Fourier transform ion cyclotron resonance mass spectrometry
Marshall, Alan G.
1998-06-01
As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.
Hourani, Nadim; Andersson, Jan T.; Mö ller, Isabelle; Amad, Maan H.; Witt, Matthí as; Sarathy, Mani
2013-01-01
oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same
Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.
Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene
2017-08-01
Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.
van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B
2015-12-01
Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.
International Nuclear Information System (INIS)
Luederwald, I.
1977-01-01
Instrumentation and technology of Ion-Cyclotron-Resonance and Fourier-Transform-Ion-Cyclotron-Resonance Spectroscopy are described. The method can be applied to studies of ion/molecule reactions in gas phase, to obtain thermodynamic data as gas phase acidity or basicity, proton and electron affinity, and to establish reaction mechanisms and ion structures. (orig.) [de
International Nuclear Information System (INIS)
Joergensen, S.I.
1985-01-01
The subject of this thesis is gas phase ion/molecule reactions as studied by Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry (chapter 2 contains a short description of this method). Three chapters are mainly concerned with mechanistic aspects of gas phase ion/molecule reactions. An equally important aspect of the thesis is the stability and reactivity of α-thio carbanions, dipole stabilized carbanions and homoenolate anions, dealt with in the other four chapters. (Auth.)
International Nuclear Information System (INIS)
Kleingeld, J.C.
1984-01-01
An important field in which Fourier-transform ion cyclotron resonance has useful applications is that of gas phase ion chemistry, the subject of this thesis. First, the general picture of ion-molecule reactions in the gas phase is discussed. Next, some positive ion-molecule reactions are described, whereas the remaining chapters deal with negative ion-molecule reactions. Most of these studies have been performed using the FT-ICR method. Reactions involving H 3 O - and NH 4 - ions are described whereas the other chapters deal with larger organic complexes. (Auth.)
Vladimirov, Gleb; Kostyukevich, Yury; Kharybin, Oleg; Nikolaev, Eugene
2017-08-01
Particle-in-cell-based realistic simulation of Fourier transform ion cyclotron resonance experiments could be used to generate ion trajectories and a signal induced on the detection electrodes. It has been shown recently that there is a modulation of "reduced" cyclotron frequencies in ion cyclotron resonance signal caused by Coulomb interaction of ion clouds. In this work it was proposed to use this modulation in order to determine frequency difference between an ion of known m/z and all other ions generating signal in ion cyclotron resonance cell. It is shown that with an increase of number of ions in ion cyclotron resonance trap, the modulation index increases, which lead to a decrease in the accuracy of determination of peak intensities by super Fourier transform resolution methods such as filter diagonalization method.
Ohta, Daisaku; Kanaya, Shigehiko; Suzuki, Hideyuki
2010-02-01
Metabolomics, as an essential part of genomics studies, intends holistic understanding of metabolic networks through simultaneous analysis of a myriad of both known and unknown metabolites occurring in living organisms. The initial stage of metabolomics was designed for the reproducible analyses of known metabolites based on their comparison to available authentic compounds. Such metabolomics platforms were mostly based on mass spectrometry (MS) technologies enabled by a combination of different ionization methods together with a variety of separation steps including LC, GC, and CE. Among these, Fourier-transform ion cyclotron resonance MS (FT-ICR/MS) is distinguished from other MS technologies by its ultrahigh resolution power in mass to charge ratio (m/z). The potential of FT-ICR/MS as a distinctive metabolomics tool has been demonstrated in nontargeted metabolic profiling and functional characterization of novel genes. Here, we discuss both the advantages and difficulties encountered in the FT-ICR/MS metabolomics studies.
Directory of Open Access Journals (Sweden)
Kevin D. Quinn
2012-01-01
Full Text Available Paper Spray Ionization is an atmospheric pressure ionization technique that utilizes an offline electro-osmotic flow to generate ions off a paper medium. This technique can be performed on a Bruker SolariX Fourier transform ion cyclotron resonance mass spectrometer by modifying the existing nanospray source. High-resolution paper spray spectra were obtained for both organic and biological samples to demonstrate the benefit of linking the technique with a high-resolution mass analyzer. Error values in the range 0.23 to 2.14 ppm were obtained for calf lung surfactant extract with broadband mass resolving power (m/Δm50% above 60,000 utilizing an external calibration standard.
Energy Technology Data Exchange (ETDEWEB)
Oldenburg, Thomas B.P; Brown, Melisa; Hsieh, Ben; Larter, Steve [Petroleum Reservoir Group (prg), Department of Geoscience, University of Calgary, Alberta (Canada)
2011-07-01
The Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (FTICRMS), developed in the 1970's by Marshall and Comisarow at the University of British Columbia, has become a commercially available tool capable of analyzing several hundred thousand components in a petroleum mixture at once. This analytical technology will probably usher a dramatic revolution in geochemical capability, equal to or greater than the molecular revolution that occurred when GCMS technologies became cheaply available. The molecular resolution and information content given by the FTICRMS petroleum analysis can be compared to the information in the human genome. With current GCMS-based petroleum geochemical protocols perhaps a few hundred components can be quantitatively determined, but with FTICRMS, 1000 times this number of components could possibly be resolved. However, fluid and other properties depend on interaction of this multitude of hydrocarbon and non-hydrocarbon components, not the components themselves, and access to the full potential of this new petroleomics will depend on the definition of this interactome.
Hourani, Nadim
2013-10-01
Rationale Polycyclic aromatic sulfur heterocycles (PASHs) are detrimental species for refining processes in petroleum industry. Current mass spectrometric Methods that determine their composition are often preceded by derivatization and dopant addition approaches. Different ionization Methods have different impact on the molecular assignment of complex PASHs. The analysis of such species under atmospheric pressure chemical ionization (APCI) is still considered limited due to uncontrolled ion generation with low- and high-mass PASHs. Methods The ionization behavior of a model mixture of five selected PASH standards was investigated using an APCI source with nitrogen as the reagent gas. A complex thiophenic fraction was separated from a vacuum gas oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same ionization pattern was observed for the real thiophenic sample. It was found that S1 class species were the major sulfur-containing species found in the VGO sample. These species indicated the presence of alkylated benzothiophenic (BT), dibenzothiophenic (DBT) and benzonaphthothiophenic (BNT) series that were detected by APCI-FTICR MS. CONCLUSIONS This study provides an established APCI-FTICR MS method for the analysis of complex PASHs. PASHs were detected without using any derivatization and without fragmentation. The method can be used for the analysis of S-containing crude oil samples. © 2013 John Wiley & Sons, Ltd.
Fourier Transform Ion Cyclotron Resonance Mass Spectrometry at the Cyclotron Frequency.
Nagornov, Konstantin O; Kozhinov, Anton N; Tsybin, Yury O
2017-04-01
The phenomenon of ion cyclotron resonance allows for determining mass-to-charge ratio, m/z, of an ensemble of ions by means of measurements of their cyclotron frequency, ω c . In Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), the ω c quantity is usually unavailable for direct measurements: the resonant state is located close to the reduced cyclotron frequency (ω + ), whereas the ω c and the corresponding m/z values may be calculated via theoretical derivation from an experimental estimate of the ω + quantity. Here, we describe an experimental observation of a new resonant state, which is located close to the ω c frequency and is established because of azimuthally-dependent trapping electric fields of the recently developed ICR cells with narrow aperture detection electrodes. We show that in mass spectra, peaks close to ω + frequencies can be reduced to negligible levels relative to peaks close to ω c frequencies. Due to reduced errors with which the ω c quantity is obtained, the new resonance provides a means of cyclotron frequency measurements with precision greater than that achieved when ω + frequency peaks are employed. The described phenomenon may be considered for a development into an FT-ICR MS technology with increased mass accuracy for applications in basic research, life, and environmental sciences. Graphical Abstract ᅟ.
Theory of peak coalescence in Fourier transform ion cyclotron resonance mass spectrometry.
Boldin, Ivan A; Nikolaev, Eugene N
2009-10-01
Peak coalescence, i.e. the merging of two close peaks in a Fourier transform ion cyclotron resonance (FTICR) mass spectrum at a high number of ions, plays an important role in various FTICR experiments. In order to describe the coalescence phenomenon we would like to propose a new theory of motion for ion clouds with close mass-to-charge ratios, driven by a uniform magnetic field and Coulomb interactions between the clouds. We describe the motion of the ion clouds in terms of their averaged drift motion in crossed magnetic and electric fields. The ion clouds are considered to be of constant size and their motion is studied in two dimensions. The theory deals with the first-order approximation of the equations of motion in relation to dm/m, where dm is the mass difference and m is the mass of a single ion. The analysis was done for an arbitrary inter-cloud interaction potential, which makes it possible to analyze finite-size ion clouds of any shape. The final analytical expression for the condition of the onset of coalescence is found for the case of uniformly charged spheres. An algorithm for finding this condition for an arbitrary interaction potential is proposed. The critical number of ions for the peak coalescence to take place is shown to depend quadratically on the magnetic field strength and to be proportional to the cyclotron radius and inversely proportional to the ion masses. Copyright (c) 2009 John Wiley & Sons, Ltd.
Energy Technology Data Exchange (ETDEWEB)
Shaw, Jared B.; Lin, Tzu-Yung; Leach, Franklin E.; Tolmachev, Aleksey V.; Tolić, Nikola; Robinson, Errol W.; Koppenaal, David W.; Paša-Tolić, Ljiljana
2016-10-12
We provide the initial performance evaluation of a 21 Tesla Fourier transform ion cyclotron resonance mass spectrometer operating at the Environmental Molecular Sciences Laboratory at Pacific Northwest National Laboratory. The spectrometer constructed for the 21T system employs a commercial dual linear ion trap mass spectrometer coupled to a FTICR spectrometer designed and built in-house. Performance gains from moving to higher magnetic field strength are exemplified by the measurement of peptide isotopic fine structure, complex natural organic matter mixtures, and large proteins. Accurate determination of isotopic fine structure was demonstrated for doubly charged substance P with minimal spectral averaging, and 8,158 molecular formulas assigned to Suwannee River Fulvic Acid standard with RMS error of 10 ppb. We also demonstrated superior performance for intact proteins; namely, broadband isotopic resolution of the entire charge state distribution of apotransferrin (78 kDa) and facile isotopic resolution of monoclonal antibody under a variety of acquisition parameters (e.g. 6 s time-domains with absorption mode processing yielded resolution of approximately 1M at m/z =2,700).
International Nuclear Information System (INIS)
Lin, Tzu-Yung; Green, Roger J.; O'Connor, Peter B.
2011-01-01
The nature of the ion signal from a 12-T Fourier-transform ion cyclotron resonance mass spectrometer and the electronic noise were studied to further understand the electronic detection limit. At minimal cost, a new transimpedance preamplifier was designed, computer simulated, built, and tested. The preamplifier design pushes the electronic signal-to-noise performance at room temperature to the limit, because of its enhanced tolerance of the capacitance of the detection device, lower intrinsic noise, and larger flat mid-band gain (input current noise spectral density of around 1 pA/√(Hz) when the transimpedance is about 85 dBΩ). The designed preamplifier has a bandwidth of ∼3 kHz to 10 MHz, which corresponds to the mass-to-charge ratio, m/z, of approximately 18 to 61 k at 12 T. The transimpedance and the bandwidth can be easily adjusted by changing the value of passive components. The feedback limitation of the circuit is discussed. With the maximum possible transimpedance of 5.3 MΩ when using an 0402 surface mount resistor, the preamplifier was estimated to be able to detect ∼110 charges in a single scan.
Taguchi, Vince Y; Nieckarz, Robert J; Clement, Ray E; Krolik, Stefan; Williams, Robert
2010-11-01
The feasibility of utilizing a gas chromatograph-tandem quadrupole-Fourier transform ion cyclotron resonance mass spectrometer (GC-MS/MS-FTICRMS) to analyze chlorinated-dioxins/furans (CDDs/CDFs) and mixed halogenated dioxins/furans (HDDs/HDFs) was investigated by operating the system in the GC-FTICRMS mode. CDDs/CDFs and mixed HDDs/HDFs could be analyzed at 50,000 to 100,000 resolving power (RP) on the capillary gas chromatographic time scale. Initial experiments demonstrated that 1 pg of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and 5 pg of 2-bromo-3,7,8-trichlorodibenzo-p-dioxin (BTrCDD) could be detected. The feasibility of utilizing an FTICRMS for screening of CDDs/CDFs, HDDs/HDFs and related compounds was also investigated by analyzing an extract from vegetation exposed to fall-out from an industrial fire. CDDs/CDFs, chlorinated pyrenes and chlorinated tetracenes could be detected from a Kendrick plot analysis of the ultrahigh resolution mass spectra. Mass accuracies were of the order of 0.5 ppm on standards with external mass calibration and 1 ppm on a sample with internal mass calibration. Copyright © 2010 American Society for Mass Spectrometry. Published by Elsevier Inc. All rights reserved.
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Tang, Yinjie; Pingitore, Francesco; Mukhopadhyay, Aindrila; Phan,Richard; Hazen, Terry C.; Keasling, Jay D.
2006-07-11
It has been proposed that during growth under anaerobic oroxygen-limited conditions Shewanella oneidensis MR-1 uses theserine-isocitrate lyase pathway common to many methylotrophic anaerobes,in which formaldehyde produced from pyruvate is condensed with glycine toform serine. The serine is then transformed through hydroxypyruvate andglycerate to enter central metabolism at phosphoglycerate. To examine itsuse of the serine-isocitrate lyase pathway under anaerobic conditions, wegrew S. oneidensis MR-1 on [1-13C]lactate as the sole carbon source witheither trimethylamine N-oxide (TMAO) or fumarate as an electron acceptor.Analysis of cellular metabolites indicates that a large percentage(>75 percent) of lactate was partially oxidized to either acetate orpyruvate. The 13C isotope distributions in amino acids and other keymetabolites indicate that, under anaerobic conditions, a complete serinepathway is not present, and lactate is oxidized via a highly reversibleserine degradation pathway. The labeling data also suggest significantactivity in the anaplerotic (malic enzyme and phosphoenolpyruvatecarboxylase) and glyoxylate shunt (isocitrate lyase and malate synthase)reactions. Although the tricarboxylic acid (TCA) cycle is often observedto be incomplete in many other anaerobes (absence of 2-oxoglutaratedehydrogenase activity), isotopic labeling supports the existence of acomplete TCA cycle in S. oneidensis MR-1 under TMAO reductioncondition.
Marto, J A; White, F M; Seldomridge, S; Marshall, A G
1995-11-01
Matrix-assisted laser desorption/ionization (MALDI) Fourier transform ion cyclotron resonance mass spectrometry provides for structural analysis of the principal biological phospholipids: glycerophosphatidylcholine, -ethanolamine, -serine, and -inositol. Both positive and negative molecular or quasimolecular ions are generated in high abundance. Isolated molecular ions may be collisionally activated in the source side of a dual trap mass analyzer, yielding fragments serving to identify the polar head group (positive ion mode) and fatty acid side chains (negative ion mode). Azimuthal quadrupolar excitation following collisionally activated dissociation refocuses productions close to the solenoid axis; subsequent transfer of product ions to the analyzer ion trap allows for high-resolution mass analysis. Cyro-cooling of the sample probe with liquid nitrogen greatly reduces matrix adduction encountered in the negative ion mode.
International Nuclear Information System (INIS)
Wunschel, David S.; Pasa Tolic, Ljiljana; Feng, Bingbing; Smith, Richard D.
2000-01-01
We have attempted to expand the size range of PCR products that can be analyzed by electroscopy ionization (ESI) Fourier transformion cyclotron resonance (FTICR) mass spectrometry. The mass measurement accuracy obtained illustrates that a signel base substitution could be identified at the size of PCR product with a 7 tesla ESI-FTICR
Nielen, M.W.F.; Engelen, M.C. van; Zuiderent, R.; Ramaker, R.
2007-01-01
An emerging trend is recognised in hormone and veterinary drug residue analysis from liquid chromatography tandem mass spectrometry (LC/MS/MS) based screening and confirmation towards accurate mass alternatives such as LC coupled with time-of-flight (TOF), Fourier transform ion cyclotron resonance
Schrader, Wolfgang; Panda, Saroj K; Brockmann, Klaus J; Benter, Thorsten
2008-07-01
We report on the successful application of the recently introduced atmospheric pressure laser ionization (APLI) method as a novel tool for the analysis of crude oil and its components. Using Fourier transform ion cyclotron resonance mass spectrometry, unambiguous determination of key compounds in this complex matrix with unprecedented sensitivity is presented.
Hegazi, Abdelrahman H; Fathalla, Eiman M; Andersson, Jan T
2014-09-01
Different weathering factors act to change petroleum composition once it is spilled into the environment. n-Alkanes, biomarkers, low-molecular weight polyaromatic hydrocarbons and sulfur heterocycles compositional changing in the environment have been extensively studied by different researchers and many parameters have been used for oil source identification and monitoring of weathering and biological degradation processes. In this work, we studied the fate of medium-molecular weight polycyclic aromatic disulfur heterocycles (PAS2Hs), up to ca. 900Da, of artificially weathered Flotta North Sea crude oil by ultra high-resolution Fourier transform ion cyclotron resonance mass spectrometry. It was found that PAS2Hs in studied crude oil having double bond equivalents (DBE) from 5 to 8 with a mass range from ca 316 to 582Da were less influenced even after six months artificial weathering experiment. However, compounds having DBEs 12, 11 and 10 were depleted after two, four and six months weathering, respectively. In addition, DBE 9 series was more susceptible to weathering than those of DBE 7 and 8. Copyright © 2014 Elsevier Ltd. All rights reserved.
Zhang, Jingdan; Zhang, Xiaoxue; Zhao, Yangyang; Song, Aihua; Sun, Wei; Yin, Ran
2018-02-01
In this study, a reliable and sensitive ultra-high performance liquid chromatography coupled with fourier transform ion cyclotron resonance mass spectrometry method was developed for the systematic study of the metabolic profile of Kudiezi injection in rat plasma, bile, urine, and feces after intravenous administration of a single dose. The chromatographic separation was performed on an Agilent Eclipse Plus C 18 column (4.6 mm × 50 mm, 1.8 μm) and the identification of prototype components and metabolites was achieved on a Bruker Solarix 7.0 T ultra-high resolution spectrometer in negative ion mode. Results indicated that a total of 76 constituents including 29 prototype compounds and 47 metabolites (10 phase I metabolites and 37 phase II metabolites) were tentatively identified. And the metabolic pathways of these prototype compounds including hydroxylation, dehydrogenation, glucuronidation, and sulfate conjugation. In conclusion, the developed method with high resolution and sensitivity was effective for screening and identification of prototypes and metabolites of Kudiezi injection in vivo. Moreover, these results would provide significant information for further pharmacokinetic and pharmacological research of Kudiezi injection in vivo. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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Belov, Mikhail E.; Anderson, Gordon A.; Wingerd, Mark A.; Udseth, Harold R.; Tang, Keqi; Prior, David C.; Swanson, Kenneth R.; Buschbach, Michael A.; Strittmatter, Eric F.; Moore, Ronald J.; Smith, Richard D.
2004-01-01
We report on a fully automated 9.4 tesla Fourier transform ion resonance cyclotron (FTICR) mass spectrometer coupled to reverse-phase chromatography for high-throughput proteomic studies. Modifications made to the front-end of a commercial FTICR instrument--a dual-ESI-emitter ion source; dual-channel electrodynamic ion funnel; and collisional-cooling, selection and accumulation quadrupoles--significantly improved the sensitivity, dynamic range and mass measurement accuracy of the mass spectrometer. A high-pressure capillary liquid chromatography (LC) system was incorporated with an autosampler that enabled 24 h/day operation. A novel method for accumulating ions in the ICR cell was also developed. Unattended operation of the instrument revealed the exceptional reproducibility (1-5% deviation in elution times for peptides from a bacterial proteome), repeatability (10-20% deviation in detected abundances for peptides from the same aliquot analyzed a few weeks apart) and robustness (high-throughput operation for 5 months without downtime) of the LC/FTICR system. When combined with modulated-ion-energy gated trapping, the internal calibration of FTICR mass spectra decreased dispersion of mass measurement errors for peptide identifications in conjunction with high resolution capillary LC separations to < 5 ppm over a dynamic range for each spectrum of 10 3
Guan, Zhibo; Wang, Miao; Cai, Yi; Yang, Hongmei; Zhao, Min; Zhao, Chunjie
2018-06-01
Sijunzi decoction, a renowned Chinese prescription has long been utilized to treat gastrointestinal problems. In the context of this research work, the use of Ultra high performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry was made to separate and characterize the components of Sijunzi decoction. The performance of Liquid chromatography was carried out on a C8 column (150 mm × 2.1 mm, 1.8 μm); moreover, the mobile phase were consisted of 0.2% formic acid (A) and acetonitrile (B). In accordance with the findings, characterization of 120 chemical compounds was performed by liquid chromatography with mass spectrometry. The key constituents among them included ginsenosides (in Radix Ginseng), 16 triterpene carboxylic acids (in Poria), sesquiterpenes (in Rhizoma Atractylodis Macrocephalae), triterpenesaponins (in Glycyrrhizae Radix et Rhizoma Praeparata Cum Melle) as well as flavonoids (in Glycyrrhizae Radix et Rhizoma Praeparata Cum Melle) in Sijunzi decoction. This research developed the bases for prospective research associated with Sijunzi decoction, together with being expected to be useful to rapidly extract and characterize the constituents in other Traditional Chinese herbal formulations. Copyright © 2018 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Yan, Jing; Zhou, Mowei; Gilbert, Joshua D.; Wolff, Jeremy J.; Somogyi, Árpád; Pedder, Randall E.; Quintyn, Royston S.; Morrison, Lindsay J.; Easterling, Michael L.; Paša-Tolić, Ljiljana; Wysocki, Vicki H.
2017-01-03
Mass spectrometry continues to develop as a valuable tool in the analysis of proteins and protein complexes. In protein complex mass spectrometry studies, surface-induced dissociation (SID) has been successfully applied in quadrupole time-of-flight (Q-TOF) instruments. SID provides structural information on non-covalent protein complexes that is complementary to other techniques. However, the mass resolution of Q-TOF instruments can limit the information that can be obtained for protein complexes by SID. Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) provides ultrahigh resolution and ultrahigh mass accuracy measurements. In this study, an SID device was designed and successfully installed in a hybrid FT-ICR instrument in place of the standard gas collision cell. The SID-FT-ICR platform has been tested with several protein complex systems (homooligomers, a heterooligomer, and a protein-ligand complex, ranging from 53 kDa to 85 kDa), and the results are consistent with data previously acquired on Q-TOF platforms, matching predictions from known protein interface information. SID fragments with the same m/z but different charge states are well-resolved based on distinct spacing between adjacent isotope peaks, and the addition of metal cations and ligands can also be isotopically resolved with the ultrahigh mass resolution available in FT-ICR.
Koch, Boris P.; Witt, Matthias; Engbrodt, Ralph; Dittmar, Thorsten; Kattner, Gerhard
2005-07-01
The chemical structure of refractory marine dissolved organic matter (DOM) is still largely unknown. Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR-MS) was used to resolve the complex mixtures of DOM and provide valuable information on elemental compositions on a molecular scale. We characterized and compared DOM from two sharply contrasting aquatic environments, algal-derived DOM from the Weddell Sea (Antarctica) and terrigenous DOM from pore water of a tropical mangrove area in northern Brazil. Several thousand molecular formulas in the mass range of 300-600 Da were identified and reproduced in element ratio plots. On the basis of molecular elemental composition and double-bond equivalents (DBE) we calculated an average composition for marine DOM. O/C ratios in the marine samples were lower (0.36 ± 0.01) than in the mangrove pore-water sample (0.42). A small proportion of chemical formulas with higher molecular mass in the marine samples were characterized by very low O/C and H/C ratios probably reflecting amphiphilic properties. The average number of unsaturations in the marine samples was surprisingly high (DBE = 9.9; mangrove pore water: DBE = 9.4) most likely due to a significant contribution of carbonyl carbon. There was no significant difference in elemental composition between surface and deep-water DOM in the Weddell Sea. Although there were some molecules with unique marine elemental composition, there was a conspicuous degree of similarity between the terrigenous and algal-derived end members. Approximately one third of the molecular formulas were present in all marine as well as in the mangrove samples. We infer that different forms of microbial degradation ultimately lead to similar structural features that are intrinsically refractory, independent of the source of the organic matter and the environmental conditions where degradation took place.
International Nuclear Information System (INIS)
Xu, Chen; Chen, Hongmei; Sugiyama, Yuko; Zhang, Saijin; Li, Hsiu-Ping; Ho, Yi-Fang; Chuang, Chia-ying; Schwehr, Kathleen A.; Kaplan, Daniel I.; Yeager, Chris; Roberts, Kimberly A.; Hatcher, Patrick G.; Santschi, Peter H.
