for the cross-spectral analysis with pseudorandom signal in electroanalytical chemistry

A digital memory device and a microcomputer are introduced to calculate correlation functions and Fourier transform in voltammetric measurements. Typical cross-spectra for simple diffusion and kinetic processes are obtained. The fast Fourier transform (FFT) modified for microcomputers was used for speed-up of the calculation. The cross-spectra obtained gave information about the electrode process such as the pattern of the accompanied chemical reaction and the kinetic parameter of the chemical reaction.     

The re-discovery of the fast Fourier transform algorithm

The discovery of the fast Fourier transform (FFT) algorithm and the subsequent development of algorithmic and numerical methods based on it have had an enormous impact on the ability of computers to process digital representations of signals, or functions. At first, the FFT was regarded as entirely new. However, attention and wide publicity led to an unfolding of its pre-electronic computer history going back to Gauss. The present paper describes the author's own involvement and experience with the FFT algorithm.The author is grateful for permission from the Association for Computing Machinery to allow the present paper to bear some similarity with the paper,How the FFT Gained Acceptance, ref. [28]     

Application of empirical mode decomposition in the field of polymer physics

Noisy data has always been a problem to the experimental community. Effective removal of noise from data is important for better understanding and interpretation of experimental results. Over the years, several methods have evolved for filtering the noise present in the data. Fast Fourier transform (FFT) based filters are widely used because they provide precise information about the frequency content of the experimental data, which is used for filtering of noise. However, FFT assumes that the experimental data is stationary. This means that: (i) the deterministic part of the experimental data obtained from a system is at steady state without any transients and has frequency components which do not vary with respect to time and (ii) noise corrupting the experimental data is wide sense stationary, that is, mean and variance of the noise does not statistically vary with respect to time. Several approaches, for example, short time Fourier transform (STFT) and wavelet transform‐based filters, have been developed to handle transient data corrupted with nonstationary noise (mean and variance of noise varies with respect to time) data. Both these approaches provide time and frequency information about the data (time at which a particular frequency is present in the signal). However, these filtering approaches have the following drawbacks: (i) STFT requires identification of an optimal window length within which the data is stationary, which is difficult and (ii) there are theoretical limits on simultaneous time and frequency resolution. Hence, filtering of noise is compromised. Recently, empirical mode decomposition (EMD) has been used in several applications to decompose a given nonstationary data segment into several characteristic oscillatory components called intrinsic mode functions (IMFs). Fourier transform of these IMFs identifies the frequency content in the signal, which can be used for removal of noisy IMFs and reconstruction of the filtered signal. In this work, we propose an algorithm for effective filtering of noise using an EMD‐based FFT approach for applications in polymer physics. The advantages of the proposed approach are: (i) it uses the precise frequency information provided by the FFT and, therefore, efficiently filters a wide variety of noise and (ii) the EMD approach can effectively obtain IMFs from both nonstationary as well as nonlinear experimental data. The utility of the proposed approach is illustrated using an analytical model and also through two typical laboratory experiments in polymer physics wherein the material response is nonstationary; standard filtering approaches are often inappropriate in such cases. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Fast Padé transform for optimal quantification of time signals from magnetic resonance spectroscopy

The fast Padé transform (FPT) is both a parametric and a nonparametric estimator that is capable of quantifying the input raw time signals without any fitting. The FPT simultaneously interpolates as well as extrapolates, and this is expected to mitigate truncation artifacts. To assess performance, it is necessary to compare the main features of the FPT with the characteristics of other parametric estimators, as well as with the fast Fourier transform (FFT), which can yield only shape spectra. The FPT can also give the shape of a spectrum, but accomplishes this in two totally different ways, with and without computing the spectral parameters (complex frequencies and amplitudes). A number of other parametric estimators used in signal processing are unable to yield shape spectra without prior extraction of the fundamental frequencies and the corresponding amplitudes. The primary goal of the present study is to assess the accuracy, robustness, and efficiency of the FPT for parametric and nonparametric estimations of experimentally measured time signals from in vivo magnetic resonance spectroscopy (MRS). Robustness and steadiness of the FPT are assessed relative to the FFT by monitoring the convergence rates of these two processors through a systematic and gradual decrease of the truncation level of the full signal length. Accuracy of the FPT is verified by performing error analysis of proven validity, using a gold standard, if available. Alternatively, comparison is made between the two complementary variants of the FPT that converge inside and outside the unit circle. Efficiency of the FPT is checked with respect to the FFT for estimation of the shape of a spectrum, as well as relative to other parametric processors, in the case of quantifications. To establish the accuracy, robustness, and efficiency of the FPT within the outlined multi‐level strategy, we use a time signal encoded via MRS at 4T from the brain of a healthy volunteer. We also assess the overall usefulness of the FPT for signal processing of data acquired from patients, in light of the emerging appreciation that spectroscopy of the tissue metabolites offers a number of vital advantages over the corresponding anatomical imaging in diagnostics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

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.     

