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     

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.     

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.     

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.     

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.     

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]     

Stimulated echo NMR spectra and their use for heteronuclear two-dimensional shift correlation

NMR spectra are obtained from Fourier transformation of the latter part of a Hahn stimulated echo. The sequence is 90°-τ_a-90°-τ_b-90°-τ_a-digitize versus τ₂. This is demonstrated for transfer RNA in H₂O using the semiselective J ® pulse (90°-τ_p-90°), developed by Plateau and Gueron in place of each 90° pulse. 2D correlation between ¹³N and protons is obtained by applying a 90°-τ₁-90° ¹⁵N sequence during τ_b and ¹⁵N decoupling while digitizing. The second Fourier transform is performed with respect to τ₁ after discarding the imaginary parts of the first transform, to obtain a real 2D map. Such a 2D spectrum has been obtained for 5 mM¹⁵NH₄Cl and several other small molecules. The sequence should be useful for studies of ¹⁵N labeled macromolecules.     

Protein–ligand docking using FFT based sampling: D3R case study

Fast Fourier transform (FFT) based approaches have been successful in application to modeling of relatively rigid protein–protein complexes. Recently, we have been able to adapt the FFT methodology to treatment of flexible protein–peptide interactions. Here, we report our latest attempt to expand the capabilities of the FFT approach to treatment of flexible protein–ligand interactions in application to the D3R PL-2016-1 challenge. Based on the D3R assessment, our FFT approach in conjunction with Monte Carlo minimization off-grid refinement was among the top performing methods in the challenge. The potential advantage of our method is its ability to globally sample the protein–ligand interaction landscape, which will be explored in further applications.     

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.     

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。     

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.     

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。     

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。     

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.     

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.     

Molecular interaction of polyimide films probed by using soft-pulse dynamic compression ATR time-resolved infrared and double Fourier-transform based 2D-IR spectroscopy

An improved time-resolved step-scan Fourier transform rheo-optical system, based on the soft-pulse dynamic compression attenuated total reflection (ATR) approach, has been introduced to analyze inter-molecular interactions of poly(p-phenylene bi-phenyltetracarboximide) (BPDA–PDA) and poly(N,N-diphenyl ether bi-phenyltetracarboximide) (BPDA–ODA) films. In order to extract the full range of frequency distributions obtained from soft-pulse dynamic compression time response (relaxation) spectra, the second-Fourier transformation was applied along the relaxation time axis in addition to the interferogram axis. In the case of the BPDA–PDA, distinct periodic higher overtone bands are observed especially at C=O stretching and C=C tangential stretching vibration bands in the FFT relaxation time contour map spectra. For the BPDA–ODA, intensities of higher overtone bands are relatively weak. We have further performed 2D-IR correlation analysis at given Fourier frequencies, which includes molecular interaction information. The results suggest that the existence of molecular interaction between C=O stretching and C=C tangential stretching vibration bands.     

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.     

Reflective interferometric fourier transform spectroscopy: a self-compensating label-free immunosensor using double-layers of porous SiO2

An interferometric biosensor comprised of two layers of porous Si, stacked one on top of the other, is described. A fast Fourier transform (FFT) of the reflectivity spectrum reveals three peaks that correspond to the optical thickness of the top layer, the bottom layer, and both layers together. Binding of immunoglobulin G to a protein A capture probe adsorbed to the surface of the top layer induces changes in reflectivity at the top layer/solution interface. The FFT method allows discrimination of target analyte binding from matrix effects due to nonspecific changes in the analyte solution. The sensor response is shown to be insensitive to the addition of 4000-fold excess sucrose or 80-fold excess bovine serum albumin interferents.     

Bias-current modulation technique of a radio-frequency glow discharge plasma for atomic emission analysis associated with a fast Fourier transform analyzer

A measuring method using a fast Fourier transform (FFT) analyzer is suggested to estimate the emission intensity from a radio-frequency (RF)-powered glow discharge plasma for atomic emission analysis. The FFT analyzer has an ability to disperse the components by frequency from an overall signal, and thus works as a selective detector in modulation spectroscopy. In the RF glow discharge plasma, a dc bias current can be introduced by connecting an external electric circuit with the discharge lamp, which predominantly enhances the emission intensities. Further, the bias current can be pulsated with a switching device to modulate the emission intensities, and then the modulated component was selectively detected with the FFT analyzer. This method greatly improved the data precision. The emission intensity of the Cu I 324.75-nm line in an Fe-based alloy sample containing 0.043 mass% Cu could be estimated with a relative standard deviation of 0.20%. The 3σ detection limits of Cu in Fe-based alloys could be obtained to be 2.3 × 10^− 6 mass% Cu for Cu I 324.75 nm and 6.8 × 10^− 6 mass% Cu for Cu I 327.40 nm.     

Experimental demonstration and simulation of electrochemical non-linear responses to glucose and its interferents with an amperometric sensor

A novel sensing system based on the multi-dimensional information contained in a dynamic non-linear response is proposed. A sinusoidal potential was applied to an amperometric-type glucose sensor and the resulting current of the sensor was analyzed by fast Fourier transformation (FFT). The amplitudes of the higher harmonics of FFT characterize the non-linear properties of the response. The amplitudes of the higher harmonics of FFT exhibit characteristic changes which depend on the concentration and the kinetics of the reactions of glucose and its interferents at the sensor surface. The essential features of the current-potential curve were reproduced by a computer simulation based on the kinetics of electrochemical reactions.