2013-01-01
Major fractions of radioiodine ( 129 I) are associated with natural organic matter (NOM) in the groundwater and surface soils of the Savannah River Site (SRS). Electrospray ionization coupled to Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICR-MS) was applied to elucidate the interactions between inorganic iodine species (iodide and iodate) and a fulvic acid (FA) extracted from a SRS surface soil. Iodate is likely reduced to reactive iodine species by the lignin- and tannin-like compounds or the carboxylic-rich alicyclic molecules (CRAM), during which condensed aromatics and lignin-like compounds were generated. Iodide is catalytically oxidized into reactive iodine species by peroxides, while FA is oxidized by peroxides into more aliphatic and less aromatic compounds. Only 9% of the total identified organo-iodine compounds derived from molecules originally present in the FA, whereas most were iodine binding to newly-produced compounds. The resulting iodinated molecules were distributed in three regions in the van Krevelen diagrams, denoting unsaturated hydrocarbons, lignin and protein. Moreover, characteristics of these organo-iodine compounds, such as their relatively low O/C ratios ( 2 or -HNCOR groups and a ring-activating functionality to favor the electrophilic substitution. The ESI-FTICR-MS technique provides novel evidence to better understand the reactivity and scavenging properties of NOM towards radioiodine and possible influence of NOM on 129 I migration. Highlights: ► IO 3 − reduced by lignin-, tannin-like compounds/carboxylic-rich alicyclic molecules ► Condensed aromatic and lignin-like compounds generated after iodate-iodination ► Aliphatic and less aromatic compounds formed after iodide-iodination ► Organo-iodine identified as unsaturated hydrocarbons, lignin and protein ► Organo-iodine with low O/C ratios imply less environmental mobility
Directory of Open Access Journals (Sweden)
Edward E. Tarver
2004-03-01
Full Text Available Abstract: Ion mobility spectrometry (IMS is recognized as one of the most sensitive and robust techniques for the detection of narcotics, explosives and chemical warfare agents. IMS is widely used in forensic, military and security applications. Increasing threat of terrorist attacks, the proliferation of narcotics, Chemical Weapons Convention (CWC treaty verification as well as humanitarian de-mining efforts have mandated that equal importance be placed on the time required to obtain results as well as the quality of the analytical data. [1] In this regard IMS is virtually unrivaled when both speed of response and sensitivity have to be considered. [2] The problem with conventional (signal averaging IMS systems is the fixed duty cycle of the entrance gate that restricts to less than 1%, the number of available ions contributing to the measured signal. Furthermore, the signal averaging process incorporates scan-to-scan variations that degrade the spectral resolution contributing to misidentifications and false positives. With external second gate, Fourier Transform ion mobility spectrometry (FT-IMS the entrance gate frequency is variable and can be altered in conjunction with other data acquisition parameters (scan time and sampling rate to increase the spectral resolution to reduce false alarms and improve the sensitivity for early warning and contamination avoidance. In addition, with FT-IMS the entrance gate operates with a 50% duty cycle and so affords a seven-fold increase in sensitivity. Recent data on high explosives are presented to demonstrate the parametric optimization in sensitivity and resolution of our system.
Habchi, Baninia; Alves, Sandra; Jouan-Rimbaud Bouveresse, Delphine; Appenzeller, Brice; Paris, Alain; Rutledge, Douglas N; Rathahao-Paris, Estelle
2018-01-01
Due to the presence of pollutants in the environment and food, the assessment of human exposure is required. This necessitates high-throughput approaches enabling large-scale analysis and, as a consequence, the use of high-performance analytical instruments to obtain highly informative metabolomic profiles. In this study, direct introduction mass spectrometry (DIMS) was performed using a Fourier transform ion cyclotron resonance (FT-ICR) instrument equipped with a dynamically harmonized cell. Data quality was evaluated based on mass resolving power (RP), mass measurement accuracy, and ion intensity drifts from the repeated injections of quality control sample (QC) along the analytical process. The large DIMS data size entails the use of bioinformatic tools for the automatic selection of common ions found in all QC injections and for robustness assessment and correction of eventual technical drifts. RP values greater than 10 6 and mass measurement accuracy of lower than 1 ppm were obtained using broadband mode resulting in the detection of isotopic fine structure. Hence, a very accurate relative isotopic mass defect (RΔm) value was calculated. This reduces significantly the number of elemental composition (EC) candidates and greatly improves compound annotation. A very satisfactory estimate of repeatability of both peak intensity and mass measurement was demonstrated. Although, a non negligible ion intensity drift was observed for negative ion mode data, a normalization procedure was easily applied to correct this phenomenon. This study illustrates the performance and robustness of the dynamically harmonized FT-ICR cell to perform large-scale high-throughput metabolomic analyses in routine conditions. Graphical abstract Analytical performance of FT-ICR instrument equipped with a dynamically harmonized cell.
Energy Technology Data Exchange (ETDEWEB)
Xu, Chen, E-mail: xuchen66@tamu.edu [Laboratory for Environmental and Oceanographic Research, Department of Marine Sciences, Texas A and M University, Building 3029, Galveston, TX 77551 (United States); Chen, Hongmei [Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, VA 23529 (United States); Sugiyama, Yuko [Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, VA 23529 (United States); University of Hyogo, 1-1-12, Shinzaike-honcho, Himeji, Hyogo 670-0092 (Japan); Zhang, Saijin; Li, Hsiu-Ping; Ho, Yi-Fang; Chuang, Chia-ying; Schwehr, Kathleen A. [Laboratory for Environmental and Oceanographic Research, Department of Marine Sciences, Texas A and M University, Building 3029, Galveston, TX 77551 (United States); Kaplan, Daniel I. [Savannah River National Laboratory, Aiken, SC 29808 (United States); Yeager, Chris [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Roberts, Kimberly A. [Savannah River National Laboratory, Aiken, SC 29808 (United States); Hatcher, Patrick G. [Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, VA 23529 (United States); Santschi, Peter H. [Laboratory for Environmental and Oceanographic Research, Department of Marine Sciences, Texas A and M University, Building 3029, Galveston, TX 77551 (United States)
2013-04-01
Major fractions of radioiodine ({sup 129}I) are associated with natural organic matter (NOM) in the groundwater and surface soils of the Savannah River Site (SRS). Electrospray ionization coupled to Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICR-MS) was applied to elucidate the interactions between inorganic iodine species (iodide and iodate) and a fulvic acid (FA) extracted from a SRS surface soil. Iodate is likely reduced to reactive iodine species by the lignin- and tannin-like compounds or the carboxylic-rich alicyclic molecules (CRAM), during which condensed aromatics and lignin-like compounds were generated. Iodide is catalytically oxidized into reactive iodine species by peroxides, while FA is oxidized by peroxides into more aliphatic and less aromatic compounds. Only 9% of the total identified organo-iodine compounds derived from molecules originally present in the FA, whereas most were iodine binding to newly-produced compounds. The resulting iodinated molecules were distributed in three regions in the van Krevelen diagrams, denoting unsaturated hydrocarbons, lignin and protein. Moreover, characteristics of these organo-iodine compounds, such as their relatively low O/C ratios (< 0.2 or < 0.4) and yet some degree of un-saturation close to that of lignin, have multiple important environmental implications concerning possibly less sterically-hindered aromatic ring system for iodine to get access to and a lower hydrophilicity of the molecules thus to retard their migration in the natural aquatic systems. Lastly, ∼ 69% of the identified organo-iodine species contains nitrogen, which is presumably present as -NH{sub 2} or -HNCOR groups and a ring-activating functionality to favor the electrophilic substitution. The ESI-FTICR-MS technique provides novel evidence to better understand the reactivity and scavenging properties of NOM towards radioiodine and possible influence of NOM on {sup 129}I migration. Highlights: ► IO{sub 3}{sup
International Nuclear Information System (INIS)
Cao, Dong; Huang, Huogao; Hu, Ming; Cui, Lin; Geng, Fanglan; Rao, Ziyu; Niu, Hongyun; Cai, Yaqi; Kang, Yuehui
2015-01-01
Highlights: • MALDI-FT-ICR-MS was firstly employed for molecular characterization of NOM. • 1,8-Bis(dimethyl-amino)-naphthalene (DMAN) was used as matrix. • Mass spectra of NOM generated by MALDI and ESI methods were compared. • Complementary molecular information of NOM was provided by MALDI. - Abstract: Natural organic matter (NOM) is a complex and non-uniform mixture of organic compounds which plays an important role in environmental processes. Due to the complexity, it is challenging to obtain fully detailed structural information about NOM. Although Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) has been demonstrated to be a powerful tool for providing molecular information about NOM, multiple ionization methods are needed for comprehensive characterization of NOM at the molecular level considering the ionizing selectivity of different ionization methods. This paper reports the first use of matrix assisted laser desorption/ionization (MALDI) method coupled with FT-ICR-MS for molecular characterization of NOM within a mass range of 200–800 Da. The mass spectral data obtained by MALDI were systematically compared with data generated by electrospray ionization (ESI). It showed that complementary molecular information about NOM which could not be detected by ESI, were provided by MALDI. More unsaturated and aromatic constituents of NOM with lower O/C ratio (O/C ratio < 0.5) were preferentially ionized in MALDI negative mode, whereas more polar constituents of NOM with higher O/C ratio were preferentially ionized in ESI negative mode. Molecular anions of NOM appearing at even m/z in MALDI negative ion mode were detected. The results show that NOM molecules with aromatic structures, moderate O/C ratio (0.7 > O/C ratio > 0.25) and lower H/C ratio were liable to form molecular anions at even m/z, whereas those with higher H/C ratio are more likely to form deprotonated ions at odd m/z. It is speculated that almost half of the NOM
Kong, H.; Wang, M.; Venema, K.; Maathuis, A.; Heijden, R. van der; Greef, J. van der; Xu, G.; Hankemeier, T.
2009-01-01
A high-performance liquid chromatography-high resolution Fourier transform ion cyclotron resonance mass spectrometry (HPLC-FTICR-MS) method was developed to investigate the metabolism of ginsenosides in in vitro models of the gastro-intestinal tract. The metabolites were identified by
Directory of Open Access Journals (Sweden)
Ryo eNakabayashi
2015-12-01
Full Text Available In metabolomics, the analysis of product ions in tandem mass spectrometry (MS/MS is noteworthy to chemically assign structural information. However, the development of relevant analytical methods are less advanced. Here, we developed a method to boost sensitivity in liquid chromatography–Fourier transform ion cyclotron resonance–tandem mass spectrometry analysis (MS/MS boost analysis. To verify the MS/MS boost analysis, both quercetin and uniformly labeled 13C quercetin were analyzed, revealing that the origin of the product ions is not the instrument, but the analyzed compounds resulting in sensitive product ions. Next, we applied this method to the analysis of monoterpene indole alkaloids (MIAs. The comparative analyses of MIAs having indole basic skeleton (ajmalicine, catharanthine, hirsuteine, and hirsutine and oxindole skeleton (formosanine, isoformosanine, pteropodine, isopteropodine, rhynchophylline, isorhynchophylline, and mitraphylline identified 86 and 73 common monoisotopic ions, respectively. The comparative analyses of the three pairs of stereoisomers showed more than 170 common monoisotopic ions in each pair. This method was also applied to the targeted analysis of MIAs in Catharanthus roseus and Uncaria rhynchophylla to profile indole and oxindole compounds using the product ions. This analysis is suitable for chemically assigning features of the metabolite groups, which contributes to targeted metabolome analysis.
Cho, Yunju; Qi, Yulin; O'Connor, Peter B; Barrow, Mark P; Kim, Sunghwan
2014-01-01
In this study, a phase-correction technique was applied to the study of crude oil spectra obtained using a 7 T Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). 7 T FT-ICR MS had not been widely used for oil analysis due to the lower resolving power compared with high field FT-ICR MS. For low field instruments, usage of data that has not been phase-corrected results in an inability to resolve critical mass splits of C3 and SH4 (3.4 mDa), and (13)C and CH (4.5 mDa). This results in incorrect assignments of molecular formulae, and discontinuous double bond equivalents (DBE) and carbon number distributions of S1, S2, and hydrocarbon classes are obtained. Application of phase correction to the same data, however, improves the reliability of assignments and produces continuous DBE and carbon number distributions. Therefore, this study clearly demonstrates that phase correction improves data analysis and the reliability of assignments of molecular formulae in crude oil anlayses.
Kostyukevich, Yury; Vlaskin, Mikhail; Borisova, Ludmila; Zherebker, Alexander; Perminova, Irina; Kononikhin, Alexey; Popov, Igor; Nikolaev, Eugene
2018-02-01
Recent research has revealed that more than 1.3 billion tons of food is wasted globally every year. The disposal of such huge biomass has become a challenge. In the present paper, we report the production of the bio-oil by hydrothermal liquefaction of three classes of food waste: meat, cheese and fruits. The highest yield of the bio-oil was observed for meat (∼60%) and cheese (∼75%), while for fruits, it was considerably low (∼10%). The molecular composition of the obtained bio-oil was investigated using ultrahigh resolution Fourier Transform Ion Cyclotron Resonance mass spectrometry and was found to be similar to that obtained from algae. Several thousand heteroatom compounds (N, N 2 , ON 2 , etc. classes) were reliably identified from each sample. It was found that bio-oils produced from meat and cheese have many compounds (∼90%) with common molecular formulas, while bio-oil produced from fruits differs considerably (∼30% of compounds are unique).
Barrow, Mark P; Peru, Kerry M; Fahlman, Brian; Hewitt, L Mark; Frank, Richard A; Headley, John V
2015-09-01
There is a growing need for environmental screening of natural waters in the Athabasca region of Alberta, Canada, particularly in the differentiation between anthropogenic and naturally-derived organic compounds associated with weathered bitumen deposits. Previous research has focused primarily upon characterization of naphthenic acids in water samples by negative-ion electrospray ionization methods. Atmospheric pressure photoionization is a much less widely used ionization method, but one that affords the possibility of observing low polarity compounds that cannot be readily observed by electrospray ionization. This study describes the first usage of atmospheric pressure photoionization Fourier transform ion cyclotron resonance mass spectrometry (in both positive-ion and negative-ion modes) to characterize and compare extracts of oil sands process water, river water, and groundwater samples from areas associated with oil sands mining activities. When comparing mass spectra previously obtained by electrospray ionization and data acquired by atmospheric pressure photoionization, there can be a doubling of the number of components detected. In addition to polar compounds that have previously been observed, low-polarity, sulfur-containing compounds and hydrocarbons that do not incorporate a heteroatom were detected. These latter components, which are not amenable to electrospray ionization, have potential for screening efforts within monitoring programs of the oil sands.
Cho, Yunjo; Jin, Jang Mi; Witt, Matthias; Birdwell, Justin E.; Na, Jeong-Geol; Roh, Nam-Sun; Kim, Sunghwan
2013-01-01
Laser desorption ionization (LDI) coupled to Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was used to analyze shale oils. Previous work showed that LDI is a sensitive ionization technique for assessing aromatic nitrogen compounds, and oils generated from Green River Formation oil shales are well-documented as being rich in nitrogen. The data presented here demonstrate that LDI is effective in ionizing high-double-bond-equivalent (DBE) compounds and, therefore, is a suitable method for characterizing compounds with condensed structures. Additionally, LDI generates radical cations and protonated ions concurrently, the distribution of which depends upon the molecular structures and elemental compositions, and the basicity of compounds is closely related to the generation of protonated ions. This study demonstrates that LDI FT-ICR MS is an effective ionization technique for use in the study of shale oils at the molecular level. To the best of our knowledge, this is the first time that LDI FT-ICR MS has been applied to shale oils.
Wang, Meng; Zhao, Suoqi; Liu, Xuxia; Shi, Quan
2016-10-04
Thiols widely occur in sediments and fossil fuels. However, the molecular composition of these compounds is unclear due to the lack of appropriate analytical methods. In this work, a characterization method for thiols in fossil fuels was developed on the basis of Michael addition reaction derivatization followed by electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS). Model thiol compound studies showed that thiols were selectively reacted with phenylvinylsulfone and transformed to sulfones with greater than 98% conversions. This method was applied to a coker naphtha, light and heavy gas oils, and crude oils from various geological sources. The results showed that long alkyl chain thiols are readily present in petroleum, which have up to 30 carbon atoms. Large DBE dispersity of thiols indicates that naphthenic and aromatic thiols are also present in the petroleum. This method is capable of detecting thiol compounds in the part per million range by weight. This method allows characterization of thiols in a complex hydrocarbon matrix, which is complementary to the comprehensive analysis of sulfur compounds in fossil fuels.
Clarke, David J; Stokes, Adam A; Langridge-Smith, Pat; Mackay, C Logan
2010-03-01
We have developed an automated quench-flow microreactor which interfaces directly to an electrospray ionization (ESI) mass spectrometer. We have used this device in conjunction with ESI Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) to demonstrate the potential of this approach for studying the mechanistic details of enzyme reactions. For the model system chosen to test this device, namely, the pre-steady-state hydrolysis of p-nitrophenyl acetate by the enzyme chymotrypsin, the kinetic parameters obtained are in good agreement with those in the literature. To our knowledge, this is the first reported use of online quench-flow coupled with FTICR MS. Furthermore, we have exploited the power of FTICR MS to interrogate the quenched covalently bound enzyme intermediate using top-down fragmentation. The accurate mass capabilities of FTICR MS permitted the nature of the intermediate to be assigned with high confidence. Electron capture dissociation (ECD) fragmentation allowed us to locate the intermediate to a five amino acid section of the protein--which includes the known catalytic residue, Ser(195). This experimental approach, which uniquely can provide both kinetic and chemical details of enzyme mechanisms, is a potentially powerful tool for studies of enzyme catalysis.
DEFF Research Database (Denmark)
Renfrow, MB; Mackay, CL; Chalmers, MJ
2007-01-01
deficiency in IgA1 proteins occurs randomly or preferentially at specific sites. We have previously demonstrated the first direct localization of multiple O-glycosylation sites on a single IgA1 myeloma protein by use of activated ion-electron capture dissociation (AI-ECD) Fourier transform ion cyclotron...... resonance (FT-ICR) tandem mass spectrometry. Here, we report the analysis of IgA1 O-glycan heterogeneity by use of FT-ICR MS and liquid chromatography FT-ICR MS to obtain unbiased accurate mass profiles of IgA1 HR glycopeptides from three different IgA1 myeloma proteins. Additionally, we report the first AI......-ECD fragmentation on an individual IgA1 O-glycopeptide from an IgA1 HR preparation that is reproducible for each IgA1 myeloma protein. These results suggest that future analysis of IgA1 HR from IgAN patients and normal healthy controls should be feasible....
Energy Technology Data Exchange (ETDEWEB)
Tfaily, Malak M.; Cooper, William T. [Florida State University, Department of Chemistry and Biochemistry, Tallahassee, FL (United States); Hodgkins, Suzanne; Chanton, Jeffrey P. [Florida State University, Department of Earth, Ocean and Atmospheric Science, Tallahassee, FL (United States); Podgorski, David C. [Florida State University, Department of Chemistry and Biochemistry, Tallahassee, FL (United States); Florida State University, National High Magnetic Field Laboratory, Tallahassee, FL (United States)
2012-08-15
We compare two methods, solid-phase extraction (SPE) and dialysis, commonly used for extraction and concentration of dissolved organic matter (DOM) prior to molecular characterization by electrospray ionization (ESI) and ultrahigh-resolution Fourier transform ion cyclotron resonance mass spectrometry. Spectra of DOM samples from Minnesota and Sweden peatlands that were extracted with styrene divinyl benzene polymer SPE sorbents included ions with formulas that had higher oxygen to carbon (O/C) ratios than spectra of DOM from the same samples after de-salting by dialysis. The SPE method was not very effective in extracting several major classes of DOM compounds that had high ESI efficiencies, including carboxylic acids and organo-sulfur compounds, and that out-competed other less-functionalized compounds (e.g., carbohydrates) for charge in the ESI source. The large abundance of carboxylic acids in the dialysisextracted DOM, likely the result of in situ microbial production, makes it difficult to see other (mainly hydrophilic) compounds with high O/C ratios. Our results indicate that, while dialysis is generally preferable for the isolation of DOM, for samples with high microbial inputs, the use of both isolation methods is recommended for a more accurate molecular representation. (orig.)
Choi, Myoung Choul; Lee, Jeong Min; Lee, Se Gyu; Choi, Sang Hwan; Choi, Yeon Suk; Lee, Kyung Jae; Kim, SeungYong; Kim, Hyun Sik; Stahl, Stefan
2012-12-18
Despite the outstanding performance of Fourier transform ion cyclotron/mass spectrometry (FTICR/MS), the complexity of the cellular proteome or natural compounds presents considerable challenges. Sensitivity is a key performance parameter of a FTICR mass spectrometer. By improving this parameter, the dynamic range of the instrument can be increased to improve the detection signal of low-abundance compounds or fragment ion peaks. In order to improve sensitivity, a cryogenic detection system was developed by the KBSI (Korean Basic Science Institute) in collaboration with Stahl-Electronics (Mettenheim, Germany). A simple, efficient liquid circulation cooling system was designed and a cryogenic preamplifier implemented inside a FTICR mass spectrometer. This cooling system circulates a cryoliquid from a Dewar to the "liquid circulation unit" through a CF flange to cool a copper block and a cryopreamplifier; the cooling medium is subsequently exhausted into the air. The cryopreamplifier can be operated over a very wide temperature range, from room temperature to low temperature environments (4.2 K). First, ion signals detected by the cryopreamplifier using a circulating liquid nitrogen cooling system were observed and showed a signal-to-noise ratio (S/N) about 130% better than that obtained at room temperature.
Han, Fei; Li, Yanting; Mao, Xinjuan; Xu, Rui; Yin, Ran
2016-05-01
In this work, an approach using high-performance liquid chromatography coupled with diode-array detection and Fourier-transform ion cyclotron resonance mass spectrometer (HPLC-FT-ICR MS) for the identification and profiling of chemical constituents in Rhodiola crenulata was developed for the first time. The chromatographic separation was achieved on an Inertsil ODS-3 column (150 mm × 4.6 mm,3 µm) using a gradient elution program, and the detection was performed on a Bruker Solarix 7.0 T mass spectrometer equipped with electrospray ionization source in both positive and negative modes. Under the optimized conditions, a total of 48 chemical compounds, including 26 alcohols and their glycosides, 12 flavonoids and their glycosides, 5 flavanols and gallic acid derivatives, 4 organic acids and 1 cyanogenic glycoside were identified or tentatively characterized. The results indicated that the developed HPLC-FT-ICR MS method with ultra-high sensitivity and resolution is suitable for identifying and characterizing the chemical constituents in R. crenulata. And it provides a helpful chemical basis for further research on R. crenulata. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Nakabayashi, Ryo; Tsugawa, Hiroshi; Kitajima, Mariko; Takayama, Hiromitsu; Saito, Kazuki
2015-01-01
In metabolomics, the analysis of product ions in tandem mass spectrometry (MS/MS) is noteworthy to chemically assign structural information. However, the development of relevant analytical methods are less advanced. Here, we developed a method to boost sensitivity in liquid chromatography–Fourier transform ion cyclotron resonance–tandem mass spectrometry analysis (MS/MS boost analysis). To verify the MS/MS boost analysis, both quercetin and uniformly labeled 13C quercetin were analyzed, revealing that the origin of the product ions is not the instrument, but the analyzed compounds resulting in sensitive product ions. Next, we applied this method to the analysis of monoterpene indole alkaloids (MIAs). The comparative analyses of MIAs having indole basic skeleton (ajmalicine, catharanthine, hirsuteine, and hirsutine) and oxindole skeleton (formosanine, isoformosanine, pteropodine, isopteropodine, rhynchophylline, isorhynchophylline, and mitraphylline) identified 86 and 73 common monoisotopic ions, respectively. The comparative analyses of the three pairs of stereoisomers showed more than 170 common monoisotopic ions in each pair. This method was also applied to the targeted analysis of MIAs in Catharanthus roseus and Uncaria rhynchophylla to profile indole and oxindole compounds using the product ions. This analysis is suitable for chemically assigning features of the metabolite groups, which contributes to targeted metabolome analysis. PMID:26734034
Oro, Nicole E; Whittal, Randy M; Lucy, Charles A
2012-09-05
Normal phase high performance liquid chromatography (HPLC) is used to separate a gas oil petroleum sample, and the fractions are collected offline and analyzed on a high resolution Fourier Transform Ion Cyclotron Resonance Mass Spectrometer (FT-ICR MS). The separation prior to MS analysis dilutes the sample significantly; therefore the fractions need to be prepared properly to achieve the best signal possible. The methods used to prepare the HPLC fractions for MS analysis are described, with emphasis placed on increasing the concentration of analyte species. The dilution effect also means that contamination in the MS spectra needs to be minimized. The contamination from molecular sieves, plastics, soap, etc. and interferences encountered during the offline fraction collection process are described and eliminated. A previously unreported MS contamination of iron formate clusters with a 0.8 mass defect in positive mode electrospray is also described. This interference resulted from the stainless steel tubing in the HPLC system. Contamination resulting from what has tentatively been assigned as palmitoylglycerol and stearoylglycerol was also observed; these compounds have not previously been reported as contaminant peaks. Copyright © 2012 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
C. Doc Richardson; Nancy W. Hinman; Timothy R. McJunkin; J. Michelle Kotler; Jill R. Scott
2008-10-01
Geomatrix-assisted laser desorption/ionization (GALDI) in conjunction with a Fourier transform ion cyclotron resonance mass spectrometer (FTICR-MS) has been employed to determine how effectively bio/organic molecules associated with the mineral thenardite (Na2SO4) can be detected. GALDI is based on the ability of the mineral host to assist desorption and ionization of bio/organic molecules without additional sample preparation. When glycine was mixed with thenardite, glycine was deprotonated to produce C2H4NO-2 at m/z 74.025. The combination of stearic acid with thenardite produced a complex cluster ion at m/z 390.258 in the negative mode, which was assigned a composition ofC18H39O7Na-. Anatural sample of thenardite from Searles Lake in California also produced a peak at m/z 390.260. The bio/organic signatures in both the laboratory-based and natural samples were heterogeneously dispersed as revealed by chemical imaging. The detection limits for the stearic acid and thenardite combination were estimated to be 3 parts per trillion or~7 zeptomoles (10-21) per laser spot. Attempts to improve the signal-to-noise ratio by co-adding FTICR-MS data predetermined to contain the biosignatures of interest revealed problems due to a lack of phase coherence between data sets.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hang, E-mail: hangwang@sjtu.edu.cn [Instrumental Analysis Center, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240 (China); Dai, Bona [Instrumental Analysis Center, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240 (China); Liu, Bin [Key Laboratory of Kidney Disease Pathogenesis and Intervention of Hubei Province, College of Medicine, Hubei Polytechnic University, Huangshi, Hubei 435003 (China); Lu, Han [Department of Anesthesiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine (SJTU-SM), 197, Rui Jin Er Road, Shanghai 200025 (China)
2015-07-02
Highlights: • Coumarins were used as new MALDI matrices. • Coumarins were used for MALDI-FT ICR MS detection of hydrophobic compounds. • DCA had improvement in detection sensitivity, stability, selectivity and reproducibility. • DCA was applied to sterols detection in yeast cells. - Abstract: Hydrophobic compounds with hydroxyl, aldehyde or ketone groups are generally difficult to detect using matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS), because these compounds have low proton affinity and are poorly ionized by MALDI. Herein, coumarins have been used as new matrices for MALDI-MS analysis of a variety of hydrophobic compounds with low ionization efficiency, including steroids, coenzyme Q10, a cyclic lipopeptide and cholesterol oleate. Five coumarins, including coumarin, umbelliferone, esculetin, 7-hydroxycoumarin-3-carboxylic acid (HCA) and 6,7-dihydroxycoumarin-3-carboxylic acid (DCA), were compared with the conventional matrices of 2,5-dihydroxybenzoic acid (DHB) and α-cyano-4-hydroxycinnamic acid (CHCA). Coumarins with hydroxyl or carboxylic acid groups enabled detection. Taking DCA as an example, this matrix proved to be superior to DHB or CHCA in detection sensitivity, stability, spot-to-spot and sample-to-sample reproducibility, and accuracy. DCA increased the stability of the target compounds and decreased the loss of water. The [M + Na]{sup +} peaks were observed for all target compounds by adding NaCl as an additive, and the [M − H{sub 2}O + H]{sup +} and [M + H]{sup +} peaks decreased. DCA was selected for the identification of sterols in yeast cells, and thirteen sterols were detected by Fourier transform ion cyclotron resonance (FT ICR) mass spectrometry. This work demonstrates the potential of DCA as a new matrix for detection of hydrophobic molecules by MALDI-MS and provides an alternative tool for screening sterols in antifungal research.