Pore structure and fractal characteristics of activated carbon fibers characterized by using HRTEM

The pore microstructures in two viscouse rayon-based ACF samples were characterized by nitrogen adsorption and HRTEM. For TEM, a two-dimensional fast Fourier transform (FFT) of the original TEM images was performed, and pores in different size ranges were extracted by the inverse FFT (IFFT) operation. The surface fractal dimensions of the samples were evaluated by using both N(2) adsorption and TEM image analysis. The results show that TEM can portray the shapes of the pore, and it can give a quantitative evaluation of surface irregularity that is consistent with nitrogen adsorption results.     

Biosensing using porous silicon double-layer interferometers: reflective interferometric Fourier transform spectroscopy

A simple, chip-based implementation of a double-beam interferometer that can separate biomolecules based on size and that can compensate for changes in matrix composition is introduced. The interferometric biosensor uses a double-layer of porous Si comprised of a top layer with large pores and a bottom layer with smaller pores. The structure is shown to provide an on-chip reference channel analogous to a double-beam spectrometer, but where the reference and sample compartments are stacked one on top of the other. The reflectivity spectrum of this structure displays a complicated interference pattern whose individual components can be resolved by fitting of the reflectivity data to a simple interference model or by fast Fourier transform (FFT). Shifts of the FFT peaks indicate biomolecule penetration into the different layers. The small molecule, sucrose, penetrates into both porous Si layers, whereas the large protein, bovine serum albumin (BSA), only enters the large pores. BSA can be detected even in a large (100-fold by mass) excess of sucrose from the FFT spectrum. Detection can be accomplished either by computing the weighted difference in the frequencies of two peaks or by computing the ratio of the intensities of two peaks in the FFT spectrum.     

Resolution enhancement as a key step towards clinical implementation of Padé-optimized magnetic resonance spectroscopy for diagnostic oncology

Our overall aim is for the full potential of magnetic resonance spectroscopy (MRS) and magnetic resonance spectroscopic imaging (MRSI) to be realized in oncology. This requires mathematics, without which encoded MRS data are entirely uninterpretable. Mathematics based on the conventional approach, the fast Fourier transform (FFT), and ambiguous fittings of Fourier spectra cannot fulfill the rigorous demands of oncology. It is vital to go beyond the FFT and fitting, to obtain reliable quantitative information via MRS about the metabolic content of tissue. None of the available MRS fitting algorithms could provide the clinically needed information with certainty, namely, the metabolite concentrations. Our more advanced method, the fast Padé transform (FPT) is firmly established as a stable, high-resolution processor, with which metabolite concentrations are unequivocally generated for in vitro MRS data associated with prostate, breast and ovarian cancer. Validation of the FPT has also been performed for in vivo MRS of normal human brain from clinical magnetic resonance scanners (1.5 T) as well as from 4 to 7 T scanners. The FPT successfully handles major problems hindering more widespread clinical application of MRS and MRSI, such as separation of noise from signal, resolution of very dense spectra with multiplet resonances (prostate) and overlapping metabolite resonances (breast, brain). In the present paper, we focus upon the implications of resolution enhancement by the FPT. We conclude that the manner by which the FPT achieves its high resolution accuracy dictates a major reformulation of the concept of data acquisition by encoding a small number of short transient time signals to secure good signal-noise ratio. Padé-guided MRS has distinct clinical advantages in combining improved diagnostic accuracy of MRS with shorter examination times. This shortens turn-around time for patients, making MRS efficient and cost-effective. With Padé-based quantification plus FPT-guided encoding of MRS and MRSI data, MRS can become a reliable, cost-effective tool for diagnostics and various aspects of patient care within oncology.     

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.     

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。     

多重栾晶钯颗粒的可见光简易合成及对乙醇的电催化氧化

以氯化钯(PdCl₂)为金属前驱体, 乙醇为还原剂, 聚乙烯吡咯烷酮(PVP)为稳定剂和导向剂, 利用普通市售节能灯产生的光热作用, 辅助制备多重栾晶钯纳米颗粒。用HRTEM、FFT、PXRD、XPS、UV-Vis和FT-IR等技术对产品的形貌、晶体结构、光学性质和稳定性进行了表征, 并通过循环伏安法研究了多重栾晶Pd修饰玻碳电极对乙醇的电催化氧化活性。结果表明, 多重栾晶钯结构的形成依赖于光和热的协同作用。该材料的表面等离子共振吸收峰在可见光区域, 对乙醇有较好的电催化活性和抗中毒能力。     

Tailored noise waveform/collision-induced dissociation of ions stored in a linear ion trap combined with liquid chromatography/Fourier transform ion cyclotron resonance mass spectrometry

A new collision-induced dissociation (CID) technique based on broadband tailored noise waveform (TNW) excitation of ions stored in a linear ion trap has been developed. In comparison with the conventional sustained off-resonance irradiation (SORI) CID method commonly used in Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), this MS/MS technique increases throughput by eliminating the long pump-down delay associated with gas introduction into the high vacuum ICR cell region. In addition, the TNW-CID method speeds spectrum acquisition since it does not require Fourier transformation, calculation of resonant frequencies and generation of the excitation waveforms. We demonstrate TNW-CID coupled with on-line capillary reverse-phase liquid chromatography separations for the identification of peptides. The experimental results are compared with data obtained using conventional quadrupole ion trap MS/MS and SORI-CID MS/MS in an ICR cell.     