Guo, Kevin; Bamforth, Fiona; Li, Liang
2011-02-01
Metabolome analysis of human cerebrospinal fluid (CSF) is challenging because of low abundance of metabolites present in a small volume of sample. We describe and apply a sensitive isotope labeling LC-MS technique for qualitative analysis of the CSF metabolome. After a CSF sample is divided into two aliquots, they are labeled by 13C-dansyl and 12C-dansyl chloride, respectively. The differentially labeled aliquots are then mixed and subjected to LC-MS using Fourier-transform ion cyclotron resonance mass spectrometry (FTICR MS). Dansylation offers significant improvement in the performance of chromatography separation and detection sensitivity. Moreover, peaks detected in the mass spectra can be readily analyzed for ion pair recognition and database search based on accurate mass and/or retention time information. It is shown that about 14,000 features can be detected in a 25-min LC-FTICR MS run of a dansyl-labeled CSF sample, from which about 500 metabolites can be profiled. Results from four CSF samples are compared to gauge the detectability of metabolites by this method. About 261 metabolites are commonly detected in replicate runs of four samples. In total, 1132 unique metabolite ion pairs are detected and 347 pairs (31%) matched with at least one metabolite in the Human Metabolome Database. We also report a dansylation library of 220 standard compounds and, using this library, about 85 metabolites can be positively identified. Among them, 21 metabolites have never been reported to be associated with CSF. These results illustrate that the dansylation LC-FTICR MS method can be used to analyze the CSF metabolome in a more comprehensive manner.
Liu, Ting; Li, Songhe; Tian, Xiumin; Li, Zhaoqin; Cui, Yue; Han, Fei; Zhao, Yunli; Yu, Zhiguo
2017-09-15
Pyrexia usually is a systemic pathological process that can lead to metabolic disorders. Metabonomics as a powerful tool not only can reveal the pathological mechanisms, but also can give insight into the progression of pyrexia from another angle. Thus, an ultra high performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry (UHPLC-FT-ICR-MS) metabonomic approach was employed for the first time to investigate the plasma biochemical characteristics of pyrexia induced by three methods and to reveal subtle metabolic changes under the condition of pyrexia so as to explore its mechanism. The acquired metabolic data of the models were subjected to principal component analysis (PCA) for allowing the clear separation of the pyrexia rats from the control rats. Variable importance for project values (VIP) and Student's t-test were used to screen the significant metabolic changes caused by pyrexia. Fifty-two endogenous metabolites were identified and putatively identified as potential biomarkers primarily associated with phospholipid metabolism, sphingolipid metabolism, fatty acid oxidation metabolism, fatty acid amides metabolism and amino acid metabolism, and related to bile acid biosynthesis and glycerolipid catabolism. LysoPC (14:0), LysoPC (18:3), LysoPC (20:4), LysoPC (16:0), phytosphingosine, Cer (d18:0/12:0), N-[(4E,8E)-1,3-dihydroxyoctadeca-4,8-dien-2-yl]hexadecanamide, oleamide, fatty acid amide C22:1, tryptophan, acetylcarnitine, palmitoylcarnitine and stearoylcarnitine were considered as common potential biomarkers of pyrexia rats induced by three methods: Our results revealed that the UHPLC-FT-ICR-MS-based metabolomic method is helpful for finding new potential metabolic markers for pyrexia detection and offers a good perspective in pyrexia research. Copyright © 2017 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Tang, Yinjie; Pingitore, Francesco; Mukhopadhyay, Aindrila; Phan, Richard; Hazen, Terry C.; Keasling, Jay D.
2007-01-01
Flux distribution in central metabolic pathways of Desulfovibrio vulgaris Hildenborough was examined using 13C tracer experiments. Consistent with the current genome annotation and independent evidence from enzyme activity assays, the isotopomer results from both GC-MS and Fourier Transform-Ion Cyclotron Resonance mass spectrometry (FT-ICR MS) indicate the lack of oxidatively functional TCA cycle and an incomplete pentose phosphate pathway. Results from this study suggest that fluxes through both pathways are limited to biosynthesis. The data also indicate that >80 percent of the lactate was converted to acetate and the reactions involved are the primary route of energy production (NAD(P)H and ATP production). Independent of the TCA cycle, direct cleavage of acetyl-CoA to CO and 5,10-methyl-THF also leads to production of NADH and ATP. Although the genome annotation implicates a ferredoxin-dependent oxoglutarate synthase, isotopic evidence does not support flux through this reaction in either the oxidative or reductive mode; therefore, the TCA cycle is incomplete. FT-ICR MS was used to locate the labeled carbon distribution in aspartate and glutamate and confirmed the presence of an atypical enzyme for citrate formation suggested in previous reports (the citrate synthesized by this enzyme is the isotopic antipode of the citrate synthesized by the (S)-citrate synthase). These findings enable a better understanding of the relation between genome annotation and actual metabolic pathways in D. vulgaris, and also demonstrate FT-ICR MS as a powerful tool for isotopomer analysis, overcoming problems in both GC-MS and NMR spectroscopy
Zhang, Haifeng; Zhang, Yahe; Shi, Quan; Ren, Shuoyi; Yu, Jianwei; Ji, Feng; Luo, Wenbin; Yang, Min
2012-10-15
Dissolved natural organic matter (DOM), particularly the low molecular weight DOM, can affect the performance of water treatment processes and serve as a main precursor of disinfection by-products (DBPs) during chlorination. In this study, electrospray ionization coupled to Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS) was used to characterize the low molecular weight DOM along the treatment trait of a conventional drinking water treatment plant. The ESI FT-ICR MS data showed that various C, H, O-only class species were the major components in the source water. According to the van Krevelen diagram analysis, lignin- and tannin-like compounds were the most abundant components. Within an isobaric group, the DOM molecules with a high degree of oxidation (high O/C value) were preferentially removed during coagulation, while those with low degree of oxidation were found to be more reactive toward chlorine. In addition, 357 one-chlorine containing products and 199 two-chlorine containing products formed during chlorination were detected in the chlorination effluent sample at a high confidence level. The chlorinated products can be arranged into series, suggesting that they were originated from C, H, O-only precursor compounds, which were in series related by the replacement of CH(4) against oxygen. For the first time, this study explored the behavior of low molecular weight DOM along a drinking water treatment trait on the molecular level, and revealed the presence of abundant unknown chlorinated products, which are probably rich in carboxylic and phenolic groups, in drinking water. Copyright © 2012 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Belov, Mikhail E.(VISITORS); Zhang, Rui (BATTELLE (PACIFIC NW LAB)); Strittmatter, Eric F.(BATTELLE (PACIFIC NW LAB)); Prior, David C.(BATTELLE (PACIFIC NW LAB)); Tang, Keqi (BATTELLE (PACIFIC NW LAB)); Smith, Richard D.(BATTELLE (PACIFIC NW LAB))
2003-08-15
When combined with capillary LC separations, Electrospray Ionization Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (ESI-FTICR MS) has increasingly been applied for advanced characterization of proteolytic digests. Incorporation of external (to the ICR cell) ion accumulation multipoles with FTICR for ion pre selection and accumulation has enhanced the dynamic range, sensitivity and duty cycle of measurements. However, the highly variable ion production rate from an LC separation can result in overfilling of the external trap, resulting in m/z discrimination and fragmentation of peptide ions. An excessive space charge trapped in the ICR cell causes significant shifts in the detected ion cyclotron frequencies, reducing the achievable mass measurement accuracy (MMA) for protein identification. To eliminate m/z discrimination in the external ion trap, further increase the duty cycle and improve MMA, we developed a capability for data-dependent adjustment of ion accumulation times in the course of an LC separation, referred to as Automated Gain Control (AGC), in combination with low kinetic energy gated ion trapping and internal calibration using a dual-channel electrodynamic ion funnel. The system was initially evaluated in the analysis of a 0.5 mg/mL tryptic digest of bovine serum albumin. The implementation of LC/ESI/AGC/FTICR with internal calibration gave rise to a {approx} 10-fold increase in the number of identified tryptic peptides within mass measurement accuracy of 2 ppm as compared to that detected during the conventional LC/FTICR run with a fixed ion accumulation time and external calibration.
Directory of Open Access Journals (Sweden)
R. M. Dickhut
2008-09-01
Full Text Available Despite the acknowledged relevance of aerosol-derived water-soluble organic carbon (WSOC to climate and biogeochemical cycling, characterization of aerosol WSOC has been limited. Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS was utilized in this study to provide detailed molecular level characterization of the high molecular weight (HMW; m/z>223 component of aerosol-derived WSOC collected from rural sites in Virginia and New York, USA. More than 3000 peaks were detected by ESI FT-ICR MS within a m/z range of 223–600 for each sample. Approximately 86% (Virginia and 78% (New York of these peaks were assigned molecular formulas using only carbon (C, hydrogen (H, oxygen (O, nitrogen (N, and sulfur (S as elemental constituents. H/C and O/C molar ratios were plotted on van Krevelen diagrams and indicated a strong contribution of lignin-like and lipid-like compounds to the aerosol-derived WSOC samples. Approximately 1–4% of the peaks in the aerosol-derived WSOC mass spectra were classified as black carbon (BC on the basis of double bond equivalents calculated from the assigned molecular formulas. In addition, several high-magnitude peaks in the mass spectra of samples from both sites corresponded to molecular formulas proposed in previous secondary organic aerosol (SOA laboratory investigations indicating that SOAs are important constituents of the WSOC. Overall, ESI FT-ICR MS provides a level of resolution adequate for detailed compositional and source information of the HMW constituents of aerosol-derived WSOC.
Guo, Kevin; Bamforth, Fiona; Li, Liang
2011-02-01
Metabolome analysis of human cerebrospinal fluid (CSF) is challenging because of low abundance of metabolites present in a small volume of sample. We describe and apply a sensitive isotope labeling LC-MS technique for qualitative analysis of the CSF metabolome. After a CSF sample is divided into two aliquots, they are labeled by (13)C-dansyl and (12)C-dansyl chloride, respectively. The differentially labeled aliquots are then mixed and subjected to LC-MS using Fourier-transform ion cyclotron resonance mass spectrometry (FTICR MS). Dansylation offers significant improvement in the performance of chromatography separation and detection sensitivity. Moreover, peaks detected in the mass spectra can be readily analyzed for ion pair recognition and database search based on accurate mass and/or retention time information. It is shown that about 14,000 features can be detected in a 25-min LC-FTICR MS run of a dansyl-labeled CSF sample, from which about 500 metabolites can be profiled. Results from four CSF samples are compared to gauge the detectability of metabolites by this method. About 261 metabolites are commonly detected in replicate runs of four samples. In total, 1132 unique metabolite ion pairs are detected and 347 pairs (31%) matched with at least one metabolite in the Human Metabolome Database. We also report a dansylation library of 220 standard compounds and, using this library, about 85 metabolites can be positively identified. Among them, 21 metabolites have never been reported to be associated with CSF. These results illustrate that the dansylation LC-FTICR MS method can be used to analyze the CSF metabolome in a more comprehensive manner. © American Society for Mass Spectrometry, 2011
Pasilis, Sofie; Somogyi, Arpád; Herrmann, Kristin; Pemberton, Jeanne E
2006-02-01
Electrospray ionization (ESI) of uranyl nitrate solutions generates a wide variety of positively and negatively charged ions, including complex adducts of uranyl ions with methoxy, hydroxy, and nitrate ligands. In the positive ion mode, ions detected by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry are sensitive to instrumental tuning parameters such as quadrupole operating frequency and trapping time. Positive ions correspond to oligomeric uranyl nitrate species that can be characterized as having a general formula of [(UO(2))(n)(A)(m)(CH(3)OH)(s)](+) or [(UO(2))(n)(O)(A)(m)(CH(3)OH)(s)](+) with n = 1-4, m = 1-7, s = 0 or 1, and A = OH, NO(3), CH(3)O or a combination of these, although the formation of NO(3)-containing species is preferred. In the negative ion mode, complexes of the form [(UO(2))(NO(3))(m)](-) (m = 1-3) are detected, although the formation of the oxo-containing ions [(UO(2))(O)(n)(NO(3))(m)](-) (n = 1-2, m = 1-2) and the hydroxy-containing ions [(UO(2))(OH)(n)(NO(3))(m)](-) (n = 1-2, m = 0-1) are also observed. The extent of coordinative unsaturation of both positive and negative ions can be determined by ligand association/exchange and H/D exchange experiments using D(2)O and CD(3)OD as neutral reaction partners in the gas-phase. Positive ions are of varying stability and reactivity and may fragment extensively upon collision with D(2)O, CD(3)OD and N(2) in sustained off-resonance irradiation/collision-induced dissociation (SORI-CID) experiments. Electron-transfer reactions, presumably occurring during electrospray ionization but also in SORI-CID, can result in reduction of U(VI) to U(V) and perhaps even U(IV).
Wu, Wenying; Chen, Yu; Wang, Binjie; Sun, Xiaoyang; Guo, Ping; Chen, Xiaohui
2017-08-01
Baidianling Capsule, which is made from 16 Chinese herbs, has been widely used for treating vitiligo clinically. In this study, the sensitive and rapid method has been developed for the analysis of chemical components in Baidianling Capsule by gas chromatography-mass spectrometry in combination with retention indices and high-performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry. Firstly, a total of 110 potential volatile compounds obtained from different extraction procedures including alkanes, alkenes, alkynes, ketones, ethers, aldehydes, alcohols, phenols, organic acids, esters, furans, pyrrole, acid amides, heterocycles, and oxides were detected from Baidianling Capsule by gas chromatography-mass spectrometry, of which 75 were identified by mass spectrometry in combination with the retention index. Then, a total of 124 components were tentatively identified by high-performance liquid chromatography combined with Fourier transform ion cyclotron resonance mass spectrometry. Fifteen constituents from Baidianling Capsule were accurately identified by comparing the retention times with those of reference compounds, others were identified by comparing the retention times and mass spectrometry data, as well as retrieving the reference literature. This study provides a practical strategy for rapidly screening and identifying the multiple constituents of a complex traditional Chinese medicine. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Jiménez-Morillo, Nicasio T.; González-Pérez, José A.; Waggoner, Derek C.; Almendros, Gonzalo; González-Vila, Francisco J.; Hatcher, Patrick G.
2016-04-01
Introduction: Fire is one of the most important modulator factors of the environment and the forest. It is able to induce chemical and biological shifts and these, in turn, can alter the physical properties of soil. Generally, fire affects the most reactive fraction, soil organic matter (SOM) (González-Pérez et al., 2004) resulting in changes to several soil properties and functions. To study changes in SOM following a wildfire, researchers can count on several traditional as well as new analytical techniques. One of the most recently employed techniques is Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS). This new powerful ultra-high resolution mass spectral technique, together with graphic interpretation tools such as van Krevelen diagrams (Kim et al, 2003), may be used to shed light on alterations caused by the burning of SOM. The objective of this research is to study fire impacts on SOM, using a sandy soil collected under a Cork oak (Quercus suber) in Doñana National Park, Southwest Spain. that was affected by a wildfire in August 2012. Methods: The impact of fire on SOM was studied in various different sieve fractions (coarse, 1-2 mm, and fine, tannins, lignin, lipids, protein and carbohydrate derived. The unburnt SOM in the coarse fraction was mainly composed of compounds with a high intensity in the tannin-like, lignin-like and carbohydrate-like regions of the van Krevelen diagram, whereas the SOM in the fine fraction showed a high intensity in the lipid-like and protein-like regions. These results suggest that the SOM in the coarse fraction was less altered than that of the fine fraction; the latter believed to be subjected to higher microbial activity. We suggest that the observed changes occurs via a methylation process, producing a SOM that is highly humified (Jiménez-Morillo et al., 2014). The SOM in the coarse fraction affected by fire, showed a high relative intensity of chemical compounds in the carbohydrate-like and
Ferrite-guided cyclotron-resonance maser
International Nuclear Information System (INIS)
Jerby, Eli; Kesar, A.; Aharony, A.; Breitmeier, G.
2002-01-01
The concept of a cyclotron-resonance maser (CRM) with a ferrite loading incorporated in its waveguide is proposed. The CRM interaction occurs between the rotating electron beam and the em wave propagating along a longitudinally magnetized ferrite medium. The ferrite anisotropic permeability resembles the CRM susceptibility in many aspects, and particularly in their similar response to the axial magnetic field (the ferrite susceptibility can be regarded as a passive analog of the active CRM interaction). The ferrite loading slows down the phase velocity of the em wave and thus the axial (Weibel) mechanism of the CRM interaction dominates. The ferrite loading enables also a mechanism of spectral tunability for CRM's. The ferrite loading is proposed, therefore, as a useful ingredient for high-power CRM devices. A linear model of the combined ferrite-guided CRM interaction reveals its useful features. Future schemes may also incorporate ferrite sections functioning as isolators, gyrators, or phase shifters within the CRM device itself for selective suppression of backward waves and spurious oscillations, and for gain and efficiency enhancement
International Nuclear Information System (INIS)
Schweikhard, Lutz; Drader, Jared J.; Shi, Stone D.-H.; Hendrickson, Christopher L.; Marshall, Alan G.
2002-01-01
Positive and negative ions may be confined simultaneously in a nested open cylindrical Malmberg-Penning trap. However, ion charge sign cannot be distinguished by conventional dipolar (linearly-polarized) detection with a single pair of opposed electrodes. Here, the signals from each of two orthogonal pairs of opposed detection electrodes are acquired simultaneously and stored as real and imaginary parts of mathematically complex data. Complex Fourier transformation yields separate spectra for positive and negative ions. For a fullerene sample, experimental quadrature detection yields C 60 + and C 60 - signals separated by ∼1440 u rather than by the mass of two electrons, ∼0.001 u in conventional dipolar detection
Ghaste, Manoj; Mistrik, Robert; Shulaev, Vladimir
2016-01-01
Metabolomics, along with other “omics” approaches, is rapidly becoming one of the major approaches aimed at understanding the organization and dynamics of metabolic networks. Mass spectrometry is often a technique of choice for metabolomics studies due to its high sensitivity, reproducibility and wide dynamic range. High resolution mass spectrometry (HRMS) is a widely practiced technique in analytical and bioanalytical sciences. It offers exceptionally high resolution and the highest degree of structural confirmation. Many metabolomics studies have been conducted using HRMS over the past decade. In this review, we will explore the latest developments in Fourier transform mass spectrometry (FTMS) and Orbitrap based metabolomics technology, its advantages and drawbacks for using in metabolomics and lipidomics studies, and development of novel approaches for processing HRMS data. PMID:27231903
Hertzog, Jasmine; Carré, Vincent; Le Brech, Yann; Mackay, Colin Logan; Dufour, Anthony; Mašek, Ondřej; Aubriet, Frédéric
2017-05-29
The comprehensive description of complex mixtures such as bio-oils is required to understand and improve the different processes involved during biological, environmental or industrial operation. In this context, we have to consider how different ionization sources can improve a non-targeted approach. Thus, the Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) has been coupled to electrospray ionization (ESI), laser desorption ionization (LDI) and atmospheric pressure photoionization (APPI) to characterize an oak pyrolysis bio-oil. Close to 90% of the all 4500 compound formulae has been attributed to C x H y O z with similar oxygen class compound distribution. Nevertheless, their relative abundance in respect with their double bound equivalent (DBE) value has evidenced significant differences depending on the ion source used. ESI has allowed compounds with low DBE but more oxygen atoms to be ionized. APPI has demonstrated the efficient ionization of less polar compounds (high DBE values and less oxygen atoms). The LDI behavior of bio-oils has been considered intermediate in terms of DBE and oxygen amounts but it has also been demonstrated that a significant part of the features are specifically detected by this ionization method. Thus, the complementarity of three different ionization sources has been successfully demonstrated for the exhaustive characterization by petroleomic approach of a complex mixture. Copyright © 2017 Elsevier B.V. All rights reserved.
Ion cyclotron-resonance heating in a toroidal octupole
International Nuclear Information System (INIS)
Barter, J.D.; Sprott, J.C.
1975-01-01
rf power near the ion cyclotron-resonance frequency has been used to produce a hundredfold increase (from approximately-less-than1 to approx.100 eV) in the ion temperature in a toroidal octupole device. The heating produces no noticeable instabilities or other deleterious effects except for a high reflux of neutrals from the walls. The heating rate is consistent with theory and the limiting ion temperature is determined by charge-exchange losses
Mo, Yangzhi; Li, Jun; Jiang, Bin; Su, Tao; Geng, Xiaofei; Liu, Junwen; Jiang, Haoyu; Shen, Chengde; Ding, Ping; Zhong, Guangcai; Cheng, Zhineng; Liao, Yuhong; Tian, Chongguo; Chen, Yingjun; Zhang, Gan
2018-08-01
Humic-like substances (HULIS) are a class of high molecular weight, light-absorbing compounds that are highly related to brown carbon (BrC). In this study, the sources and compositions of HULIS isolated from fine particles collected in Beijing, China during the 2014 Asia-Pacific Economic Cooperation (APEC) summit were characterized based on carbon isotope ( 13 C and 14 C) and Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR MS) analyses, respectively. HULIS were the main light-absorbing components of water-soluble organic carbon (WSOC), accounting for 80.2 ± 6.1% of the WSOC absorption capacity at 365 nm. The carbon isotope data showed that HULIS had a lower non-fossil contribution (53 ± 4%) and were less enriched with 13 C (-24.2 ± 0.6‰) relative to non-HULIS (62 ± 8% and -20.8 ± 0.3‰, respectively). The higher relative intensity fraction of sulfur-containing compounds in HULIS before and after APEC was attributed to higher sulfur dioxide levels emitted from fossil fuel combustion, whereas the higher fraction of nitrogen-containing compounds during APEC may have been due to the relatively greater contribution of non-fossil compounds or the influence of nitrate radical chemistry. The results of investigating the relationships among the sources, elemental compositions, and optical properties of HULIS demonstrated that the light absorption of HULIS appeared to increase with increasing unsaturation degree, but decrease with increasing oxidation level. The unsaturation of HULIS was affected by both sources and aging level. Copyright © 2018 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Hertzog, Jasmine [LCP-A2MC, FR 2843 Institut Jean Barriol de Chimie et Physique Moléculaires et Biomoléculaires, FR 3624 Réseau National de Spectrométrie de Masse FT-ICR à très haut champ, Université de Lorraine, ICPM, 1 boulevard Arago, 57078 Metz Cedex 03 (France); Carré, Vincent, E-mail: vincent.carre@univ-lorraine.fr [LCP-A2MC, FR 2843 Institut Jean Barriol de Chimie et Physique Moléculaires et Biomoléculaires, FR 3624 Réseau National de Spectrométrie de Masse FT-ICR à très haut champ, Université de Lorraine, ICPM, 1 boulevard Arago, 57078 Metz Cedex 03 (France); Le Brech, Yann [LRGP, CNRS, Université de Lorraine, ENSIC, 1, Rue Grandville, 54000 Nancy (France); Mackay, Colin Logan [SIRCAMS, School of Chemistry, University of Edinburgh, Edinburgh, EH9 3FJ, Scotland (United Kingdom); Dufour, Anthony [LRGP, CNRS, Université de Lorraine, ENSIC, 1, Rue Grandville, 54000 Nancy (France); Mašek, Ondřej [UK Biochar Research Center, School of Geosciences, University of Edinburgh, Kings Buildings, Edinburgh, EH9 3JN (United Kingdom); and others
2017-05-29
The comprehensive description of complex mixtures such as bio-oils is required to understand and improve the different processes involved during biological, environmental or industrial operation. In this context, we have to consider how different ionization sources can improve a non-targeted approach. Thus, the Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) has been coupled to electrospray ionization (ESI), laser desorption ionization (LDI) and atmospheric pressure photoionization (APPI) to characterize an oak pyrolysis bio-oil. Close to 90% of the all 4500 compound formulae has been attributed to C{sub x}H{sub y}O{sub z} with similar oxygen class compound distribution. Nevertheless, their relative abundance in respect with their double bound equivalent (DBE) value has evidenced significant differences depending on the ion source used. ESI has allowed compounds with low DBE but more oxygen atoms to be ionized. APPI has demonstrated the efficient ionization of less polar compounds (high DBE values and less oxygen atoms). The LDI behavior of bio-oils has been considered intermediate in terms of DBE and oxygen amounts but it has also been demonstrated that a significant part of the features are specifically detected by this ionization method. Thus, the complementarity of three different ionization sources has been successfully demonstrated for the exhaustive characterization by petroleomic approach of a complex mixture. - Highlights: • Non-targeted mass spectrometry by combining electrospray ionization, atmospheric pressure photoionization and laser/desorption ionization. • Exhaustive description of pyrolytic bio-oil components. • Distinction of sugaric derivatives, lignin derivatives and lipids contained in a woody-based pyrolytic bio-oil.
Nakabayashi, Ryo; Sawada, Yuji; Yamada, Yutaka; Suzuki, Makoto; Hirai, Masami Yokota; Sakurai, Tetsuya; Saito, Kazuki
2013-02-05
Phytochemicals containing heteroatoms (N, O, S, and halogens) often have biological activities that are beneficial to humans. Although targeted profiling methods for such phytochemicals are expected to contribute to rapid chemical assignments, thus making phytochemical genomics and crop breeding much more efficient, there are few profiling methods for the metabolites. Here, as an ultrahigh performance approach, we propose a practical profiling method for S-containing metabolites (S-omics) using onions (Allium cepa) as a representative species and (12)C- and (13)C-based mass spectrometry (MS) and tandem mass spectrometry (MS/MS) analyses by liquid chromatography-Fourier transform ion cyclotron resonance-mass spectrometry (LC-FTICR-MS). Use of the ultrahigh quality data from FTICR-MS enabled simplifying the previous methods to determine specific elemental compositions. MS analysis with a resolution of >250,000 full width at half-maximum and a mass accuracy of ions from other ions on the basis of the natural abundance of (32)S and (34)S and the mass differences among the S isotopes. Comprehensive peak picking using the theoretical mass difference (1.99579 Da) between (32)S-containing monoisotopic ions and their (34)S-substituted counterparts led to the assignment of 67 S-containing monoisotopic ions from the (12)C-based MS spectra, which contained 4693 chromatographic ions. The unambiguous elemental composition of 22 ions was identified through comparative analysis of the (12)C- and (13)C-based MS spectra. Finally, of these, six ions were found to be derived from S-alk(en)ylcysteine sulfoxides and glutathione derivatives. This S-atom-driven approach afforded an efficient chemical assignment of S-containing metabolites, suggesting its potential application for screening not only S but also other heteroatom-containing metabolites in MS-based metabolomics.
Directory of Open Access Journals (Sweden)
Hannelore Waska
2016-07-01
Full Text Available In recent years, electrospray-ionization mass spectrometry (ESI-MS has been increasingly used to complement the bulk determination of metal-ligand equilibria, for example via competitive ligand exchange-adsorptive cathodic stripping voltammetry (CLE-ACSV. However, ESI-MS speciation analyses may be impacted by instrumental artefacts such as reduction reactions, fragmentation, and adduct formation at the ESI source, changes in the ionization efficiencies of the detected species in relation to sample matrix, and peak overlaps in response to increasing sample complexity. In our study, equilibria of the known artificial ligands citrate, ethylenediaminetetraacetic acid (EDTA, 1-nitroso-2-naphthol (NN, and salicylaldoxime (SA with iron (Fe and copper (Cu were investigated by ultra-high resolution ESI-MS, Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR-MS, under a variety of sample matrix and ionization settings. The acquired mass spectra were compared with metal-ligand equilibrium data from the literature as well as an adapted speciation model. Overall, the mass spectra produced representative species mentioned in previous reports and predicted by the speciation calculations, such as Fe(Cit, Cu(Cit2, Fe(EDTA, Cu(EDTA, Fe(NN3, and Cu(SA2. The analyses furthermore revealed new species which had been hypothesized but not measured directly using other methods, for example ternary complexes of citrate with Fe and Cu, Cu(SA monomers, and the dimer Fe(SA2. Finally, parallel measurements of a Cu+SA calibration series and a Cu+SA+EDTA competition series indicated that FT-ICR-MS can produce linear responses and low detection limits analogous to those of ACSV. We propose that ultra-high resolution FT-ICR-MS can be used as a representative tool to study interactions of trace metals with artificial as well as natural, unknown ligands at the molecular level.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yaping [Department of Biophysics and Structural Biology, Institute of Basic Medical Sciences, Chinese Academy of Medical Sciences and School of Basic Medicine, Peking Union Medical College, 5 Dongdan San Tiao, Beijing 100005 (China); Wang, Yanmin [Department of Clinical Laboratory, Heze Municipal Hospital, Shandong (China); Guo, Shuai; Guo, Yumei; Liu, Hui [Department of Biophysics and Structural Biology, Institute of Basic Medical Sciences, Chinese Academy of Medical Sciences and School of Basic Medicine, Peking Union Medical College, 5 Dongdan San Tiao, Beijing 100005 (China); Li, Zhili, E-mail: lizhili@ibms.pumc.edu.cn [Department of Biophysics and Structural Biology, Institute of Basic Medical Sciences, Chinese Academy of Medical Sciences and School of Basic Medicine, Peking Union Medical College, 5 Dongdan San Tiao, Beijing 100005 (China)
2013-09-10
Graphical abstract: -- Highlights: •A novel MALDI matrix for the detection of serum free fatty acids is ammonia-treated N-(1-naphthyl) ethylenediamine dihydrochloride. •Multiple point internal standard calibration curves were constructed for nine FFAs, respectively, with excellent correlation coefficients between 0.991 and 0.999. •The MALDI-MS approach was used to rapidly differentiate the patients with and without hyperglycemia and healthy controls. -- Abstract: The blood free fatty acids (FFAs), which provide energy to the cell and act as substrates in the synthesis of fats, lipoproteins, liposaccharides, and eicosanoids, involve in a number of important physiological processes. In the present study, matrix-assisted laser desorption/ionization-Fourier transform ion cyclotron resonance mass spectrometry (MALDI-FTICR MS) with ammonia-treated N-(1-naphthyl) ethylenediamine dihydrochloride (ATNEDC) as a novel MALDI matrix in a negative ion mode was employed to directly quantify serum FFAs. Multiple point internal standard calibration curves between the concentration ratios of individual fatty acids to internal standard (IS, C{sub 17:0}) versus their corresponding intensity ratios were constructed for C{sub 14:0}, C{sub 16:1}, C{sub 16:0}, C{sub 18:0}, C{sub 18:1}, C{sub 18:2}, C{sub 18:3}, C{sub 20:4}, and C{sub 22:6}, respectively, in their mixture, with correlation coefficients between 0.991 and 0.999 and limits of detection (LODs) between 0.2 and 5.4 μM, along with the linear dynamic range of more than two orders of magnitude. The results indicate that the multiple point internal standard calibration could reduce the impact of ion suppression and improve quantification accuracy in the MALDI mode. The quantitative results of nine FFAs from 339 serum samples, including 161 healthy controls, 118 patients with hyperglycemia and 60 patients without hyperglycemia show that FFAs levels in hyperglycemic patient sera are significantly higher than those in healthy
Noah, M.; Vieth-Hillebrand, A.; Wilkes, H.
2012-04-01
subsequent separation into asphaltenes, aliphatic hydrocarbons, aromatic hydrocarbons, neutral nitrogen, sulphur, oxygen (NSO) compounds and carboxylic acids. The asphaltene fractions are analysed using pyrolysis-GC, all other fractions are analysed by GC-MS. Additionally Fourier transform-ion cyclotron resonance-mass spectrometry (FT-ICR-MS) is used to study the chemical composition of the samples on the molecular level using different ionisation methods.
International Nuclear Information System (INIS)
Zhang, Yaping; Wang, Yanmin; Guo, Shuai; Guo, Yumei; Liu, Hui; Li, Zhili
2013-01-01
Graphical abstract: -- Highlights: •A novel MALDI matrix for the detection of serum free fatty acids is ammonia-treated N-(1-naphthyl) ethylenediamine dihydrochloride. •Multiple point internal standard calibration curves were constructed for nine FFAs, respectively, with excellent correlation coefficients between 0.991 and 0.999. •The MALDI-MS approach was used to rapidly differentiate the patients with and without hyperglycemia and healthy controls. -- Abstract: The blood free fatty acids (FFAs), which provide energy to the cell and act as substrates in the synthesis of fats, lipoproteins, liposaccharides, and eicosanoids, involve in a number of important physiological processes. In the present study, matrix-assisted laser desorption/ionization-Fourier transform ion cyclotron resonance mass spectrometry (MALDI-FTICR MS) with ammonia-treated N-(1-naphthyl) ethylenediamine dihydrochloride (ATNEDC) as a novel MALDI matrix in a negative ion mode was employed to directly quantify serum FFAs. Multiple point internal standard calibration curves between the concentration ratios of individual fatty acids to internal standard (IS, C 17:0 ) versus their corresponding intensity ratios were constructed for C 14:0 , C 16:1 , C 16:0 , C 18:0 , C 18:1 , C 18:2 , C 18:3 , C 20:4 , and C 22:6 , respectively, in their mixture, with correlation coefficients between 0.991 and 0.999 and limits of detection (LODs) between 0.2 and 5.4 μM, along with the linear dynamic range of more than two orders of magnitude. The results indicate that the multiple point internal standard calibration could reduce the impact of ion suppression and improve quantification accuracy in the MALDI mode. The quantitative results of nine FFAs from 339 serum samples, including 161 healthy controls, 118 patients with hyperglycemia and 60 patients without hyperglycemia show that FFAs levels in hyperglycemic patient sera are significantly higher than those in healthy controls and patients without
Reiding, Karli R.; Ruhaak, L. Renee; Uh, Hae-Won; el Bouhaddani, Said; van den Akker, Erik B.; Plomp, Rosina; McDonnell, Liam A.; Houwing-Duistermaat, Jeanine J.; Slagboom, P. Eline; Beekman, Marian; Wuhrer, Manfred
2017-01-01
Glycosylation is an abundant co- and post-translational protein modification of importance to protein processing and activity. Although not template-defined, glycosylation does reflect the biological state of an organism and is a high-potential biomarker for disease and patient stratification. However, to interpret a complex but informative sample like the total plasma N-glycome, it is important to establish its baseline association with plasma protein levels and systemic processes. Thus far, large-scale studies (n >200) of the total plasma N-glycome have been performed with methods of chromatographic and electrophoretic separation, which, although being informative, are limited in resolving the structural complexity of plasma N-glycans. MS has the opportunity to contribute additional information on, among others, antennarity, sialylation, and the identity of high-mannose type species. Here, we have used matrix-assisted laser desorption/ionization (MALDI)-Fourier transform ion cyclotron resonance (FTICR)-MS to study the total plasma N-glycome of 2144 healthy middle-aged individuals from the Leiden Longevity Study, to allow association analysis with markers of metabolic health and inflammation. To achieve this, N-glycans were enzymatically released from their protein backbones, labeled at the reducing end with 2-aminobenzoic acid, and following purification analyzed by negative ion mode intermediate pressure MALDI-FTICR-MS. In doing so, we achieved the relative quantification of 61 glycan compositions, ranging from Hex4HexNAc2 to Hex7HexNAc6dHex1Neu5Ac4, as well as that of 39 glycosylation traits derived thereof. Next to confirming known associations of glycosylation with age and sex by MALDI-FTICR-MS, we report novel associations with C-reactive protein (CRP), interleukin 6 (IL-6), body mass index (BMI), leptin, adiponectin, HDL cholesterol, triglycerides (TG), insulin, gamma-glutamyl transferase (GGT), alanine aminotransferase (ALT), and smoking. Overall, the
Reiding, Karli R; Ruhaak, L Renee; Uh, Hae-Won; El Bouhaddani, Said; van den Akker, Erik B; Plomp, Rosina; McDonnell, Liam A; Houwing-Duistermaat, Jeanine J; Slagboom, P Eline; Beekman, Marian; Wuhrer, Manfred
2017-02-01
Glycosylation is an abundant co- and post-translational protein modification of importance to protein processing and activity. Although not template-defined, glycosylation does reflect the biological state of an organism and is a high-potential biomarker for disease and patient stratification. However, to interpret a complex but informative sample like the total plasma N-glycome, it is important to establish its baseline association with plasma protein levels and systemic processes. Thus far, large-scale studies (n >200) of the total plasma N-glycome have been performed with methods of chromatographic and electrophoretic separation, which, although being informative, are limited in resolving the structural complexity of plasma N-glycans. MS has the opportunity to contribute additional information on, among others, antennarity, sialylation, and the identity of high-mannose type species.Here, we have used matrix-assisted laser desorption/ionization (MALDI)-Fourier transform ion cyclotron resonance (FTICR)-MS to study the total plasma N-glycome of 2144 healthy middle-aged individuals from the Leiden Longevity Study, to allow association analysis with markers of metabolic health and inflammation. To achieve this, N-glycans were enzymatically released from their protein backbones, labeled at the reducing end with 2-aminobenzoic acid, and following purification analyzed by negative ion mode intermediate pressure MALDI-FTICR-MS. In doing so, we achieved the relative quantification of 61 glycan compositions, ranging from Hex 4 HexNAc 2 to Hex 7 HexNAc 6 dHex 1 Neu5Ac 4 , as well as that of 39 glycosylation traits derived thereof. Next to confirming known associations of glycosylation with age and sex by MALDI-FTICR-MS, we report novel associations with C-reactive protein (CRP), interleukin 6 (IL-6), body mass index (BMI), leptin, adiponectin, HDL cholesterol, triglycerides (TG), insulin, gamma-glutamyl transferase (GGT), alanine aminotransferase (ALT), and smoking. Overall
Kunenkov, Erast V; Kononikhin, Alexey S; Perminova, Irina V; Hertkorn, Norbert; Gaspar, Andras; Schmitt-Kopplin, Philippe; Popov, Igor A; Garmash, Andrew V; Nikolaev, Evgeniy N
2009-12-15
The ultrahigh-resolution Fourier transform ion cyclotron resonance (FTICR) mass spectrum of natural organic matter (NOM) contains several thousand peaks with dozens of molecules matching the same nominal mass. Such a complexity poses a significant challenge for automatic data interpretation, in which the most difficult task is molecular formula assignment, especially in the case of heavy and/or multielement ions. In this study, a new universal algorithm for automatic treatment of FTICR mass spectra of NOM and humic substances based on total mass difference statistics (TMDS) has been developed and implemented. The algorithm enables a blind search for unknown building blocks (instead of a priori known ones) by revealing repetitive patterns present in spectra. In this respect, it differs from all previously developed approaches. This algorithm was implemented in designing FIRAN-software for fully automated analysis of mass data with high peak density. The specific feature of FIRAN is its ability to assign formulas to heavy and/or multielement molecules using "virtual elements" approach. To verify the approach, it was used for processing mass spectra of sodium polystyrene sulfonate (PSS, M(w) = 2200 Da) and polymethacrylate (PMA, M(w) = 3290 Da) which produce heavy multielement and multiply-charged ions. Application of TMDS identified unambiguously monomers present in the polymers consistent with their structure: C(8)H(7)SO(3)Na for PSS and C(4)H(6)O(2) for PMA. It also allowed unambiguous formula assignment to all multiply-charged peaks including the heaviest peak in PMA spectrum at mass 4025.6625 with charge state 6- (mass bias -0.33 ppm). Application of the TMDS-algorithm to processing data on the Suwannee River FA has proven its unique capacities in analysis of spectra with high peak density: it has not only identified the known small building blocks in the structure of FA such as CH(2), H(2), C(2)H(2)O, O but the heavier unit at 154.027 amu. The latter was
Nonlinear cyclotron-resonance accelerations by a generalized EM wave
International Nuclear Information System (INIS)
Akimoto, K.; Hojo, H.
2004-01-01
Particle accelerations by a one-dimensional, electromagnetic, dispersive pulse in an external magnetic field are investigated. It is found that the well-known cyclotron resonance may be classified into three regimes as the length and/or the amplitude of the pulse are varied. Namely, as the pulse amplitude increases, the transit-time cyclotron-resonance acceleration (CRA) evolves to phase trapping, and reflect particles. The amplitude and wave dispersion as well as the pulse length strongly affect those accelerations. The interesting phenomena of quantization of resonance velocities in between the two regimes are also investigated. This new mechanism may lead to wave amplification at some discrete frequencies other than the cyclotron frequency. (authors)
Directory of Open Access Journals (Sweden)
E. E. Woodfield
2013-10-01
Full Text Available Jupiter has the most intense radiation belts of all the outer planets. It is not yet known how electrons can be accelerated to energies of 10 MeV or more. It has been suggested that cyclotron-resonant wave-particle interactions by chorus waves could accelerate electrons to a few MeV near the orbit of Io. Here we use the chorus wave intensities observed by the Galileo spacecraft to calculate the changes in electron flux as a result of pitch angle and energy diffusion. We show that, when the bandwidth of the waves and its variation with L are taken into account, pitch angle and energy diffusion due to chorus waves is a factor of 8 larger at L-shells greater than 10 than previously shown. We have used the latitudinal wave intensity profile from Galileo data to model the time evolution of the electron flux using the British Antarctic Survey Radiation Belt (BAS model. This profile confines intense chorus waves near the magnetic equator with a peak intensity at ∼5° latitude. Electron fluxes in the BAS model increase by an order of magnitude for energies around 3 MeV. Extending our results to L = 14 shows that cyclotron-resonant interactions with chorus waves are equally important for electron acceleration beyond L = 10. These results suggest that there is significant electron acceleration by cyclotron-resonant interactions at Jupiter contributing to the creation of Jupiter's radiation belts and also increasing the range of L-shells over which this mechanism should be considered.
Phase and gain measurements in a distributed-loss cyclotron-resonance maser amplifier
International Nuclear Information System (INIS)
Kesar, Amit; Jerby, Eli
2002-01-01
The control of gain and phase delay in a cyclotron-resonance maser (CRM) amplifier is essential for a variety of applications. In this experiment, the gain and phase-delay variations are measured with respect to controlling parameters; the electron-beam current and the axial magnetic field. Following Chu et al. [Phys. Rev. Lett. 74, 1103 (1995)], the CRM amplifier comprises of a distributed-loss waveguide to enable high gain without oscillations. Our experiment yields an amplification up to 26 dB, and a phase-delay control range of 360 deg. In order to keep a fixed gain with the varying phase delay, the two controlling parameters (i.e., the solenoid field and the beam current) are operated together in a compensating mode. The experiment is conducted in a frequency of 7.3 GHz, with an electron beam of 18-kV voltage and 0.25-0.4-A current. The experimental results are compared with a theoretical model. Practical implementations of gain and phase control in CRM devices are discussed
Spatial Steering of Cyclotron-Resonance Maser Array Antenna by Magnetic Fields
International Nuclear Information System (INIS)
Kesar, A.; Jerby, E.
2001-01-01
The novel concept of radiation lobe generation and steering by cyclotron-resonance maser (CRM) array is presented. In this scheme the gain and phase of each CRM-element in the array are tuned by magnetic fields which control the cyclotron synchronism condition and the pitch-ratio of each CRM-element. These operating parameters are controlled by the magnetic fields of the solenoid and the kicker, respectively. A numerical example of a CRM-array operating in a gyro-TWT mode is presented. The radiation pattern of a 10-element CRM phased array (15 kV, 1A each) is calculated. The radiation lobe steering by the magnetic field controls is demonstrated in this analysis. A 40 lobe steering range is shown for the 10-element CRM-array at 7.3 GHz. An experimental device is built in our laboratory to demonstrate the active CRM-array antenna concept. Preliminary experimental results of gain and phase-delay of a single CRM-element, as function of electron-beam parameters are presented. These results are compared to the numerical model
Fourier Transform Mass Spectrometry
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-01-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Hoch, Jeffrey C.
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.
Hoch, Jeffrey C
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.
Czech Academy of Sciences Publication Activity Database
Pól, Jaroslav; Vidová, Veronika; Kruppa, G.; Kobliha, Václav; Novák, Petr; Lemr, Karel; Kotiaho, T.; Kostiainen, R.; Havlíček, Vladimír; Volný, Michael
2009-01-01
Roč. 81, č. 20 (2009), s. 8479-8487 ISSN 0003-2700 R&D Projects: GA MŠk LC07017 Institutional research plan: CEZ:AV0Z50200510 Keywords : ATMOSPHERIC-PRESSURE PHOTOIONIZATION * COMPREHENSIVE CLASSIFICATION-SYSTEM * mass spectrometry Subject RIV: EE - Microbiology, Virology Impact factor: 5.214, year: 2009
Indian Academy of Sciences (India)
polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.
Indian Academy of Sciences (India)
The theory of Fourier series deals with periodic functions. By a periodic ..... including Dirichlet, Riemann and Cantor occupied themselves with the problem of ... to converge only on a set which is negligible in a certain sense (Le. of measure ...
App. 1. Fourier series and Fourier transform
International Nuclear Information System (INIS)
Anon.
1977-01-01
Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr
NIEMELÄ, EERO
2008-01-01
Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...
International Nuclear Information System (INIS)
Hallenga, K.
1991-01-01
This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
Gates, Paul J; Lopes, Norberto P; Pinto, Emani; Colepicolo, Pio; Cardozo, Karina H M
2011-01-01
This study reports the application of "double isolation" in sustained off-resonance irradiation collisionally-induced dissociation tandem mass spectrometry (SORI-CID-MS/MS) to remove radio- frequency (RF) fragment ions of very close mass isobaric ions (0.02 m/z apart). Analyses were performed with a fraction of a biological extract isolated from a macroalgae containing the mycosporine-like amino acid asterina-330. Direct isolation of the precursor ion by narrowing the isolation window proved ineffective as it impinged upon the required ion thus substantially reducing its intensity. By increasing the correlated sweep time, ejection efficiency of the isolation was improved, but caused the unwanted side-effect of RF fragmentation of labile ions. Finally, by skipping the ion activation step and performing a second isolation (in the MS(3) module) the RF fragments from the first isolation were removed leaving a very pure isolation of the required precursor ion and allowed a very clean CID fragmentation. We demonstrated that the m/z 272.1351 ion is derived from the loss of NH(3) from m/z 289.1620 isobaric impurity and is not related to asterina-330. This application represents a powerful tool to remove unwanted ions in the MS/MS spectrum that result from fragmentation of isobaric ions.
Sleighter, R. L.; Hatcher, S. A.; Hatcher, P. G.
2006-12-01
The ultrahigh resolving power of FTICR-MS allows for the intense characterization of dissolved organic matter (DOM). DOM is the largest reactive component of the global carbon cycle, and an improved understanding of its composition is necessary to determine the transport and eventual fate of pollutants. The seasonal and spatial variations in DOM composition are investigated by taking surface water samples from five different sampling sites, four times a year. Water sampling begins at the Dismal Swamp in North Carolina, continues north up the Elizabeth River to the Chesapeake Bay, and concludes approximately ten miles off the coast in the Atlantic Ocean. DOM was extracted from the water samples using C18 extraction disks and were prepared in 50:50 methanol:water. Ammonium hydroxide was added prior to nanospray in order to solubilize the DOM as well as to increase the ionization efficiency. The samples were continuously infused into the Apollo II ion source with an Advion TriVersa NanoMate system of a Bruker 12 Tesla Apex QE FTICR-MS with resolving powers exceeding 400,000. All samples were analyzed in negative ion mode and were externally and internally calibrated prior to data analysis. Our DOM mass spectra consist of a multitude of peaks spanning the range of 200-850 m/z. Complexity is apparent from the detection of up to 20 peaks per nominal mass at nearly every mass throughout that range. A molecular formula calculator generated molecular formula matches from which van Krevelen plots were constructed for characterization purposes. A wide range of molecules were observed each containing oxygen, sulfur and nitrogen functional groups. We utilize the van Krevelen diagram to assist in clustering the molecules according to their functional group compositions. To test the hypothesis that formation of adducts to DOM serve to protect peptides from bacterial degradation, microcosm experiments were performed with a small isotopically enriched peptide, GGGR. This peptide was predicted to covalently bond to DOM via a Michael addition reaction or Schiff base formation. Following the incubation of GGGR with DOM, adduct formation was examined by FTICR-MS. Covalent binding of GGGR to DOM is a process that may reduce the bioavailability and degradation of proteins in the environment and could potentially lead to their preservation on longer time scales. FTICR-MS is clearly a powerful technique used to examine the complex composition of DOM and allow for advancements in the areas of aquatic and analytical chemistry.
DEFF Research Database (Denmark)
Kjeldsen, Frank; Haselmann, Kim F; Sørensen, Esben Skipper
2003-01-01
In hot electron capture dissociation (HECD), multiply protonated polypeptides fragment upon capturing approximately 11-eV electrons. The excess of energy upon the primary c, z* cleavage induces secondary fragmentation in z* fragments. The resultant w ions allow one to distinguish between the isom...
The cyclic heptapeptide microcystin toxins produced by a strain of Microcystis aeruginosa that has not been investigated previously were separated by liquid chromatography and identified by high-accuracy m/z measurements of their [M + H]+ ions and the fragment i...
Energy Technology Data Exchange (ETDEWEB)
Rodgers, R.P.; Blumer, E.N.; Emmett, M.R.; Marshall, A.G.
2000-02-01
The authors present a method and example to establish complete incorporation of hydrocarbons into membrane phospholipids of putatively bioremediative bacteria. Bacteria are grown on minimal media containing a specified carbon source, either natural abundance or enriched. After extraction (but no other prior separation) of the membrane lipids, electrospray ionization yields a negative-ion FT-ICR mass spectrum containing prominent phospholipid parent ions. If {sup 13}C-enriched hydrocarbon incorporation is complete, then the mass of the parent ion will increase by n Da, in which n is the number of its constituent carbon atoms; moreover, the {sup 13}C isotopic distribution pattern will be reversed. The identities of the constituent fatty acids and polar headgroup are obtained by collisional dissociation (MS/MS), and their extent of {sup 13}C incorporation determined individually. The method is demonstrated for Rhodococcus rhodochrous (ATCC No. 53968), for which all 44 carbons of a representative phosphatidylinositol are shown to derive from the hydrocarbon source. Interestingly, although only C{sub 16} and C{sub 18} alkanes are provided in the growth medium, the bacteria synthesize uniformly enriched C16:0 and C19:0 fatty acids.