多重栾晶钯颗粒的可见光简易合成及对乙醇的电催化氧化

以氯化钯(PdCl₂)为金属前驱体,乙醇为还原剂,聚乙烯吡咯烷酮(PVP)为稳定剂和导向剂,利用普通市售节能灯产生的光热作用,辅助制备多重栾晶钯纳米颗粒.用HRTEM、FFT、PXRD、XPS、UV-Vis和FT-IR等技术对产品的形貌、晶体结构、光学性质和稳定性进行了表征,并通过循环伏安法研究了多重栾晶Pd修饰玻碳电极对乙醇的电催化氧化活性.结果表明,多重栾晶钯结构的形成依赖于光和热的协同作用.该材料的表面等离子共振吸收峰在可见光区域,对乙醇有较好的电催化活性和抗中毒能力.     

基于傅立叶变换的人工神经网络近红外光谱定量分析法

将原始光谱进行一定的预处理后,以其快速傅立叶变换FFT的前N个系数作为人工神经网络(ANN)的输入量,不仅确保了大量有用信息参与模型的建立,同时实现了优越的滤波功能。以汽油的辛烷值和煤粉干燥基高位发热量(Qgr.d)的近红外光谱建模,当采用前20个FFT系数的傅立叶变换-径向基网络(FFT-RBF)时,辛烷值模型的预测误差均方根(RMSEP)可达0.152,相关系数为0.976,当采用前30个FFT系数时,快速FFT-RBF煤粉干燥基高位发热量模型的RMSEP为0.256,相关系数为0.923,说明FFT-RBF模型有着很好的预测能力。研究表明基于傅立叶变换的人工神经网络近红外光谱定量分析法,特别是FFT-RBF具有良好的预测能力。     

Fourier transform microwave spectroscopy and Fourier transform microwave-millimeter wave double resonance spectroscopy of the ClOO radical

Pure rotational spectra of the ClOO radical for the (35)Cl and (37)Cl isotopomers have been observed using Fourier transform microwave and Fourier transform microwave-millimeter wave double resonance spectroscopy. The rotational, centrifugal, spin-rotation coupling, and hyperfine coupling constants have been determined by least-squares fits of the observed transition frequencies. The molecular constants indicate that the electronic ground state is 2A". The r(0) structure is determined to be r(0)(ClO)=2.075 A, r(0)(OO)=1.227 A, and theta;(0)(ClOO)=116.4 degrees . Several highly accurate ab initio calculations have also been performed. Some of them turned out to be inaccurate because it is necessary to take into account both static and dynamic electronic correlations. Only multireference (single and double) configuration interaction calculations with large basis sets reproduce the present experimental results. The anharmonic force constants obtained by the ab initio calculations are used to determine the r(e) structure, r(e)(ClO)=2.084(1) A, r(e)(OO)=1.206(2) A, and theta;(e)(ClOO)=115.4(1) degrees . Unique features of the ClOO radical have become clear by the present experiment and the ab initio calculations.     

Characterization of an Electron Ionization Source Trap Operating in the Presence of a Magnetic Field Through Computer Simulation

We explore the feasibility of conducting electron ionization (EI) in a radio-frequency (rf) ion source trap for mass spectrometry applications. Electrons are radially injected into a compact linear ion trap in the presence of a magnetic field used essentially to lengthen the path of the electrons in the trap. The device can either be used as a stand-alone mass spectrometer or can be coupled to a mass analyzer. The applied parallel magnetic field and the oscillating rf electric field produced by the trap give rise to a set of coupled Mathieu equations of motion. Via numerical simulations, electron trajectories are studied under varying intensities of the magnetic field in order to determine the conditions that enhance ion production. Likewise, the dynamic behavior of the ions are investigated in the proposed EI source trap and the fast Fourier transform FFT formalism is used to obtain the frequency spectrum from the numerical simulations to study the motional frequencies of the ions which include combinations of the low-frequency secular and the high-frequency micromotion with magnetron and cyclotron frequencies. The dependence of these motional frequencies on the trapping conditions is examined and particularly, the limits of applying a radial magnetic field to the EI ion trap are characterized.

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.