International Nuclear Information System (INIS)
Tang, Yinjie; Pingitore, Francesco; Mukhopadhyay, Aindrila; Phan, Richard; Hazen, Terry C.; Keasling, Jay D.
2006-01-01
It has been proposed that during growth under anaerobic or oxygen-limited conditions Shewanella oneidensis MR-1 uses the serine-isocitrate lyase pathway common to many methylotrophic anaerobes, in which formaldehyde produced from pyruvate is condensed with glycine to form serine. The serine is then transformed through hydroxypyruvate and glycerate to enter central metabolism at phosphoglycerate. To examine its use of the serine-isocitrate lyase pathway under anaerobic conditions, we grew S. oneidensis MR-1 on [1-13C] lactate as the sole carbon source with either trimethylamine N-oxide (TMAO) or fumarate as an electron acceptor. Analysis of cellular metabolites indicates that a large percentage (>75 percent) of lactate was partially oxidized to either acetate or pyruvate. The 13C isotope distributions in amino acids and other key metabolites indicate that, under anaerobic conditions, a complete serine pathway is not present, and lactate is oxidized via a highly reversible serine degradation pathway. The labeling data also suggest significant activity in the anaplerotic (malic enzyme and phosphoenolpyruvatecarboxylase) and glyoxylate shunt (isocitrate lyase and malate synthase) reactions. Although the tricarboxylic acid (TCA) cycle is often observed to be incomplete in many other anaerobes (absence of 2-oxoglutaratede hydrogenase activity), isotopic labeling supports the existence of a complete TCA cycle in S. oneidensis MR-1 under TMAO reduction condition
Stanford, Lateefah A; Kim, Sunghwan; Klein, Geoffrey C; Smith, Donald F; Rodgers, Ryan P; Marshall, Alan G
2007-04-15
We identify water-soluble (23 degrees C) crude oil NSO nonvolatile acidic, basic, and neutral crude oil hydrocarbons by negative-ion ESI and continuous flow FD FT-ICR MS at an average mass resolving power, m/deltam50% = 550,000. Of the 7000+ singly charged acidic species identified in South American crude oil, surprisingly, many are water-soluble, and much more so in pure water than in seawater. The truncated m/z distributions for water-soluble components exhibit preferential molecular weight, size, and heteroatom class influences on hydrocarbon solubility. Acidic water-soluble heteroatomic classes detected at >1% relative abundance include O, O2, O3, O4, OS, O2S, O3S, O4S, NO2, NO3, and NO4. Parent oil class abundance does not directly relate to abundance in the water-soluble fraction. Acidic oxygen-containing classes are most prevalent in the water-solubles, whereas acidic nitrogen-containing species are least soluble. In contrast to acidic nitrogen-containing heteroatomic classes, basic nitrogen classes are water-soluble. Water-soluble heteroatomic basic classes detected at >1% relative abundance include N, NO, NO2, NS, NS2, NOS, NO2S, N2, N2O, N2O2, OS, O2S, and O2S2.
Fractional finite Fourier transform.
Khare, Kedar; George, Nicholas
2004-07-01
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Fourier analysis an introduction
Stein, Elias M
2003-01-01
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th
Debnath, Lokenath
2012-01-01
This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
Fourier transformation for engineering and natural science
International Nuclear Information System (INIS)
Klingen, B.
2001-01-01
The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
Fourier plane imaging microscopy
Energy Technology Data Exchange (ETDEWEB)
Dominguez, Daniel, E-mail: daniel.dominguez@ttu.edu; Peralta, Luis Grave de [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Alharbi, Nouf; Alhusain, Mdhaoui [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Bernussi, Ayrton A. [Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)
2014-09-14
We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonic crystals.
Fourier Transform Mass Spectrometry.
Gross, Michael L.; Rempel, Don L.
1984-01-01
Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)
Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
Axelrod, Jeremy
2015-01-01
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
Fourier transforms principles and applications
Hansen, Eric W
2014-01-01
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
Fourier transforms in spectroscopy
Kauppinen, Jyrki
2000-01-01
This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
Fast Fourier transform telescope
International Nuclear Information System (INIS)
Tegmark, Max; Zaldarriaga, Matias
2009-01-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog 2 N rather than N 2 ) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Fourier Transform Spectrometer System
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Fourier-Hermite communications; where Fourier meets Hermite
Korevaar, C.W.; Kokkeler, Andre B.J.; de Boer, Pieter-Tjerk; Smit, Gerardus Johannes Maria
A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency
On fractional Fourier transform moments
Alieva, T.; Bastiaans, M.J.
2000-01-01
Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their
Grafakos, Loukas
2014-01-01
This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews fr...
Fourier phase in Fourier-domain optical coherence tomography
Uttam, Shikhar; Liu, Yang
2015-01-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Quadrature formulas for Fourier coefficients
Bojanov, Borislav; Petrova, Guergana
2009-01-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Fourier transform nuclear magnetic resonance
International Nuclear Information System (INIS)
Geick, R.
1981-01-01
This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...
Fourier series, Fourier transform and their applications to mathematical physics
Serov, Valery
2017-01-01
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...
Fourier series and orthogonal polynomials
Jackson, Dunham
2004-01-01
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe
Agneta, Rosa; Rivelli, Anna Rita; Ventrella, Emanuela; Lelario, Filomena; Sarli, Giulio; Bufo, Sabino Aurelio
2012-08-01
Within the family of Brassicaceae, an important source of glucosinolates (GLSs) is represented by horseradish ( Armoracia rusticana P. Gaertner, B. Meyer & Scherbius), cultivated for its roots, which are grated fresh or processed into a sauce and used as a condiment. The characteristic pungent flavor of the root depends on the abundance of the bioactive GLS molecules. In crude plant extracts (sprouts and roots) of an accession of horseradish largely diffused in the Basilicata region (southern Italy), which develops many sprouts and produces white, fiery, and sharp-flavored marketable roots, we characterized the GLS profile by LC-ESI-LTQ-FTICR-MS and IRMPD. In sprouts and roots we identified 16 and 11 GLSs, respectively. We confirmed the presence of sinigrin, 4-hydroxyglucobrassicin, glucobrassicin, gluconasturtin, and 4-methoxyglucobrassicin and identified glucoiberin, gluconapin, glucocochlearin, glucoconringianin, glucosativin, glucoibarin, 5-hydroxyglucobrassicin, glucocapparilinearisin or glucobrassicanapin, glucotropaeolin, and glucoarabishirsutain, not previously characterized in horseradish. Of particular note was the presence of the putative 2-methylsulfonyl-oxo-ethyl-GLS.
Mareike Noah; Andrea Vieth-Hillebrand; Heinz Wilkes
2012-01-01
The Athabasca region of northern Alberta, Canada, is home to deposits of oil sands containing vast amounts (~ 173 billion barrels) of heavily biodegraded petroleum. Oil sands are recovered by surface mining or by in situ steam injection. The extraction of bitumen from oil sands by caustic hot water processing results in large volumes of fluid tailings, which are stored in on-site settling basins. There the tailings undergo a compaction and dewatering process, producing a slowly densifying sus...
Somogyi, Arpád
2008-12-01
The usefulness of gas-phase H/D exchange is demonstrated to probe heterogeneous fragment and parent ion populations. Singly and multiply protonated peptides/proteins were fragmented by using sustained off-resonance irradiation collision-induced dissociation (SORI-CID). The fragments and the surviving precursor ions then all undergo H/D exchange in the gas-phase with either D(2)O or CD(3)OD under the same experimental conditions. Usually, 10 to 60 s of reaction time is adequate to monitor characteristic differences in the H/D exchange kinetic rates. These differences are then correlated to isomeric ion structures. The SORI-HDX method can be used to rapidly test fragment ion structures and provides useful insights into peptide fragmentation mechanisms.
FOURIER SERIES MODELS THROUGH TRANSFORMATION
African Journals Online (AJOL)
DEPT
monthly temperature data (1996 – 2005) collected from the National Root ... KEY WORDS: Fourier series, square transformation, multiplicative model, ... fluctuations or movements are often periodic(Ekpeyong,2005). .... significant trend or not, if the trend is not significant, the grand mean may be used as an estimate of trend.
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
Uncertainty Principles and Fourier Analysis
Indian Academy of Sciences (India)
analysis on the part of the reader. Those who are not fa- miliar with Fourier analysis are encouraged to look up Box. 1 along with [3]. (A) Heisenberg's inequality: Let us measure concentration in terms of standard deviation i.e. for a square integrable func-. 00 tion defined on 1R and normalized so that J If(x)12d,x = 1,. -00. 00.
An introduction to Fourier series and integrals
Seeley, Robert T
2006-01-01
This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Properties of the distributional finite Fourier transform
Carmichael, Richard D.
2016-01-01
The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.
Fourier techniques in X-ray timing
van der Klis, M.
1988-01-01
Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum
Improved Fourier-transform profilometry
International Nuclear Information System (INIS)
Mao Xianfu; Chen Wenjing; Su Xianyu
2007-01-01
An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object
Fourier-transform optical microsystems
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
Fourier Transform Methods. Chapter 4
Kaplan, Simon G.; Quijada, Manuel A.
2015-01-01
This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..
Fourier Spectroscopy: A Bayesian Way
Directory of Open Access Journals (Sweden)
Stefan Schmuck
2017-01-01
Full Text Available The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.
Pointwise convergence of Fourier series
Arias de Reyna, Juan
2002-01-01
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
Applications of Fourier transforms to generalized functions
Rahman, M
2011-01-01
This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Fourier transform n.m.r. spectroscopy
International Nuclear Information System (INIS)
Shaw, D.
1976-01-01
This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques
A simple approach to Fourier aliasing
International Nuclear Information System (INIS)
Foadi, James
2007-01-01
In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and structured, introductions to the topic, commonly met in advanced, specialized books
Tunable fractional-order Fourier transformer
International Nuclear Information System (INIS)
Malyutin, A A
2006-01-01
A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)
Fourier transform n. m. r. spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Shaw, D [Varian Ltd., Walton (UK)
1976-01-01
This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques.
Fourier Transfrom Ion Cyclotron Resonance Mass Spectrometry at High Magnetic Field
Marshall, Alan G.
1998-03-01
At high magnetic field (9.4 tesla at NHMFL), Fourier transform ion cyclotron resonance mass spectrometry performance improves dramatically: mass resolving power, axialization efficiency, and scan speed (each proportional to B), maximum ion mass, dynamic range, ion trapping period, kinetic energy, and electron self-cooling rate for sympathetic cooling (each proportional to B^2), and ion coalescence tendency (proportional 1/B^2). These advantages may apply singly (e.g., unit mass resolution for proteins of >100,000 Da), or compound (e.g., 10-fold improvement in S/N ratio for 9.4 T vs. 6 T at the same resolving power). Examples range from direct determination of molecular formulas of diesel fuel components by accurate mass measurement (=B10.1 ppm) to protein structure and dynamics probed by H/D exchange. This work was supported by N.S.F. (CHE-93-22824; CHE-94-13008), N.I.H. (GM-31683), Florida State University, and the National High Magnetic Field Laboratory in Tallahassee, FL.
Matrix-assisted laser desorption fourier transform mass spectrometry for biological compounds
Energy Technology Data Exchange (ETDEWEB)
Hettich, R.; Buchanan, M.
1990-01-01
The recent development of matrix-assisted UV laser desorption (LD) mass spectrometry has made possible the ionization and detection of extremely large molecules (with molecular weights exceeding 100,000 Daltons). This technique has generated enormous interest in the biological community for the direct examination of large peptides and oligonucleotides. Although this matrix-assisted ionization method has been developed and used almost exclusively with time-of-flight (TOF) mass spectrometers, research is currently in progress to demonstrate this technique with trapped ion mass spectrometers, such as Fourier transform ion cyclotron resonance mass spectrometry (FTMS). The potential capabilities of FTMS for wide mass range, high resolution measurement, and ion trapping experiments suggest that this instrumental technique should be useful for the detailed structural characterization of large ions generated by the matrix-assisted technique. We have recently demonstrated that matrix-assisted ultraviolet laser desorption can be successfully used with FTMS for the ionization of small peptides. The objective of this report is to summarize the application and current limitations of matrix-assisted laser desorption FTMS for the characterization of peptides and oligonucleotides at the isomeric level. 4 refs., 3 figs., 2 tabs.
Metasurface Enabled Wide-Angle Fourier Lens.
Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo
2018-06-01
Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Dziekonski, Eric T; Johnson, Joshua T; McLuckey, Scott A
2017-04-18
Mass resolution (M/ΔM fwhm) is observed to linearly increase with harmonic order in a Fourier transform electrostatic linear ion trap (ELIT) mass spectrometer. This behavior was predicted by Grosshans and Marshall for frequency-multiple detection in a Fourier transform ion cyclotron resonance mass spectrometer only for situations when the prominent mechanism for signal decay is ion ejection from the trap. As the analyzer pressure in our ELIT chamber is relatively high, such that collisional scattering and collision-induced dissociation are expected to underlie much of the ion loss, we sought to explore the relationship between harmonic order and mass resolution. Mass resolutions of 36 900 (fundamental), 75 850 (2nd harmonic), and 108 200 (3rd harmonic) were obtained for GdO + (avg. m/z 173.919) with a transient length of 300 ms. To demonstrate that the mass resolution was truly increasing with harmonic order, the unresolved isotopes at the fundamental distribution of cytochrome c +8 (m/z ∼ 1549) were nearly baseline, resolved at the third harmonic (mass resolution ≈ 23 000) with a transient length of only 200 ms. This experiment demonstrates that, when the ion density is sufficiently low, ions with frequency differences of less than 4 Hz remain uncoalesced. Higher harmonics can be used to increase the effective mass resolution for a fixed transient length and thereby may enable the resolution of closely spaced masses, determination of a protein ion's charge state, and study of the onset of peak coalescence when the resolution at the fundamental frequency is insufficient.
Quantum arithmetic with the Quantum Fourier Transform
Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos
2014-01-01
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.
On the inverse windowed Fourier transform
Rebollo Neira, Laura; Fernández Rubio, Juan Antonio
1999-01-01
The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.; Boashash, B.
2003-01-01
We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept
The fractional Fourier transform and applications
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
Teaching Fourier optics through ray matrices
International Nuclear Information System (INIS)
Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F
2005-01-01
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Replica Fourier Transform: Properties and applications
International Nuclear Information System (INIS)
Crisanti, A.; De Dominicis, C.
2015-01-01
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically
Fourier transforms in radar and signal processing
Brandwood, David
2011-01-01
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit
Scheibler, Robin; Hurley, Paul
2012-03-01
We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.
X-ray interferometric Fourier holography
International Nuclear Information System (INIS)
Balyan, M.K.
2016-01-01
The X-ray interferometric Fourier holography is proposed and theoretically investigated. Fourier The X-ray interferometric Young fringes and object image reconstruction are investigated. It is shown that the interference pattern of two slits formed on the exit surface of the crystal-analyzer (the third plate of the interferometer) is the X-ray interferometric Young fringes. An expression for X-ray interferometric Young fringes period is obtained. The subsequent reconstruction of the slit image as an object is performed by means of Fourier transform of the intensity distribution on the hologram. Three methods of reconstruction of the amplitude transmission complex function of the object are presented: analytical - approximate method, method of iteration and step by step method. As an example the X-ray Fourier interferometric hologram recording and the complex amplitude transmission function reconstruction for a beryllium circular wire are considered
New focus on Fourier optics techniques
Calvo, M.L.; Alieva, T.; Bastiaans, M.J.; Rodrigo Martín-Romo, J.A.; Rodríguez Merlo, D.; Vlad, V.I.
2004-01-01
We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.
The finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
On the Scaled Fractional Fourier Transformation Operator
International Nuclear Information System (INIS)
Hong-Yi, Fan; Li-Yun, Hu
2008-01-01
Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched
Mountain Wave Analysis Using Fourier Methods
National Research Council Canada - National Science Library
Roadcap, John R
2007-01-01
...) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms...
A new twist to fourier transforms
Meikle, Hamish D
2004-01-01
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs
Mapped Fourier Methods for stiff problems in toroidal geometry
Guillard , Herve
2014-01-01
Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the compositio...
Fourier phasing with phase-uncertain mask
International Nuclear Information System (INIS)
Fannjiang, Albert; Liao, Wenjing
2013-01-01
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)
Direct fourier method reconstruction based on unequally spaced fast fourier transform
International Nuclear Information System (INIS)
Wu Xiaofeng; Zhao Ming; Liu Li
2003-01-01
First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)
Fourier optical cryptosystem using complex spatial modulation
International Nuclear Information System (INIS)
Sarkadi, T; Koppa, P
2014-01-01
Our goal is to enhance the security level of a Fourier optical encryption system. Therefore we propose a Mach–Zehnder interferometer based encryption setup. The input data is organized in a binary array, and it is encoded in the two wave fronts propagated in the arms of the interferometer. Both input wave fronts are independently encrypted by Fourier systems, hence the proposed method has two encryption keys. During decryption, the encrypted wave fronts are propagated through the interferometer setup. The interference pattern of the output shows the reconstructed data in cases where the correct decryption Fourier keys are used. We propose a novel input image modulation method with a user defined phase parameter. We show that the security level of the proposed cryptosystem can be enhanced by an optimally chosen phase parameter. (paper)
Harmonic analysis from Fourier to wavelets
Pereyra, Maria Cristina
2012-01-01
In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...
Projective Fourier duality and Weyl quantization
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs
Fourier duality as a quantization principle
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Group-invariant finite Fourier transforms
International Nuclear Information System (INIS)
Shenefelt, M.H.
1988-01-01
The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible
Implementation of quantum and classical discrete fractional Fourier transforms
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-01-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
An optical Fourier transform coprocessor with direct phase determination.
Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D
2017-10-20
The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.
Fourier analysis in several complex variables
Ehrenpreis, Leon
2006-01-01
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations.The three-part treatment begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis. Topics include the geometric structure of ideals and modules, quantitative estimates, and examples in which the theory can be applied. The second part focuses on applications to partial differential equations and covers the solution of homogeneous and inh
Fourier transforms and convolutions for the experimentalist
Jennison, RC
1961-01-01
Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Ross, Charles W; Simonsick, William J; Bogusky, Michael J; Celikay, Recep W; Guare, James P; Newton, Randall C
2016-06-28
Ceramides are a central unit of all sphingolipids which have been identified as sites of biological recognition on cellular membranes mediating cell growth and differentiation. Several glycosphingolipids have been isolated, displaying immunomodulatory and anti-tumor activities. These molecules have generated considerable interest as potential vaccine adjuvants in humans. Accurate analyses of these and related sphingosine analogues are important for the characterization of structure, biological function, and metabolism. We report the complementary use of direct laser desorption ionization (DLDI), sheath flow electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) and high-field nuclear magnetic resonance (NMR) analysis for the rapid, accurate identification of hexacosanoylceramide and starting materials. DLDI does not require stringent sample preparation and yields representative ions. Sheath-flow ESI yields ions of the product and byproducts and was significantly better than monospray ESI due to improved compound solubility. Negative ion sheath flow ESI provided data of starting materials and products all in one acquisition as hexacosanoic acid does not ionize efficiently when ceramides are present. NMR provided characterization of these lipid molecules complementing the results obtained from MS analyses. NMR data was able to differentiate straight chain versus branched chain alkyl groups not easily obtained from mass spectrometry.
Directory of Open Access Journals (Sweden)
Charles W. Ross
2016-06-01
Full Text Available Ceramides are a central unit of all sphingolipids which have been identified as sites of biological recognition on cellular membranes mediating cell growth and differentiation. Several glycosphingolipids have been isolated, displaying immunomodulatory and anti-tumor activities. These molecules have generated considerable interest as potential vaccine adjuvants in humans. Accurate analyses of these and related sphingosine analogues are important for the characterization of structure, biological function, and metabolism. We report the complementary use of direct laser desorption ionization (DLDI, sheath flow electrospray ionization (ESI Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS and high-field nuclear magnetic resonance (NMR analysis for the rapid, accurate identification of hexacosanoylceramide and starting materials. DLDI does not require stringent sample preparation and yields representative ions. Sheath-flow ESI yields ions of the product and byproducts and was significantly better than monospray ESI due to improved compound solubility. Negative ion sheath flow ESI provided data of starting materials and products all in one acquisition as hexacosanoic acid does not ionize efficiently when ceramides are present. NMR provided characterization of these lipid molecules complementing the results obtained from MS analyses. NMR data was able to differentiate straight chain versus branched chain alkyl groups not easily obtained from mass spectrometry.
The periodogram at the Fourier frequencies
Kokoszka, P; Mikosch, T
In the time series literature one can often find the claim that the periodogram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,
Pi, Fourier Transform and Ludolph van Ceulen
Vajta, Miklos
2000-01-01
The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of p (first by hand and then from the mid-20th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as
Fourier transform infrared spectrometery: an undergraduate experiment
International Nuclear Information System (INIS)
Lerner, L
2016-01-01
Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory. (paper)
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.
2001-01-01
The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution
The Fourier transform of tubular densities
Prior, C B; Goriely, A
2012-01-01
molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Fourier analysis in combinatorial number theory
International Nuclear Information System (INIS)
Shkredov, Il'ya D
2010-01-01
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Fourier analysis in combinatorial number theory
Energy Technology Data Exchange (ETDEWEB)
Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-09-16
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
A Fourier analysis of extremal events
DEFF Research Database (Denmark)
Zhao, Yuwei
is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
The Fourier modal method for aperiodic structures
Pisarenco, M.; Maubach, J.M.L.; Setija, I.D.; Mattheij, R.M.M.
2010-01-01
This paper extends the area of application of the Fourier modal method from periodic structures to non-periodic ones illuminated under arbitrary angles. This is achieved by placing perfectly matched layers at the lateral boundaries and reformulating the problem in terms of a contrast field.
Discrete Fourier analysis of multigrid algorithms
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2011-01-01
The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Fourier inversion on a reductive symmetric space
Ban, E.P. van den
1999-01-01
Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we
Fractional-Fourier-domain weighted Wigner distribution
Stankovic, L.; Alieva, T.; Bastiaans, M.J.
2001-01-01
A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the
Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Schlichtkrull, H.
1994-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Carmona, J.; Delorme, P.
1997-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
Automatic Fourier transform and self-Fourier beams due to parabolic potential
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2015-12-15
We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2007-01-01
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found
Fourier analysis: from cloaking to imaging
Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping
2016-04-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.
Fourier analysis: from cloaking to imaging
International Nuclear Information System (INIS)
Wu, Kedi; Ping Wang, Guo; Cheng, Qiluan
2016-01-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers. (review)
Multichannel Dynamic Fourier-Transform IR Spectrometer
Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.
2017-09-01
A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.
Discrete Fourier transform in nanostructures using scattering
International Nuclear Information System (INIS)
Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.
2004-01-01
In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed
The PROSAIC Laplace and Fourier Transform
International Nuclear Information System (INIS)
Smith, G.A.
1994-01-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting
Fourier transform of momentum distribution in vanadium
International Nuclear Information System (INIS)
Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.
1985-01-01
Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)
Correcting sample drift using Fourier harmonics.
Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L
2018-07-01
During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-01-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-09-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples covering the case of amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Quantum Fourier Transform Over Galois Rings
Zhang, Yong
2009-01-01
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...
Fourier Transform Spectrometer Controller for Partitioned Architectures
DEFF Research Database (Denmark)
Tamas-Selicean, Domitian; Keymeulen, D.; Berisford, D.
2013-01-01
The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Resear......, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture....
A Fourier analysis of extreme events
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
Fourier transform resampling: Theory and application
International Nuclear Information System (INIS)
Hawkins, W.G.
1996-01-01
One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)
Sets of Fourier coefficients using numerical quadrature
International Nuclear Information System (INIS)
Lyness, J. N.
2001-01-01
One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r)=(line i ntegral)(sub 0)(sup 1) f(x)e(sup -2(pi)irx)dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x)= h(sub p-1)(x)+ g(sub p)(x), where h(sub -1)(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g(sub p)(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h(sub p-1)(x) and numerical quadrature to approximately those of g(sub p)(x)
The derivative-free Fourier shell identity for photoacoustics.
Baddour, Natalie
2016-01-01
In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.
Fourier spectral simulations for wake fields in conducting cavities
International Nuclear Information System (INIS)
Min, M.; Chin, Y.-H.; Fischer, P.F.; Chae, Y.-Chul; Kim, K.-J.
2007-01-01
We investigate Fourier spectral time-domain simulations applied to wake field calculations in two-dimensional cylindrical structures. The scheme involves second-order explicit leap-frogging in time and Fourier spectral approximation in space, which is obtained from simply replacing the spatial differentiation operator of the YEE scheme by the Fourier differentiation operator on nonstaggered grids. This is a first step toward investigating high-order computational techniques with the Fourier spectral method, which is relatively simple to implement.
A Note on Fourier and the Greenhouse Effect
Postma, Joseph E.
2015-01-01
Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...
Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
Zhang, Zhihua
2014-01-01
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842
Some Applications of Fourier's Great Discovery for Beginners
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…
Alternating multivariate trigonometric functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2008-01-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel
Validation of Fourier analysis of videokeratographic data.
Sideroudi, Haris; Labiris, Georgios; Ditzel, Fienke; Tsaragli, Efi; Georgatzoglou, Kimonas; Siganos, Haralampos; Kozobolis, Vassilios
2017-06-15
The aim was to assess the repeatability of Fourier transfom analysis of videokeratographic data using Pentacam in normal (CG), keratoconic (KC) and post-CXL (CXL) corneas. This was a prospective, clinic-based, observational study. One randomly selected eye from all study participants was included in the analysis: 62 normal eyes (CG group), 33 keratoconus eyes (KC group), while 34 eyes, which had already received CXL treatment, formed the CXL group. Fourier analysis of keratometric data were obtained using Pentacam, by two different operators within each of two sessions. Precision, repeatability and Intraclass Correlation Coefficient (ICC), were calculated for evaluating intrassesion and intersession repeatability for the following parameters: Spherical Component (SphRmin, SphEcc), Maximum Decentration (Max Dec), Regular Astigmatism, and Irregularitiy (Irr). Bland-Altman analysis was used for assessing interobserver repeatability. All parameters were presented to be repeatable, reliable and reproductible in all groups. Best intrasession and intersession repeatability and reliability were detected for parameters SphRmin, SphEcc and Max Dec parameters for both operators using ICC (intrasession: ICC > 98%, intersession: ICC > 94.7%) and within subject standard deviation. Best precision and lowest range of agreement was found for the SphRmin parameter (CG: 0.05, KC: 0.16, and CXL: 0.2) in all groups, while the lowest repeatability, reliability and reproducibility was detected for the Irr parameter. The Pentacam system provides accurate measurements of Fourier tranform keratometric data. A single Pentacam scan will be sufficient for most clinical applications.
Fourier optics treatment of classical relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2006-08-15
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)
Fourier transforms in the complex domain
Wiener, N
1934-01-01
With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of MÃ¼nz and SzÃ¡sz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,
Analog fourier transform channelizer and OFDM receiver
2007-01-01
An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...
Bruzzo, Ugo; Maciocia, Antony
2017-12-01
This special issue celebrates the 34 years since the discovery of the Fourier-Mukai Transform by Shigeru Mukai. It mostly contains papers presented at the conference held in the Mathematics Research Centre of the University of Warwick, 15th to 19th June 2015 as part of a year long Warwick symposium on Derived categories and applications. The conference was also the annual conference of the Vector Bundles on Algebraic Curves series led by Peter Newstead. The symposium was principally supported by the Engineering and Physical Sciences Research Council of the UK and there was further funding from the London Mathematical Society and the Foundation Compositio.
Noise figure of amplified dispersive Fourier transformation
International Nuclear Information System (INIS)
Goda, Keisuke; Jalali, Bahram
2010-01-01
Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.
Fourier transform infrared spectroscopy of peptides.
Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell
2014-01-01
Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data.
Complex nonlinear Fourier transform and its inverse
International Nuclear Information System (INIS)
Saksida, Pavle
2015-01-01
We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)
Functional Fourier transforms and the loop equation
International Nuclear Information System (INIS)
Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.
1986-01-01
The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables
Fourier transform spectroscopy of six stars
Energy Technology Data Exchange (ETDEWEB)
Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia
1981-01-01
This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.
Generalized Fourier transforms Fk,a
DEFF Research Database (Denmark)
Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent
2009-01-01
We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....
Fourier-transforming with quantum annealers
Directory of Open Access Journals (Sweden)
Itay eHen
2014-07-01
Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.
The Fourier transform of tubular densities
Prior, C B
2012-05-18
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.
Approximate modal analysis using Fourier decomposition
International Nuclear Information System (INIS)
Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana
2010-01-01
The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.
Fourier transform inequalities for phylogenetic trees.
Matsen, Frederick A
2009-01-01
Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.
The Fourier transform of tubular densities
International Nuclear Information System (INIS)
Prior, C B; Goriely, A
2012-01-01
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. (paper)
Fourier transform zero field NMR and NQR
International Nuclear Information System (INIS)
Zax, D.B.
1985-01-01
In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI
Resolution optimization with irregularly sampled Fourier data
International Nuclear Information System (INIS)
Ferrara, Matthew; Parker, Jason T; Cheney, Margaret
2013-01-01
Image acquisition systems such as synthetic aperture radar (SAR) and magnetic resonance imaging often measure irregularly spaced Fourier samples of the desired image. In this paper we show the relationship between sample locations, their associated backprojection weights, and image resolution as characterized by the resulting point spread function (PSF). Two new methods for computing data weights, based on different optimization criteria, are proposed. The first method, which solves a maximal-eigenvector problem, optimizes a PSF-derived resolution metric which is shown to be equivalent to the volume of the Cramer–Rao (positional) error ellipsoid in the uniform-weight case. The second approach utilizes as its performance metric the Frobenius error between the PSF operator and the ideal delta function, and is an extension of a previously reported algorithm. Our proposed extension appropriately regularizes the weight estimates in the presence of noisy data and eliminates the superfluous issue of image discretization in the choice of data weights. The Frobenius-error approach results in a Tikhonov-regularized inverse problem whose Tikhonov weights are dependent on the locations of the Fourier data as well as the noise variance. The two new methods are compared against several state-of-the-art weighting strategies for synthetic multistatic point-scatterer data, as well as an ‘interrupted SAR’ dataset representative of in-band interference commonly encountered in very high frequency radar applications. (paper)
Fourier transform spectra of quantum dots
Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.
2010-05-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
On localization for double Fourier series
Goffman, Casper; Waterman, Daniel
1978-01-01
The localization theorems for Fourier series of functions of a single variable are classical and easy to prove. The situation is different for Fourier series of functions of several variables, even if one restricts consideration to rectangular, in particular square, partial sums. We show that the answer to the problem can be obtained by considering the notion of generalized bounded variation, which we introduced. Given a nondecreasing sequence {λn} of positive numbers such that Σ 1/λn diverges, a function g defined on an interval I of R1 is said to be of Λ-bounded variation (ΛBV) if Σ|g(an) — g(bn)|/λn converges for every sequence of nonoverlapping intervals (an, bn) [unk]I. If λn = n, we say that g is of harmonic bounded variation (HBV). The definition suitably modified can be extended to functions of several variables. We show that in the case of two variables the localization principle holds for rectangular partial sums if ΛBV = HBV, and that if ΛBV is not contained in HBV, then the localization principle does not hold for ΛBV even in the case of square partial sums. PMID:16592492
The prosaic Laplace and Fourier transform
International Nuclear Information System (INIS)
Smith, G.A.
1995-01-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics
Digital Fourier microscopy for soft matter dynamics
International Nuclear Information System (INIS)
Giavazzi, Fabio; Cerbino, Roberto
2014-01-01
Soft matter is studied with a large portfolio of methods. Light scattering and video microscopy are the most employed at optical wavelengths. Light scattering provides ensemble-averaged information on soft matter in the reciprocal space. The wave-vectors probed correspond to length scales ranging from a few nanometers to fractions of millimetre. Microscopy probes the sample directly in the real space, by offering a unique access to the local properties. However, optical resolution issues limit the access to length scales smaller than approximately 200 nm. We describe recent work that bridges the gap between scattering and microscopy. Several apparently unrelated techniques are found to share a simple basic idea: the correlation properties of the sample can be characterized in the reciprocal space via spatial Fourier analysis of images collected in the real space. We describe the main features of such digital Fourier microscopy (DFM), by providing examples of several possible experimental implementations of it, some of which not yet realized in practice. We also provide an overview of experimental results obtained with DFM for the study of the dynamics of soft materials. Finally, we outline possible future developments of DFM that would ease its adoption as a standard laboratory method. (topical review)
Kuijpers, A.H.W.M.; Verbeek, G.; Verheij, J.W.
1997-01-01
Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be
Lin, Tzu-Yung; Green, Roger J; O'Connor, Peter B
2012-09-01
A novel single-transistor transimpedance preamplifier has been introduced for improving performance in Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometry. A low noise junction field-effect transistor (JFET), BF862, is used as the main amplification stage of this trans-impedance preamplifier, and a T-shaped feedback network is introduced as both the feedback and the gate biasing solutions. The T feedback network has been studied using an operational amplifier (Op Amp), AD8099. Such a feedback system allows ~100-fold less feedback resistance at a given transimpedance, hence preserving bandwidth, which is beneficial to applications demanding high gain. The single-transistor preamplifier yields a tested transimpedance of ~10(4) Ω (80 dBΩ) in the frequency range between 1 kHz and 1 MHz (mass-to-charge ratio, m/z, of around 180-180k for a 12-T FT-ICR system), with a low power consumption of ~6 mW, which implies that this preamplifier is well suited to a 12-T FT-ICR mass spectrometer. In trading noise performance for higher trans-impedance, an alternative preamplifier design, an AD8099 preamplifier with the T feedback network, has also been studied with a capability of ~10(6) Ω (120 dBΩ) transimpedance in the same frequency range. The resistive components in the T feedback network reported here can be replaced by complex impedances, which allows adaptation of this feedback system to other frequency, transimpedance, and noise characteristics for applications not only in other mass spectrometers, such as Orbitrap, time-of-flight (TOF), and ion trap systems, but also in other charge/current detecting systems such as spectroscopy systems, microscopy systems, optical communication systems, or charge-coupled devices (CCDs).
Fourier transform and its application to 1D and 2D NMR
International Nuclear Information System (INIS)
Canet, D.
1988-01-01
In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr
Fourier rebinning algorithm for inverse geometry CT.
Mazin, Samuel R; Pele, Norbert J
2008-11-01
Inverse geometry computed tomography (IGCT) is a new type of volumetric CT geometry that employs a large array of x-ray sources opposite a smaller detector array. Volumetric coverage and high isotropic resolution produce very large data sets and therefore require a computationally efficient three-dimensional reconstruction algorithm. The purpose of this work was to adapt and evaluate a fast algorithm based on Defrise's Fourier rebinning (FORE), originally developed for positron emission tomography. The results were compared with the average of FDK reconstructions from each source row. The FORE algorithm is an order of magnitude faster than the FDK-type method for the case of 11 source rows. In the center of the field-of-view both algorithms exhibited the same resolution and noise performance. FORE exhibited some resolution loss (and less noise) in the periphery of the field-of-view. FORE appears to be a fast and reasonably accurate reconstruction method for IGCT.
Multicomplementary operators via finite Fourier transform
International Nuclear Information System (INIS)
Klimov, Andrei B; Sanchez-Soto, Luis L; Guise, Hubert de
2005-01-01
A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail
Fractional Fourier transform for confluent hypergeometric beams
International Nuclear Information System (INIS)
Tang, Bin; Jiang, Chun; Zhu, Haibin
2012-01-01
Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.
Rotational Fourier tracking of diffusing polygons.
Mayoral, Kenny; Kennair, Terry P; Zhu, Xiaoming; Milazzo, James; Ngo, Kathy; Fryd, Michael M; Mason, Thomas G
2011-11-01
We use optical microscopy to measure the rotational Brownian motion of polygonal platelets that are dispersed in a liquid and confined by depletion attractions near a wall. The depletion attraction inhibits out-of-plane translational and rotational Brownian fluctuations, thereby facilitating in-plane imaging and video analysis. By taking fast Fourier transforms (FFTs) of the images and analyzing the angular position of rays in the FFTs, we determine an isolated particle's rotational trajectory, independent of its position. The measured in-plane rotational diffusion coefficients are significantly smaller than estimates for the bulk; this difference is likely due to the close proximity of the particles to the wall arising from the depletion attraction.
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
On a General Class of Trigonometric Functions and Fourier Series
Pavao, H. Germano; Capelas de Oliveira, E.
2008-01-01
We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)
Reducing Approximation Error in the Fourier Flexible Functional Form
Directory of Open Access Journals (Sweden)
Tristan D. Skolrud
2017-12-01
Full Text Available The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie
2015-10-20
In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.
Lacunary Fourier Series and a Qualitative Uncertainty Principle for ...
Indian Academy of Sciences (India)
We define lacunary Fourier series on a compact connected semisimple Lie group . If f ∈ L 1 ( G ) has lacunary Fourier series and vanishes on a non empty open subset of , then we prove that vanishes identically. This result can be viewed as a qualitative uncertainty principle.
Bilaterally symmetric Fourier approximations of the skull outlines of ...
Indian Academy of Sciences (India)
Present work illustrates a scheme of quantitative description of the shape of the skull outlines of temnospondyl amphibians using bilaterally symmetric closed Fourier curves. Some special points have been identified on the Fourier fits of the skull outlines, which are the local maxima, or minima of the distances from the ...
Fourier transformations for difference analogs of the harmonic oscillator
International Nuclear Information System (INIS)
Askey, R.; Atakishiyev, N.M.
1995-01-01
The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs
The Fourier Transform for Certain HyperKähler Fourfolds
Shen, M.; Vial, C.
2016-01-01
Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle
Infrared Fourier spectres of pectin obtained from pumpkin
International Nuclear Information System (INIS)
Usmanova, S.R.; Dzhonmurodov, A.S.; Nazirova, Kh.I.; Mukhidinov, Z.K.
2015-01-01
Present article is devoted to infrared Fourier spectres of pectin obtained from pumpkin. The analysis of pectin obtained from pumpkin was conducted by means of infrared spectrophotometer with Fourier transformation. The infrared spectroscopic study of pectin polysaccharide fraction of pectin matter, as well as pectin helium and micro helium obtained by means of fast extraction was conducted.
Time-of-flight Fourier spectrometry of UCN
International Nuclear Information System (INIS)
Kulin, G.V.; Frank, A.I.; Goryunov, S.V.; Kustov, D.V.; Geltenbort, P.; Jentshel, M.; Strepetov, A.N.; Bushuev, V.A.
2014-01-01
The results of preliminary experiments on TOF Fourier UCN spectrometry are presented. The description of the new Fourier spectrometer that may be used for the measurement of the UCN spectra arising from diffraction by a moving grating is given. The results of preliminary experiments and Monte Carlo calculations give reason to hope for the success of the planned experiment.
Fourier path-integral Monte Carlo methods: Partial averaging
International Nuclear Information System (INIS)
Doll, J.D.; Coalson, R.D.; Freeman, D.L.
1985-01-01
Monte Carlo Fourier path-integral techniques are explored. It is shown that fluctuation renormalization techniques provide an effective means for treating the effects of high-order Fourier contributions. The resulting formalism is rapidly convergent, is computationally convenient, and has potentially useful variational aspects
Exploring Fourier Series and Gibbs Phenomenon Using Mathematica
Ghosh, Jonaki B.
2011-01-01
This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of…
Fourier transform in multimode systems in the Bargmann representation
International Nuclear Information System (INIS)
Lei, C; Vourdas, A
2007-01-01
A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag-Leffler states are discussed
Revisiting the quantum harmonic oscillator via unilateral Fourier transforms
International Nuclear Information System (INIS)
Nogueira, Pedro H F; Castro, Antonio S de
2016-01-01
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)
Fast algorithm of adaptive Fourier series
Gao, You; Ku, Min; Qian, Tao
2018-05-01
Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was originated for the goal of positive frequency representations of signals. It achieved the goal and at the same time offered fast decompositions of signals. There then arose several types of AFDs. AFD merged with the greedy algorithm idea, and in particular, motivated the so-called pre-orthogonal greedy algorithm (Pre-OGA) that was proven to be the most efficient greedy algorithm. The cost of the advantages of the AFD type decompositions is, however, the high computational complexity due to the involvement of maximal selections of the dictionary parameters. The present paper offers one formulation of the 1-D AFD algorithm by building the FFT algorithm into it. Accordingly, the algorithm complexity is reduced, from the original $\\mathcal{O}(M N^2)$ to $\\mathcal{O}(M N\\log_2 N)$, where $N$ denotes the number of the discretization points on the unit circle and $M$ denotes the number of points in $[0,1)$. This greatly enhances the applicability of AFD. Experiments are carried out to show the high efficiency of the proposed algorithm.
Realization of quantum Fourier transform over ZN
International Nuclear Information System (INIS)
Fu Xiang-Qun; Bao Wan-Su; Li Fa-Da; Zhang Yu-Chao
2014-01-01
Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z N . According to probability amplitude, we prove that the transform can be used to realize QFT over Z N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z N . (general)
First order deformations of the Fourier matrix
Energy Technology Data Exchange (ETDEWEB)
Banica, Teodor, E-mail: teo.banica@gmail.com [Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise (France)
2014-01-15
The N × N complex Hadamard matrices form a real algebraic manifold C{sub N}. The singularity at a point H ∈ C{sub N} is described by a filtration of cones T{sub H}{sup ×}C{sub N}⊂T{sub H}{sup ∘}C{sub N}⊂T{sub H}C{sub N}⊂T{sup ~}{sub H}C{sub N}, coming from the trivial, affine, smooth, and first order deformations. We study here these cones in the case where H = F{sub N} is the Fourier matrix, (w{sup ij}) with w = e{sup 2πi/N}, our main result being a simple description of T{sup ~}{sub H}C{sub N}. As a consequence, the rationality conjecture dim{sub R}(T{sup ~}{sub H}C{sub N})=dim{sub Q}(T{sup ~}{sub H}C{sub N}∩M{sub N}(Q)) holds at H = F{sub N}.
Three dimensional image reconstruction in the Fourier domain
International Nuclear Information System (INIS)
Stearns, C.W.; Chesler, D.A.; Brownell, G.L.
1987-01-01
Filtered backprojection reconstruction algorithms are based upon the relationship between the Fourier transform of the imaged object and the Fourier transforms of its projections. A new reconstruction algorithm has been developed which performs the image assembly operation in Fourier space, rather than in image space by backprojection. This represents a significant decrease in the number of operations required to assemble the image. The new Fourier domain algorithm has resolution comparable to the filtered backprojection algorithm, and, after correction by a pointwise multiplication, demonstrates proper recovery throughout image space. Although originally intended for three-dimensional imaging applications, the Fourier domain algorithm can also be developed for two-dimensional imaging applications such as planar positron imaging systems
The relationship between shock response spectrum and fast Fourier transform
International Nuclear Information System (INIS)
Zola, Maurizio
2001-01-01
In this paper the basic relationship between response spectrum and fast Fourier transform is laid down. Since a long time the response spectrum has been used by structural engineers in the seismic domain and nowadays it is going to be used to define transient motions. This way to define the excitation is more general and more real than the use of classical shape pulses for the reproduction of real environment. Nevertheless the response spectrum of a real excitation represents a loss of some information with respect to the Fourier transform. A useful discussion could arise from these observations. Appendix A gives the relationship between the mathematic Fourier transform and the digital Fourier transform given by computers, while Appendix B gives some examples of response spectra and Fourier transforms of simple functions. (author)
Mathematical principles of signal processing Fourier and wavelet analysis
Brémaud, Pierre
2002-01-01
Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...
Applied Fourier analysis from signal processing to medical imaging
Olson, Tim
2017-01-01
The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medical i maging, and heat and wave equations. Fo...
Solution of 3-dimensional diffusion equation by finite Fourier transformation
International Nuclear Information System (INIS)
Krishnani, P.D.
1978-01-01
Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)
Fourier convergence analysis applied to neutron diffusion Eigenvalue problem
International Nuclear Information System (INIS)
Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook
2004-01-01
Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge
The morphing of geographical features by Fourier transformation.
Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang
2018-01-01
This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.
Double Fourier analysis for Emotion Identification in Voiced Speech
International Nuclear Information System (INIS)
Sierra-Sosa, D.; Bastidas, M.; Ortiz P, D.; Quintero, O.L.
2016-01-01
We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented. (paper)
The Scope Of Fourier Transform Infrared (FTIR)
Hirschfeld, T.
1981-10-01
Three auarters of a century after its inception, a generation after its advantages were recognized, and a decade after its first commercialization, FT-IR dominates the growth of the IR market, and reigns alone over its high performance end. What lies ahead for FT-IR now? On one hand, the boundary between it and the classical scanning spectrometers is becoming fuzzy, as gratings attempt to use as much of FT-IR's computer technology as they can handle, and smaller FT systems invade the medium cost instrument range. On the other hand, technology advances in IR detectors, non-Fourier interference devices, and the often announced tunable laser are at long last getting set to make serious inroads in the field (although not necessarily in the manner most of us expected). However, the dominance of FT-IR as the leading edge of IR spectroscopy seems assured for a good many years. The evolution of FT-IR will be dominated by demands not yet fully satisfied such as rapid sample turnover, better quantitation, automated interpretation, higher GC-IR sensitivity, improved LC-IR, and, above all else, reliability and ease of use. These developments will be based on multiple small advances in hardware, large advances in the way systems are put together, and the traditional yearly revolutionary advances of the computer industry. The big question in the field will, however, still be whether our ambition and our skill can continue to keep up with the advances of our tools. It will be fun.
Fourier transform based scalable image quality measure.
Narwaria, Manish; Lin, Weisi; McLoughlin, Ian; Emmanuel, Sabu; Chia, Liang-Tien
2012-08-01
We present a new image quality assessment (IQA) algorithm based on the phase and magnitude of the 2D (twodimensional) Discrete Fourier Transform (DFT). The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the Human Visual Systems (HVSs) sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of nonuniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Lastly, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is therefore further scalable for RR scenarios. We report extensive experimental results using a total of 9 publicly available databases: 7 image (with a total of 3832 distorted images with diverse distortions) and 2 video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing fullreference (FR) algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar.
Cryogenic Scan Mechanism for Fourier Transform Spectrometer
Brasunas, John C.; Francis, John L.
2011-01-01
A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear
A transformada de Fourier em basic The Fourier transform (FFT in basic
Directory of Open Access Journals (Sweden)
Mauricio Gomes Constantino
2000-06-01
Full Text Available In this paper we describe three computer programs in Basic language about the Fourier transform (FFT which are available in the Internet site http://artemis.ffclrp.usp.br/SoftwareE.htm (in English or http://artemis.ffclrp.usp.br/softwareP.htm (in Portuguese since October 1998. Those are addresses to the Web Page of our Laboratory of Organic Synthesis. The programs can be downloaded and used by anyone who is interested on the subject. The texts, menus and captions in the programs are written in English.
Corrected Fourier series and its application to function approximation
Directory of Open Access Journals (Sweden)
Qing-Hua Zhang
2005-01-01
Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.
Residual Stress Studies Using the Cairo Fourier Diffractometer Facility
International Nuclear Information System (INIS)
Maayouf, R.M.A.; El-Shaer, Y.H.
2002-01-01
The present paper deals with residual stress studies using the Cairo Fourier diffractometer facility CFDF. The CFDF is a reverse - time of -flight (RTOF) diffractometer; applies a Fourier chopper. The measurements were performed for copper samples in order to study the residual stress after welding. The maximum modulation of the Fourier chopper during the measurements was 136 khz; leading to a time resolution half-width of about 7 μ s. It has been found from the present measurements that, the resulting diffraction spectra could be successfully used for studying the residual stress; in the wavelength range between 0.7-2.9 A degree at ∼ 0.45 % relative resolution
From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
2001-01-01
A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm
The application and improvement of Fourier transform spectrometer experiment
Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning
2017-08-01
According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.
Image reconstruction from pairs of Fourier-transform magnitude
International Nuclear Information System (INIS)
Hunt, B.R.; Overman, T.L.; Gough, P.
1998-01-01
The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms. copyright 1998 Optical Society of America
Fourier transform spectroscopy of semiconductor materials
International Nuclear Information System (INIS)
Jonak-Auer, I.
1996-11-01
In order to determine the type of charge carriers, i.e. electrons or holes, participating in optical transitions, cyclotron resonance experiments using circularly polarized radiation were performed on strained-layer [111]-oriented InGaAs/(Al)GaAs multiple quantum wells and on a [100]-oriented InAs/GaSb double-heterostructure. Because of the rather complicated band-structures of these samples it is a priori unknown which carriers take part in transitions. The measurements yield the surprising result, that for the InGaAs/GaAs multiple quantum well the experimentally observed cyclotron resonance appears in the electron-active polarization in the frequency-regime of the Far Infrared (FIR), but in the hole-active polarization in the range of millimeter waves, whereas for the InGaAs/AlGaAs sample the resonance is caused by holes also in the FIR. Since by theoretical considerations the possibility of electrons causing the FIR cyclotron resonance could be excluded, the measurements are interpreted as being caused by holes due to broken selection rules. In the InAs/GaSb sample hole cyclotron resonance could for the first time be measured on a double-heterostructure. As for the application oriented measurements, they comprised a study of the hydrogen content of amorphous silicon nitride layers, and were performed in collaboration with Austria Mikro Systeme International AG. Fourier spectroscopy is a fast and non-destructive means for determining impurity concentrations. Radiation in the Mid Infrared regime stimulates N-H and Si-H stretching vibrations which lead to absorption peaks and can directly be attributed to the hydrogen concentration via calibration factors taken from the literature. In comparison with recommended procedures in the literature, a much higher accuracy in determining the areas of the absorption peaks could be gained in the course of this thesis by a proper polynomial fit of the background spectrum outside the absorption lines. The hydrogen content of
CSIR Research Space (South Africa)
Fedotov, I
2006-07-01
Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...
Almost everywhere convergence over cubes of multiple trigonometric Fourier series
International Nuclear Information System (INIS)
Antonov, N Yu
2004-01-01
Under certain conditions on a function φ:[0,+∞)→[0,+∞) we prove a theorem asserting that the convergence almost everywhere of trigonometric Fourier series for all functions of class φ(L) [-π,π) implies the convergence over cubes of the multiple Fourier series and all its conjugates for an arbitrary function f element of φ(L)(log + L) d-1 ) [-π,π) d , d element of N. It follows from this and an earlier result of the author on the convergence almost everywhere of Fourier series of functions of one variable and class L(log + L)(log + log + log + L)) [-π,π) that if f element of L(log + L) d (log + log + log + L)) [-π,π) d , d element of N, then the Fourier series of f and all its conjugates converge over cubes almost everywhere
On the Equisummability of Hermite and Fourier Expansions
Indian Academy of Sciences (India)
We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.
q-Generalization of the inverse Fourier transform
International Nuclear Information System (INIS)
Jauregui, M.; Tsallis, C.
2011-01-01
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.
On Sums of Numerical Series and Fourier Series
Pavao, H. Germano; de Oliveira, E. Capelas
2008-01-01
We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)
On the physical relevance of the discrete Fourier transform
CSIR Research Space (South Africa)
Greben, JM
1991-11-01
Full Text Available This paper originated from the author's dissatisfaction with the way the discrete Fourier transform is usually presented in the literature. Although mathematically correct, the physical meaning of the common representation is unsatisfactory...
Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems
Leuschner, Matthias; Fritzen, Felix
2017-11-01
Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.
Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
Said-Houari, Belkacem
2013-02-01
In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo\\'s laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier\\'s law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U0 ∈ Hs(ℝ) ∩ L1(ℝ). In addition, by restricting the initial data to U0 ∈ Hs(ℝ) ∩ L1,γ(ℝ) and γ ∈ [0, 1], we can derive faster decay estimates with the decay rate improvement by a factor of t-γ/2. © 2013 Copyright Taylor and Francis Group, LLC.
Extending Single-Molecule Microscopy Using Optical Fourier Processing
2015-01-01
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862
Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
Said-Houari, Belkacem
2013-01-01
In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent
A fourier transform quality measure for iris images
CSIR Research Space (South Africa)
Makinana, S
2014-08-01
Full Text Available to ensure that good quality images are selected for feature extraction, in order to improve iris recognition system. In addition, this research proposes a measure of iris image quality using a Fourier Transform. The experimental results demonstrate...
Error Analysis for Fourier Methods for Option Pricing
Hä ppö lä , Juho
2016-01-01
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE
Surface Fourier-transform lens using a metasurface
International Nuclear Information System (INIS)
Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun
2015-01-01
We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)
Fourier-Based Transmit Beampattern Design Using MIMO Radar
Lipor, John; Ahmed, Sajid; Alouini, Mohamed-Slim
2014-01-01
a constant-envelope or drawing from a finite alphabet. In this paper, a closed-form method to design for a uniform linear array is proposed that utilizes the discrete Fourier transform (DFT) coefficients and Toeplitz matrices. The resulting
The Fourier law in a momentum-conserving chain
Giardinà, C.; Kurchan, J.
2005-01-01
We introduce a family of models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases the Fourier law is verified in one dimension.
Innovative design method of automobile profile based on Fourier descriptor
Gao, Shuyong; Fu, Chaoxing; Xia, Fan; Shen, Wei
2017-10-01
Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.
Fourier transform wavefront control with adaptive prediction of the atmosphere.
Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre
2007-09-01
Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.
Fourier analysis in dynamic non periodic phenomena in nuclear medicine
International Nuclear Information System (INIS)
Constantinesco, A.; Lallot, C.
1984-01-01
The success of Fourier analysis in assessing cardiac function has led us to investigate other possible uses of this technique. We show that phase analysis applied to dynamic non periodic activity changes gives useful parametric functional images. The phase image is comparable to a transit time image, the amplitude image is comparable to the maximum variations of activity and the mean image corresponds to a normalized sum of images. Exemples of this powerful application of Fourier analysis are discussed [fr
Simple optical setup implementation for digital Fourier transform holography
Energy Technology Data Exchange (ETDEWEB)
De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passo da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); Rodrigues, D M C; Dos Santos, P A M, E-mail: pams@if.uff.br [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)
2011-01-01
In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.
A New Nonlinear Unit Root Test with Fourier Function
Güriş, Burak
2017-01-01
Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an Exponential Smooth Threshold Autore...
A discrete Fourier transform for virtual memory machines
Galant, David C.
1992-01-01
An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.
Self-Fourier functions and coherent laser combination
International Nuclear Information System (INIS)
Corcoran, C J; Pasch, K A
2004-01-01
The Gaussian and Comb functions are generally quoted as being the two basic functions that are their own Fourier transforms. In 1991, Caola presented a recipe for generating functions that are their own Fourier transforms by symmetrizing any transformable function and then adding its own Fourier transform to it. In this letter, we present a new method for generating a set of functions that are exactly their own Fourier transforms, and which have direct application to laser cavity design for a wide variety of applications. The generated set includes the Gaussian and Comb functions as special cases and forms a continuous bridge of functions between them. The new generating method uses the Gaussian and Comb functions as bases and does not rely on the Fourier operator itself. This self-Fourier function promises to be particularly useful in high-power laser design through coherent laser beam combination. Although these results are presented in a single dimension as with a linear array, the results are equally valid in two dimensions. (letter to the editor)
Li, Shu-Nan; Cao, Bing-Yang
2017-09-01
The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.
Iterative wave-front reconstruction in the Fourier domain.
Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry
2017-05-15
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.
Electro-Optical Imaging Fourier-Transform Spectrometer
Chao, Tien-Hsin; Zhou, Hanying
2006-01-01
An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.
Fast Fourier single-pixel imaging via binary illumination.
Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang
2017-09-20
Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.
Ballooning modes or Fourier modes in a toroidal plasma?
International Nuclear Information System (INIS)
Connor, J.W.; Taylor, J.B.
1987-01-01
The relationship between two different descriptions of eigenmodes in a torus is investigated. In one the eigenmodes are similar to Fourier modes in a cylinder and are highly localized near a particular rational surface. In the other they are the so-called ballooning modes that extend over many rational surfaces. Using a model that represents both drift waves and resistive interchanges the transition from one of these structures to the other is investigated. In this simplified model the transition depends on a single parameter which embodies the competition between toroidal coupling of Fourier modes (which enhances ballooning) and variation in frequency of Fourier modes from one rational surface to another (which diminishes ballooning). As the coupling is increased each Fourier mode acquires a sideband on an adjacent rational surface and these sidebands then expand across the radius to form the extended mode described by the conventional ballooning mode approximation. This analysis shows that the ballooning approximation is appropriate for drift waves in a tokamak but not for resistive interchanges in a pinch. In the latter the conventional ballooning effect is negligible but they may nevertheless show a ballooning feature. This is localized near the same rational surface as the primary Fourier mode and so does not lead to a radially extended structure
Comparative analysis of imaging configurations and objectives for Fourier microscopy.
Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid
2015-11-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.
Screening retinal transplants with Fourier-domain OCT
Rao, Bin
2009-02-01
Transplant technologies have been studied for the recovery of vision loss from retinitis pigmentosa (RP) and age-related macular degeneration (AMD). In several rodent retinal degeneration models and in patients, retinal progenitor cells transplanted as layers to the subretinal space have been shown to restore or preserve vision. The methods for evaluation of transplants are expensive considering the large amount of animals. Alternatively, time-domain Stratus OCT was previously shown to be able to image the morphological structure of transplants to some extent, but could not clearly identify laminated transplants. The efficacy of screening retinal transplants with Fourier-domain OCT was studied on 37 S334ter line 3 rats with retinal degeneration 6-67 days after transplant surgery. The transplants were morphologically categorized as no transplant, detachment, rosettes, small laminated area and larger laminated area with both Fourier-domain OCT and histology. The efficacy of Fourier-domain OCT in screening retinal transplants was evaluated by comparing the categorization results with OCT and histology. Additionally, 4 rats were randomly selected for multiple OCT examinations (1, 5, 9, 14 and 21days post surgery) in order to determine the earliest image time of OCT examination since the transplanted tissue may need some time to show its tendency of growing. Finally, we demonstrated the efficacy of Fourier-domain OCT in screening retinal transplants in early stages and determined the earliest imaging time for OCT. Fourier-domain OCT makes itself valuable in saving resource spent on animals with unsuccessful transplants.
Fourier imaging of non-linear structure formation
International Nuclear Information System (INIS)
Brandbyge, Jacob; Hannestad, Steen
2017-01-01
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
Fourier imaging of non-linear structure formation
Energy Technology Data Exchange (ETDEWEB)
Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)
2017-04-01
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.
Fourier domain asymmetric cryptosystem for privacy protected multimodal biometric security
Choudhury, Debesh
2016-04-01
We propose a Fourier domain asymmetric cryptosystem for multimodal biometric security. One modality of biometrics (such as face) is used as the plaintext, which is encrypted by another modality of biometrics (such as fingerprint). A private key is synthesized from the encrypted biometric signature by complex spatial Fourier processing. The encrypted biometric signature is further encrypted by other biometric modalities, and the corresponding private keys are synthesized. The resulting biometric signature is privacy protected since the encryption keys are provided by the human, and hence those are private keys. Moreover, the decryption keys are synthesized using those private encryption keys. The encrypted signatures are decrypted using the synthesized private keys and inverse complex spatial Fourier processing. Computer simulations demonstrate the feasibility of the technique proposed.
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
The Fourier U(2 Group and Separation of Discrete Variables
Directory of Open Access Journals (Sweden)
Kurt Bernardo Wolf
2011-06-01
Full Text Available The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R, whose maximal compact subgroup is the Fourier group U(2_F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4. Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle coordinates, thus realizing one case of separation in two discrete coordinates. The N^2-vectors in this space are digital (pixellated images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.
Spectrums Transform Operators in Bases of Fourier and Walsh Functions
Directory of Open Access Journals (Sweden)
V. V. Syuzev
2017-01-01
Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel
Some applications of Fourier's great discovery for beginners
International Nuclear Information System (INIS)
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency ω = 2π/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students should be familiar with this subject. A suitable device for demonstrating spectra of electrical signals is a digital storage oscilloscope. Spectra of various waveforms and of AM and FM signals are demonstrated, as well as AM signals from a broadcasting station. Changes in the signals filtered by frequency-selective circuits are seen by comparing the spectra of the input and output voltages. All the experiments are suitable for undergraduate laboratories and usable as classroom demonstrations. (paper)
On the Alignment of Shapes Represented by Fourier Descriptors
DEFF Research Database (Denmark)
Sjöstrand, Karl; Ericsson, Anders; Larsen, Rasmus
2006-01-01
The representation of shapes by Fourier descriptors is a time-honored technique that has received relatively little attention lately. Nevertheless, it has many benefits and is applicable for describing a range of medical structures in two dimensions. Delineations in medical applications often...... consist of continuous outlines of structures, where no information of correspondence between samples exist. In this article, we discuss an alignment method that works directly with the functional representation of Fourier descriptors, and that is optimal in a least-squares sense. With corresponding...... represented by common landmarks can be constructed in an automatic fashion. If the aligned Fourier descriptors are inverse transformed from the frequency domain to the spatial domain, a set of roughly aligned landmarks are obtained. The positions of these are then adjusted along the contour of the objects...
International conference Fourier Analysis and Pseudo-Differential Operators
Turunen, Ville; Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations
2014-01-01
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. This collection of 20 refereed articles is based on selected talks given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
Fourier analysis of the parametric resonance in neutrino oscillations
International Nuclear Information System (INIS)
Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe
2009-01-01
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.
Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.
Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda
2017-09-13
This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.
Application of Fourier analysis to multispectral/spatial recognition
Hornung, R. J.; Smith, J. A.
1973-01-01
One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.
Advantage of Fast Fourier Interpolation for laser modeling
International Nuclear Information System (INIS)
Epatko, I.V.; Serov, R.V.
2006-01-01
The abilities of a new algorithm: the 2-dimensional Fast Fourier Interpolation (FFI) with magnification factor (zoom) 2 n whose purpose is to improve the spatial resolution when necessary, are analyzed in details. FFI procedure is useful when diaphragm/aperture size is less than half of the current simulation scale. The computation noise due to FFI procedure is less than 10 -6 . The additional time for FFI is approximately equal to one Fast Fourier Transform execution time. For some applications using FFI procedure, the execution time decreases by a 10 4 factor compared with other laser simulation codes. (authors)
Fourier transform infrared spectra applications to chemical systems
Ferraro, John R
1985-01-01
The final and largest volume to complete this four-volume treatise is published in response to the intense commercial and research interest in Fourier Transform Interferometry.Presenting current information from leading experts in the field, Volume 4 introduces new information on, for example, applications of Diffuse Reflectance Spectroscopy in the Far-Infrared Region. The editors place emphasis on surface studies and address advances in Capillary Gas Chromatography - Fourier Transform Interferometry.Volume 4 especially benefits spectroscopists and physicists, as well as researchers
Fourier analysis of the aerodynamic behavior of cup anemometers
International Nuclear Information System (INIS)
Pindado, Santiago; Pérez, Imanol; Aguado, Maite
2013-01-01
The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force. (paper)
Fourier transform infrared spectra applications to chemical systems
Ferraro, John R
1978-01-01
Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems presents the chemical applications of the Fourier transform interferometry (FT-IR).The book contains discussions on the applications of FT-IR in the fields of chromatography FT-IR, polymers and biological macromolecules, emission spectroscopy, matrix isolation, high-pressure interferometry, and far infrared interferometry. The final chapter is devoted to the presentation of the use of FT-IR in solving national technical problems such as air pollution, space exploration, and energy related subjects.Researc
Fourier Multipliers on Anisotropic Mixed-Norm Spaces of Distributions
DEFF Research Database (Denmark)
Cleanthous, Galatia; Georgiadis, Athanasios; Nielsen, Morten
2018-01-01
A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operat......A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity...
A Fourier Optical Model for the Laser Doppler Velocimeter
DEFF Research Database (Denmark)
Lading, Lars
1972-01-01
The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. ldquodifferential moderdquo and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions. The particles are represented...... filtering ability vanishes as the aperture size converges towards zero. The results based on fourier optics are compared with the rough estimates obtainable by using the "antenna formular" for heterodyning (ArΩr≈λ2)....
From Fourier Series to Rapidly Convergent Series for Zeta(3)
DEFF Research Database (Denmark)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions on this such ......The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions...
Connection between Fourier coefficient and Discretized Cartesian path integration
International Nuclear Information System (INIS)
Coalson, R.D.
1986-01-01
The relationship between so-called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier-like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on-diagonal statistical density matrix elements for a number of prototypical 1-d potentials. A consistent convergence order among these prescriptions is established
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Decay of the Fourier transform analytic and geometric aspects
Iosevich, Alex
2014-01-01
The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
Transformation of a Free-Wilson matrix into Fourier coefficients
Czech Academy of Sciences Publication Activity Database
Holík, M.; Halámek, Josef
2002-01-01
Roč. 20, - (2002), s. 422 - 428 ISSN 0931-8771 Institutional research plan: CEZ:AV0Z2065902 Keywords : Free-Wilson matrix * Fourier transform * multivariate regression Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.558, year: 2002
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit ...
Application of Migration Velocity Using Fourier Transform Approach ...
African Journals Online (AJOL)
Application of velocity by Fourier transform to process 3-D unmigrated seismic sections has been carried out in Fabi Field, Niger Delta – Nigeria. Usually, all seismic events (sections) are characterized by spikes or noise (random or coherent), multiples and shear waves so that when a seismic bed is dipping, the apparent ...
Fourier-transform infrared spectroscopic studies of dithia ...
Indian Academy of Sciences (India)
Unknown
limited region 1000–1150 cm–1.10 Therefore, in the present paper we report and analyse Fourier-trans- form infrared (FT-IR) spectra of S2TPP and its chemically prepared cation. 2. Experimental. Dithia tetraphenyl porphyrine was received from. Professor A L Verma as a gift and used without fur- ther purification. However ...
Properties of the Simpson discrete fourier transform | Singh ...
African Journals Online (AJOL)
The Simpson discrete Fourier transform (SDFT) and its inverse are transformations relating the time and frequency domains. In this paper we state and prove the important properties of shift, circular convolution, conjugation, time reversal and Plancherel's theorem. In addition, we provide an alternative representation of the ...
Fourier transformation methods in the field of gamma spectrometry
Indian Academy of Sciences (India)
The basic principles of a new version of Fourier transformation is presented. This new version was applied to solve some main problems such as smoothing, and denoising in gamma spectroscopy. The mathematical procedures were first tested by simulated data and then by actual experimental data.
A new analytical solution to the diffusion problem: Fourier series ...
African Journals Online (AJOL)
This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.
Overcoming Spurious Regression Using time-Varying Fourier ...
African Journals Online (AJOL)
Non-stationary time series data have been traditionally analyzed in the frequency domain by assuming constant amplitudes regardless of the timelag. A new approach called time-varying amplitude method (TVAM) is presented here. Oscillations are analyzed for changes in the magnitude of Fourier Coefficients which are ...
Embedding relations connected with strong approximation of Fourier ...
Indian Academy of Sciences (India)
ing only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl. 11(4) (2008) 749–756] which is a generalization of Tikhonov's results [Anal. Math. 31 (2005) 183–194]. We also ...
Fourier transform infrared spectrophotometry and X-ray powder ...
African Journals Online (AJOL)
This study aimed at demonstrating complementary roles offered by both Fourier transform infrared (FTIR) spectrophotometry and x-ray powder diffraction (XRPD) techniques in characterizing clay size fraction of kaolins. The clay size fraction of kaolin samples obtained from Kgwakgwe, Makoro, Lobatse and Serule kaolin ...
Multipliers for the Absolute Euler Summability of Fourier Series
Indian Academy of Sciences (India)
In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with multipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.
Novel properties of the Fourier decomposition of the sinogram
International Nuclear Information System (INIS)
Edholm, P.R.; Lewitt, R.M.; Lindholm, B.
1986-01-01
The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency ω (continuous) and angular harmonic number n (discrete). For absolute value of ω large, the Fourier coefficients on the line n=kω of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed
Fourier transform distribution function of relaxation times; application and limitations
Boukamp, Bernard A.
2015-01-01
A simple Fourier transform (FT) method is presented for obtaining a Distribution Function of Relaxation Times (DFRT) for electrochemical impedance spectroscopy (EIS) data. By using a special data extension procedure the FT is performed over the range from -∞ ≤ lnω ≤ + ∞. The integration procedure is
Beschrijving van een computerprogramma voor Fourier-analyse
Sannes, A.jr.
1975-01-01
During my practical work at the NIOZ Texel, from May until August 1974, I have been engaged with the Fourier- transformation. The direct motive was the problem of a guest-investigator who studied the regularity in the frequency of pulsations of the hearts of guillemots. A computerprogram that can
Power filtering of nth order in the fractional Fourier domain
International Nuclear Information System (INIS)
Alieva, Tatiana; Calvo, Maria Luisa; Bastiaans, Martin J.
2002-01-01
The main properties of the power filtering operation in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of linear power filtering for solving the phase retrieval problem from intensity distributions only is proposed. The optical configuration for the experimental realization of the method is discussed. (author)
Discrete frequency identification using the HP 5451B Fourier analyser
International Nuclear Information System (INIS)
Holland, L.; Barry, P.
1977-01-01
The frequency analysis by the HP5451B discrete frequency Fourier analyser is studied. The advantages of cross correlation analysis to identify discrete frequencies in a background noise are discussed in conjuction with the elimination of aliasing and wraparound error. Discrete frequency identification is illustrated by a series of graphs giving the results of analysing 'electrical' and 'acoustical' white noise and sinusoidal signals [pt
Prototypes and matrix relevance learning in complex fourier space
Straat, M.; Kaden, M.; Gay, M.; Villmann, T.; Lampe, Alexander; Seiffert, U.; Biehl, M.; Melchert, F.
2017-01-01
In this contribution, we consider the classification of time-series and similar functional data which can be represented in complex Fourier coefficient space. We apply versions of Learning Vector Quantization (LVQ) which are suitable for complex-valued data, based on the so-called Wirtinger
An introduction to non-harmonic Fourier series
Young, Robert M
2001-01-01
An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.
Fourier coefficientes computation in two variables, a distributional version
Directory of Open Access Journals (Sweden)
Carlos Manuel Ulate R.
2015-01-01
Full Text Available The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.
SPICA/SAFARI fourier transform spectrometer mechanism evolutionary design
Dool, T.C. van den; Kruizinga, B.; Braam, B.C.; Hamelinck, R.F.M.M.; Loix, N.; Loon, D. van; Dams, J.
2012-01-01
TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme in 2022. JAXA leads the development
Quaternion Fourier transforms for signal and image processing
Ell, Todd A; Sangwine, Stephen J
2014-01-01
Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book's attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.
The RC Circuit: An Approach with Fourier Transforms
Indian Academy of Sciences (India)
The RC Circuit: An Approach with Fourier Transforms. Classroom Volume 21 Issue 11 November 2016 pp 1029-1042 ... But a lot of things, (including the complex impedanceitself, and some insight into complex analysis) can be understoodbetter if we use the FT approach to solve the differentialequations that come up in ...
Fourier transform infrared (FTIR) spectroscopy for identification of ...
African Journals Online (AJOL)
Fourier transform infrared (FTIR) spectroscopy was used in this study to identify and determine spectral features of Chlorella vulgaris Beijerinck 1890 and Scenedesmus obliquus (Turpin) Kützing 1833. Two cultures were grown in a chemically-defined media under photoautotrophic culture conditions isolated from eutrophic ...
Testing a Fourier Accelerated Hybrid Monte Carlo Algorithm
Catterall, S.; Karamov, S.
2001-01-01
We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for dynamical fermion simulations of non-gauge models. We test the algorithm in supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice field theory. We find dramatic reductions in the autocorrelation time of the algorithm in comparison to standard HMC.
Critical points of multidimensional random Fourier series: variance estimates
Nicolaescu, Liviu I.
2013-01-01
To any positive number $\\varepsilon$ and any nonnegative even Schwartz function $w:\\mathbb{R}\\to\\mathbb{R}$ we associate the random function $u^\\varepsilon$ on the $m$-torus $T^m_\\varepsilon:=\\mathbb{R}^m/(\\varepsilon^{-1}\\mathbb{Z})^m$ defined as the real part of the random Fourier series $$ \\sum_{\
Closed contour fractal dimension estimation by the Fourier transform
International Nuclear Information System (INIS)
Florindo, J.B.; Bruno, O.M.
2011-01-01
Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.
HEART ABNORMALITY CLASSIFICATIONS USING FOURIER TRANSFORMS METHOD AND NEURAL NETWORKS
Directory of Open Access Journals (Sweden)
Endah Purwanti
2014-05-01
Full Text Available Health problems with cardiovascular system disorder are still ranked high globally. One way to detect abnormalities in the cardiovascular system especially in the heart is through the electrocardiogram (ECG reading. However, reading ECG recording needs experience and expertise, software-based neural networks has designed to help identify any abnormalities ofthe heart through electrocardiogram digital image. This image is processed using image processing methods to obtain ordinate chart which representing the heart’s electrical potential. Feature extraction using Fourier transforms which are divided into several numbers of coefficients. As the software input, Fourier transforms coefficient have been normalized. Output of this software is divided into three classes, namely heart with atrial fibrillation, coronary heart disease and normal. Maximum accuracy rate ofthis software is 95.45%, with the distribution of the Fourier transform coefficients 1/8 and number of nodes 5, while minimum accuracy rate of this software at least 68.18% by distribution of the Fourier transform coefficients 1/32 and the number of nodes 32. Overall result accuracy rate of this software has an average of86.05% and standard deviation of7.82.
Fourier coefficientes computation in two variables, a distributional version
Carlos Manuel Ulate R.
2015-01-01
The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.
Closed form fourier-based transmit beamforming for MIMO radar
Lipor, John J.; Ahmed, Sajid; Alouini, Mohamed-Slim
2014-01-01
-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform
Free Sixteen Harmonic Fourier Series Web App with Sound
Ruiz, Michael J.
2018-01-01
An online HTML5 Fourier synthesizer app is provided that allows students to manipulate sixteen harmonics and construct periodic waves. Students can set the amplitudes and phases for each harmonic, seeing the resulting waveforms and hearing the sounds. Five waveform presets are included: sine, triangle, square, ramp (sawtooth), and pulse train. The…
The linogram algorithm and direct fourier method with linograms
International Nuclear Information System (INIS)
Edholm, P.R.
1990-01-01
This text is an attempt to describe the linogram algorithm based on a somewhat simplified mathematical description of the algorithm which is also more similar to the actual digital implementation. Another algorithm with linograms, which may be called a direct fourier method is also presented. (K.A.E.)
Fourier beamformation of multistatic synthetic aperture ultrasound imaging
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2015-01-01
A new Fourier beamformation (FB) algorithm is presented for multistatic synthetic aperture ultrasound imaging. It can reduce the number of computations by a factor of 20 compared to conventional Delay-and-Sum (DAS) beamformers. The concept is based on the wavenumber algorithm from radar and sonar...
Synthetic aperture ultrasound Fourier beamformation using virtual sources
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2016-01-01
An efficient Fourier beamformation algorithm is presented for multistatic synthetic aperture ultrasound imaging using virtual sources (FBV). The concept is based on the frequency domain wavenumber algorithm from radar and sonar and is extended to a multi-element transmit/receive configuration using...
Grating-assisted superresolution of slow waves in Fourier space
DEFF Research Database (Denmark)
Thomas, N. Le; Houdré, R.; Frandsen, Lars Hagedorn
2007-01-01
with a high numerical aperture Fourier space imaging set-up. A high-resolution spectroscopy of the far-field emission diagram allows us to accurately and efficiently determine the dispersion curve and the group-index dispersion of planar photonic waveguides operating in the slow light regime....
Nonlinear Fourier transform for dual-polarization optical communication system
DEFF Research Database (Denmark)
Gaiarin, Simone
communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...
Grid-Independent Compressive Imaging and Fourier Phase Retrieval
Liao, Wenjing
2013-01-01
This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem. Many situations in optics, medical imaging and signal processing call…
Education and Utopia: Robert Owen and Charles Fourier
Leopold, David
2011-01-01
The aims of education, and the appropriate means of realising them, are a recurring preoccupation of utopian authors. The utopian socialists Robert Owen (1771-1858) and Charles Fourier (1772-1837) both place human nature at the core of their educational views, and both see education as central to their wider objective of social and political…
Accelerated radial Fourier-velocity encoding using compressed sensing
International Nuclear Information System (INIS)
Hilbert, Fabian; Han, Dietbert
2014-01-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Accelerated radial Fourier-velocity encoding using compressed sensing
Energy Technology Data Exchange (ETDEWEB)
Hilbert, Fabian; Han, Dietbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wech, Tobias; Koestler, Herbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wuerzburg Univ. (Germany). Comprehensive Heart Failure Center (CHFC)
2014-10-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Accelerated radial Fourier-velocity encoding using compressed sensing.
Hilbert, Fabian; Wech, Tobias; Hahn, Dietbert; Köstler, Herbert
2014-09-01
Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. We imaged the femoral artery of healthy volunteers with ECG-triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6-fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity distribution in vessels in the order of the voxel size. Thus
Study of diffused particles by an electron cyclotron-resonance ions source plasma
International Nuclear Information System (INIS)
Klein, J.P.
1995-01-01
A double electrostatic analyser has been built mainly to study the loss cone electron population. The analysis of the ions can help to determine the plasma potential. The possibility of applying two analysing potentials along the extraction decaying magnetic filed allowed us to determine the anisotropy of the electron distribution function, of parallel temperature Tpar and perpendicular temperature Tper outside the plasma. The Tpar temperature remains constant at around 10 eV when Tper increases from 30 eV to 150 eV with improved confinement. The electron cyclotron heating provides mainly perpendicular energy to the electrons. The perpendicular electron energy is then converted to parallel energy predominantly by electron ion collisions and leave the plasma with a frequency depending on v per -3 . Taking a Maxwellian function of temperature T per cent to describe the electron function distribution f cent (v per ) in the center of the plasma is in line with the experimental electron characteristics obtained with a single electrostatic potential. Temperatures of 2 keV have been reached at 10 Ghz and 6 keV at 18 Ggz. Measurements of density and diamagnetism can complete the description of this warm population: the warm electrons dominate in number but leave the plasma quicker than the very hot electron population (analysed with the X ray diagnostic). For this reason the energy density of warm electrons is less than that of the very hot population by warm electrons consume most of the injected rf power. (author). 52 refs., 100 figs
Application of Fourier transforms for microwave radiometric inversions
Holmes, J. J.; Balanis, C. A.; Truman, W. M.
1975-01-01
Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.
On the finite Fourier transforms of functions with infinite discontinuities
Directory of Open Access Journals (Sweden)
Branko Saric
2002-01-01
Full Text Available The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.
Discrete Fourier Transform Analysis in a Complex Vector Space
Dean, Bruce H.
2009-01-01
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
Fourier transform digital holographic adaptive optics imaging system
Liu, Changgeng; Yu, Xiao; Kim, Myung K.
2013-01-01
A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541
On frame properties for Fourier-like systems
DEFF Research Database (Denmark)
Christensen, Ole; Osgooei, Elnaz
2013-01-01
Fourier-like systems are formed by multiplying a class of exponentials with a set of window functions. Via the Fourier transform they are equivalent to shift-invariant systems. We present sufficient and easily verifiable conditions for such systems to form a frame with a dual frame having the same...... structure. An attractive class of frames is formed by letting the window functions be trigonometric polynomials, restricted to compact intervals. We prove, under weak conditions, that such systems generate a frame with a dual that is also generated by a trigonometric polynomial. For polynomial windows......, a result of this type does not hold. Throughout the paper the results are related to the well established theory for Gabor systems....
Fourier-based magnetic induction tomography for mapping resistivity
International Nuclear Information System (INIS)
Puwal, Steffan; Roth, Bradley J.
2011-01-01
Magnetic induction tomography is used as an experimental tool for mapping the passive electromagnetic properties of conductors, with the potential for imaging biological tissues. Our numerical approach to solving the inverse problem is to obtain a Fourier expansion of the resistivity and the stream functions of the magnetic fields and eddy current density. Thus, we are able to solve the inverse problem of determining the resistivity from the applied and measured magnetic fields for a two-dimensional conducting plane. When we add noise to the measured magnetic field, we find the fidelity of the measured to the true resistivity is quite robust for increasing levels of noise and increasing distances of the applied and measured field coils from the conducting plane, when properly filtered. We conclude that Fourier methods provide a reliable alternative for solving the inverse problem.
An introduction to Laplace transforms and Fourier series
Dyke, Phil
2014-01-01
Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...
Matrix-Vector Based Fast Fourier Transformations on SDR Architectures
Directory of Open Access Journals (Sweden)
Y. He
2008-05-01
Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.
Meso-optical Fourier transform microscope with double focusing
International Nuclear Information System (INIS)
Batusov, Yu.A.; Soroko, L.M.; Tereshchenko, V.V.
1992-01-01
The meso-optical Fourier transform microscope (MFTM) with double focusing for particle tracks of low ionization level in the nuclear emulsion is described. It is shown experimentally that this device enables one to get high concentration of information about the position of the particle track in the nuclear emulsion and thus to increase the signal-to-noise ratio. It is shown that spreading of the meso-optical image of the particle track in the sagittal section of the MFTM can be eliminated completely in the frame of the diffraction limit. The number of the additional degrees of freedom in this new MFTM system along depth coordinate is equal to 20 in comparison to single degree of freedom in the Fourier transform microscope of the direct observation. 10 refs.; 15 figs
Fourier-positivity constraints on QCD dipole models
Directory of Open Access Journals (Sweden)
Bertrand G. Giraud
2016-09-01
Full Text Available Fourier-positivity (F-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position space r. They are Bessel transforms of positive transverse momentum dependent gluon distributions. Using mathematical F-positivity constraints on the limit r→0 behavior of the dipole amplitudes, we identify the common origin of the violation of F-positivity for various, however phenomenologically convenient, dipole models. It is due to the behavior r2+ϵ, ϵ>0 softer, even slightly, than color transparency. F-positivity seems thus to conflict with the present dipole formalism when it includes a QCD running coupling constant α(r.
Limitations on continuous variable quantum algorithms with Fourier transforms
International Nuclear Information System (INIS)
Adcock, Mark R A; Hoeyer, Peter; Sanders, Barry C
2009-01-01
We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.
The Fourier transform for certain hyperkähler fourfolds
Shen, Mingmin
2016-01-01
Using a codimension-1 algebraic cycle obtained from the PoincarÃ© line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring \\mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe"Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of HyperkÃ¤hler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.
Fourier acceleration of iterative processes in disordered systems
International Nuclear Information System (INIS)
Batrouni, G.G.; Hansen, A.
1988-01-01
Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria
High resolution integral holography using Fourier ptychographic approach.
Li, Zhaohui; Zhang, Jianqi; Wang, Xiaorui; Liu, Delian
2014-12-29
An innovative approach is proposed for calculating high resolution computer generated integral holograms by using the Fourier Ptychographic (FP) algorithm. The approach initializes a high resolution complex hologram with a random guess, and then stitches together low resolution multi-view images, synthesized from the elemental images captured by integral imaging (II), to recover the high resolution hologram through an iterative retrieval with FP constrains. This paper begins with an analysis of the principle of hologram synthesis from multi-projections, followed by an accurate determination of the constrains required in the Fourier ptychographic integral-holography (FPIH). Next, the procedure of the approach is described in detail. Finally, optical reconstructions are performed and the results are demonstrated. Theoretical analysis and experiments show that our proposed approach can reconstruct 3D scenes with high resolution.
10th International Conference on Progress in Fourier Transform Spectroscopy
Keresztury, Gábor; Kellner, Robert
1997-01-01
19 plenary lectures and 203 poster papers presented at the 10th International Conference of Fourier Transform Spectroscopy in Budapest 1995 give an overview on the state-of-the art of this technology and its wide range of applications. The reader will get information on any aspects of FTS including the latest instrumental developments, e.g. in diode array detection, time resolution FTS, microscopy and spectral mapping, double modulation and two-dimensional FTS.
Vanishing dissipation limit for the Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2016-01-01
Roč. 14, č. 6 (2016), s. 1535-1551 ISSN 1539-6746 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : inviscid limit * compressible fluid * Navier–Stokes–Fourier system Subject RIV: BA - General Mathematics Impact factor: 1.425, year: 2016 http://intlpress.com/site/pub/pages/journals/items/cms/content/vols/0014/0006/a004/index.html
Free sixteen harmonic Fourier series web app with sound
Ruiz, Michael J.
2018-03-01
An online HTML5 Fourier synthesizer app is provided that allows students to manipulate sixteen harmonics and construct periodic waves. Students can set the amplitudes and phases for each harmonic, seeing the resulting waveforms and hearing the sounds. Five waveform presets are included: sine, triangle, square, ramp (sawtooth), and pulse train. The program is free for non-commercial use and can also be downloaded for running offline.
Some studies on Fourier analysis in students experiment
大崎, 正雄
2016-01-01
Here we give some troubles in teaching and their solutions occured during the Software Science Experiment course, which is opened for the 4th semester in the Department of Software Science. One of the subjects of this experiment course is Fourier analysis using MyPC. Some students are not familiar with calculating the integration of sinusoidal function, and also some need support for drawing graphs with MS Excel. Typical mistakes and their settlements are given.
Symmetrized neutron transport equation and the fast Fourier transform method
International Nuclear Information System (INIS)
Sinh, N.Q.; Kisynski, J.; Mika, J.
1978-01-01
The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations
An algorithm for the basis of the finite Fourier transform
Santhanam, Thalanayar S.
1995-01-01
The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.
Fourier expansions and multivariable Bessel functions concerning radiation programmes
International Nuclear Information System (INIS)
Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.
1996-01-01
The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)
Optically compressed sensing by under sampling the polar Fourier plane
International Nuclear Information System (INIS)
Stern, A; Levi, O; Rivenson, Y
2010-01-01
In a previous work we presented a compressed imaging approach that uses a row of rotating sensors to capture indirectly polar strips of the Fourier transform of the image. Here we present further developments of this technique and present new results. The advantages of our technique, compared to other optically compressed imaging techniques, is that its optical implementation is relatively easy, it does not require complicate calibrations and that it can be implemented in near-real time.
Fast Fourier transformation results from gamma-ray burst profiles
Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.
1992-01-01
Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.
Calibration of the Herschel SPIRE Fourier Transform Spectrometer
Swinyard, Bruce; Polehampton, E. T.; Hopwood, R.; Valtchanov, I.; Lu, N.; Fulton, T.; Benielli, D.; Imhof, P.; Marchili, N.; Baluteau, J.- P.; Bendo, G. J.; Ferlet, M.; Griffin, Matthew Jason; Lim, T. L.; Makiwa, G.
2014-01-01
The Herschel Spectral and Photometric REceiver (SPIRE) instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of ∼450–1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a sp...
Dimension reduction for the full Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Březina, J.; Kreml, Ondřej; Mácha, Václav
2017-01-01
Roč. 19, č. 4 (2017), s. 659-683 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier–Stokes–Fourier system * dimension reduction * relative entropy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.106, year: 2016 https://link.springer.com/article/10.1007%2Fs00021-016-0301-6
Fourier-Malliavin volatility estimation theory and practice
Mancino, Maria Elvira; Sanfelici, Simona
2017-01-01
This volume is a user-friendly presentation of the main theoretical properties of the Fourier-Malliavin volatility estimation, allowing the readers to experience the potential of the approach and its application in various financial settings. Readers are given examples and instruments to implement this methodology in various financial settings and applications of real-life data. A detailed bibliographic reference is included to permit an in-depth study. .
The Convergence Acceleration of Two-Dimensional Fourier Interpolation
Directory of Open Access Journals (Sweden)
Anry Nersessian
2008-07-01
Full Text Available Hereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.
Fourier and wavelet analysis of skin laser doppler flowmetry signals
Qi, Wei
2011-01-01
ObjectiveThis thesis examines the measurement of skin microvascular blood flows from Laser Doppler Flowmetry (LDF) signals. Both healthy subjects and those with features of the metabolic syndrome are studied using signal processing techniques such as the Fourier and Wavelet transforms. An aim of this study is to investigate whether change in blood flow at rest can be detected from the spectral content of the processed signals in the diferent subject groups. Additionally the effect of insulin ...
Ghost telescope and ghost Fourier telescope with thermal light
International Nuclear Information System (INIS)
Gong Wenlin; Han Shensheng
2011-01-01
As important observation tools, telescopes are very useful in remote observations. We report a proof-of-principle experimental demonstration of ghost telescope scheme and show that, by measuring the intensity correlation of two light fields and only changing the position of the detector in the reference path, ghost telescope and ghost Fourier telescope can be obtained even if a single-pixel detector is fixed in Fresnel region of the object. Differences between conventional telescope and ghost telescope are also discussed.
An OTDM-To-WDM Converter Using Optical Fourier Transformation
Khin Su Myat Min; Zaw Myo Lwin; Hla Myo Tun
2015-01-01
We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements ar...
Solving singular convolution equations using the inverse fast Fourier transform
Czech Academy of Sciences Publication Activity Database
Krajník, E.; Montesinos, V.; Zizler, P.; Zizler, Václav
2012-01-01
Roč. 57, č. 5 (2012), s. 543-550 ISSN 0862-7940 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular convolution equations * fast Fourier transform * tempered distribution Subject RIV: BA - General Mathematics Impact factor: 0.222, year: 2012 http://www.springerlink.com/content/m8437t3563214048/
Integrable systems with quadratic nonlinearity in Fourier space
International Nuclear Information System (INIS)
Marikhin, V.G.
2003-01-01
The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed
Periodic transonic flow simulation using fourier-based algorithm
International Nuclear Information System (INIS)
Mohaghegh, Mohammad Reza; Malekjafarian, Majid
2014-01-01
The present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady Euler and Navier-Stokes equations, using time spectral method (TSM) and compares it with the traditional methods like BDF and explicit structured adaptive grid method. The TSM uses a Fourier representation in time and hence solves for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. The TSM has been validated with 2D external aerodynamics test cases. These test cases are NACA 64A010 (CT6) and NACA 0012 (CT1 and CT5) pitching airfoils. Because of turbulent nature of flow, Baldwin-Lomax turbulence model has been used in viscous flow analysis with large oscillation amplitude (CT5 type). The results presented by the TSM are compared with experimental data and the two other methods. By enforcing periodicity and using Fourier representation in time that has a spectral accuracy, tremendous reduction of computational cost has been obtained compared to the conventional time-accurate methods. Results verify the small number of time intervals per pitching cycle (just four time intervals) required to capture the flow physics with small oscillation amplitude (CT6) and large oscillation amplitude (CT5) as compared to the other two methods.
Miniaturized Fourier-plane fiber scanner for OCT endoscopy
International Nuclear Information System (INIS)
Vilches, Sergio; Kretschmer, Simon; Ataman, Çağlar; Zappe, Hans
2017-01-01
A forward-looking endoscopic optical coherence tomography (OCT) probe featuring a Fourier-plane fiber scanner is designed, manufactured and characterized. In contrast to common image-plane fiber scanners, the Fourier-plane scanner is a telecentric arrangement that eliminates vignetting and spatial resolution variations across the image plane. To scan the OCT beam in a spiral pattern, a tubular piezoelectric actuator is used to resonate an optical fiber bearing a collimating GRIN lens at its tip. The free-end of the GRIN lens sits at the back focal plane of an objective lens, such that its rotation replicates the beam angles in the collimated region of a classical telecentric 4f optical system. Such an optical arrangement inherently has a low numerical aperture combined with a relatively large field-of-view, rendering it particularly useful for endoscopic OCT imaging. Furthermore, the optical train of the Fourier-plane scanner is shorter than that of a comparable image-plane scanner by one focal length of the objective lens, significantly shortening the final arrangement. As a result, enclosed within a 3D printed housing of 2.5 mm outer diameter and 15 mm total length, the developed probe is the most compact forward-looking endoscopic OCT imager to date. Due to its compact form factor and compatibility with real-time OCT imaging, the developed probe is also ideal for use in the working channel of flexible endoscopes as a potential optical biopsy tool. (paper)
Miniaturized Fourier-plane fiber scanner for OCT endoscopy
Vilches, Sergio; Kretschmer, Simon; Ataman, Çağlar; Zappe, Hans
2017-10-01
A forward-looking endoscopic optical coherence tomography (OCT) probe featuring a Fourier-plane fiber scanner is designed, manufactured and characterized. In contrast to common image-plane fiber scanners, the Fourier-plane scanner is a telecentric arrangement that eliminates vignetting and spatial resolution variations across the image plane. To scan the OCT beam in a spiral pattern, a tubular piezoelectric actuator is used to resonate an optical fiber bearing a collimating GRIN lens at its tip. The free-end of the GRIN lens sits at the back focal plane of an objective lens, such that its rotation replicates the beam angles in the collimated region of a classical telecentric 4f optical system. Such an optical arrangement inherently has a low numerical aperture combined with a relatively large field-of-view, rendering it particularly useful for endoscopic OCT imaging. Furthermore, the optical train of the Fourier-plane scanner is shorter than that of a comparable image-plane scanner by one focal length of the objective lens, significantly shortening the final arrangement. As a result, enclosed within a 3D printed housing of 2.5 mm outer diameter and 15 mm total length, the developed probe is the most compact forward-looking endoscopic OCT imager to date. Due to its compact form factor and compatibility with real-time OCT imaging, the developed probe is also ideal for use in the working channel of flexible endoscopes as a potential optical biopsy tool.
Fourier analysis of conductive heat transfer for glazed roofing materials
Energy Technology Data Exchange (ETDEWEB)
Roslan, Nurhana Lyana; Bahaman, Nurfaradila; Almanan, Raja Noorliyana Raja; Ismail, Razidah [Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia); Zakaria, Nor Zaini [Faculty of Applied Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia)
2014-07-10
For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heat transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate.
Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.
Caple, Jodi; Byrd, John; Stephan, Carl N
2017-11-01
The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.
Evaluation of gastric motility by Fourier analysis of condensed images
International Nuclear Information System (INIS)
Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K.
2000-01-01
In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)
The short time Fourier transform and local signals
Okumura, Shuhei
In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.
Error Analysis for Fourier Methods for Option Pricing
Häppölä, Juho
2016-01-06
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.
Evaluation of gastric motility by Fourier analysis of condensed images
Energy Technology Data Exchange (ETDEWEB)
Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K. [Dept. of Nuclear Medicine, Univ. of Munich, Munich (Germany)
2000-10-01
In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)
Taylor–Fourier spectra to study fractional order systems
International Nuclear Information System (INIS)
Barbé, Kurt; Lauwers, Lieve; Fuentes, Lee Gonzales
2016-01-01
In measurement science mathematical models are often used as an indirect measurement of physical properties which are mapped to measurands through the mathematical model. Dynamical systems describing a physical process with a dominant diffusion or dispersion phenomenon requires a large dimensional model due to its long memory. Ignoring a dominant difussion or dispersion component acts as a confounder which may introduce a bias in the estimated quantities of interest. For linear systems it has been observed that fractional order models outperform classical rational forms in terms of the number of parameters for the same fitting error. However it is not straightforward to deal with a fractional order system or long memory effects without prior knowledge. Since the parametric modeling of a fractional system is very involved, we put forward the question whether fractional insight can be gathered in a non-parametric way. In this paper we show that classical Fourier basis leading to the frequency response function lacks fractional insight. To circumvent this problem, we introduce a fractional Taylor–Fourier basis to obtain non-parametric insight in the fractional system. This analysis proposes a novel type of spectrum to visualize the spectral content of a fractional system: Taylor–Fourier spectrum. This spectrum is fully measurement driven which can be used as a first to explore the fractional dynamics of a measured diffusion or dispersion system. (paper)
Fourier acceleration in lattice gauge theories. I. Landau gauge fixing
International Nuclear Information System (INIS)
Davies, C.T.H.; Batrouni, G.G.; Katz, G.R.; Kronfeld, A.S.; Lepage, G.P.; Wilson, K.G.; Rossi, P.; Svetitsky, B.
1988-01-01
Fourier acceleration is a useful technique which can be applied to many different numerical algorithms in order to alleviate the problem of critical slowing down. Here we describe its application to an optimization problem in the simulation of lattice gauge theories, that of gauge fixing a configuration of link fields to the Landau gauge (partial/sub μ/A/sup μ/ = 0). We find that a steepest-descents method of gauge fixing link fields at β = 5.8 on an 8 4 lattice can be made 5 times faster using Fourier acceleration. This factor will grow as the volume of the lattice is increased. We also discuss other gauges that are useful to lattice-gauge-theory simulations, among them one that is a combination of the axial and Landau gauges. This seems to be the optimal gauge to impose for the Fourier acceleration of two other important algorithms, the inversion of the fermion matrix and the updating of gauge field configurations
The tomography inside of a Fourier Optics course: some opto-mechanical illustrative arrays
International Nuclear Information System (INIS)
Rodriguez Z, G.; Rodriguez V, R.; Luna C, A.
1999-01-01
The introduction of tomography as an advanced topic to be included in a Fourier optics course at graduated level is proposed. It is shown a possible presentation sequence which features the use of typical Fourier optics techniques, as well as some well known opto-mechanical devices as examples. Finally, a simplified apparatus which illustrates the central Fourier theorem as an experimental project on Fourier optics is described. Corresponding experimental results are also shown. (Author)
International Nuclear Information System (INIS)
Long, L.L.
1976-01-01
Fourier series and statistical communication theory techniques are utilized in the estimation of river water temperature increases caused by external thermal inputs. An example estimate assuming a constant thermal input is demonstrated. A regression fit of the Fourier series approximation of temperature is then used to forecast daily average water temperatures. Also, a 60-day prediction of daily average water temperature is made with the aid of the Fourier regression fit by using significant Fourier components
On the Cooley-Turkey Fast Fourier algorithm for arbitrary factors ...
African Journals Online (AJOL)
Atonuje and Okonta in [1] developed the Cooley-Turkey Fast Fourier transform algorithm and its application to the Fourier transform of discretely sampled data points N, expressed in terms of a power y of 2. In this paper, we extend the formalism of [1] Cookey-Turkey Fast Fourier transform algorithm. The method is developed ...
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
"Cracking Open the Natural Teleology": Walter Benjamin, Charles Fourier and the Figure of the Child
Dolbear, Sam; Proctor, Hannah
2016-01-01
The French utopian socialist Charles Fourier is a key figure in Walter Benjamin's "Arcades Project". For Benjamin, one of the most significant aspects of Fourier's utopian vision was its conceptualisation of work as a form of play. According to Fourier it would be possible to build a world around people's inherent desires. In such a…
Introduction to partial differential equations from Fourier series to boundary-value problems
Broman, Arne
2010-01-01
This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.
Mei, Liang; Svanberg, Sune
2015-03-20
This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.
[Continuum based fast Fourier transform processing of infrared spectrum].
Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai
2009-12-01
To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.
Deploying Fourier Coefficients to Unravel Soybean Canopy Diversity.
Jubery, Talukder Z; Shook, Johnathon; Parmley, Kyle; Zhang, Jiaoping; Naik, Hsiang S; Higgins, Race; Sarkar, Soumik; Singh, Arti; Singh, Asheesh K; Ganapathysubramanian, Baskar
2016-01-01
Soybean canopy outline is an important trait used to understand light interception ability, canopy closure rates, row spacing response, which in turn affects crop growth and yield, and directly impacts weed species germination and emergence. In this manuscript, we utilize a methodology that constructs geometric measures of the soybean canopy outline from digital images of canopies, allowing visualization of the genetic diversity as well as a rigorous quantification of shape parameters. Our choice of data analysis approach is partially dictated by the need to efficiently store and analyze large datasets, especially in the context of planned high-throughput phenotyping experiments to capture time evolution of canopy outline which will produce very large datasets. Using the Elliptical Fourier Transformation (EFT) and Fourier Descriptors (EFD), canopy outlines of 446 soybean plant introduction (PI) lines from 25 different countries exhibiting a wide variety of maturity, seed weight, and stem termination were investigated in a field experiment planted as a randomized complete block design with up to four replications. Canopy outlines were extracted from digital images, and subsequently chain coded, and expanded into a shape spectrum by obtaining the Fourier coefficients/descriptors. These coefficients successfully reconstruct the canopy outline, and were used to measure traditional morphometric traits. Highest phenotypic diversity was observed for roundness, while solidity showed the lowest diversity across all countries. Some PI lines had extraordinary shape diversity in solidity. For interpretation and visualization of the complexity in shape, Principal Component Analysis (PCA) was performed on the EFD. PI lines were grouped in terms of origins, maturity index, seed weight, and stem termination index. No significant pattern or similarity was observed among the groups; although interestingly when genetic marker data was used for the PCA, patterns similar to canopy
Quantitative lung perfusion evaluation using Fourier decomposition perfusion MRI.
Kjørstad, Åsmund; Corteville, Dominique M R; Fischer, Andre; Henzler, Thomas; Schmid-Bindert, Gerald; Zöllner, Frank G; Schad, Lothar R
2014-08-01
To quantitatively evaluate lung perfusion using Fourier decomposition perfusion MRI. The Fourier decomposition (FD) method is a noninvasive method for assessing ventilation- and perfusion-related information in the lungs, where the perfusion maps in particular have shown promise for clinical use. However, the perfusion maps are nonquantitative and dimensionless, making follow-ups and direct comparisons between patients difficult. We present an approach to obtain physically meaningful and quantifiable perfusion maps using the FD method. The standard FD perfusion images are quantified by comparing the partially blood-filled pixels in the lung parenchyma with the fully blood-filled pixels in the aorta. The percentage of blood in a pixel is then combined with the temporal information, yielding quantitative blood flow values. The values of 10 healthy volunteers are compared with SEEPAGE measurements which have shown high consistency with dynamic contrast enhanced-MRI. All pulmonary blood flow (PBF) values are within the expected range. The two methods are in good agreement (mean difference = 0.2 mL/min/100 mL, mean absolute difference = 11 mL/min/100 mL, mean PBF-FD = 150 mL/min/100 mL, mean PBF-SEEPAGE = 151 mL/min/100 mL). The Bland-Altman plot shows a good spread of values, indicating no systematic bias between the methods. Quantitative lung perfusion can be obtained using the Fourier Decomposition method combined with a small amount of postprocessing. Copyright © 2013 Wiley Periodicals, Inc.
Random sampling of evolution time space and Fourier transform processing
International Nuclear Information System (INIS)
Kazimierczuk, Krzysztof; Zawadzka, Anna; Kozminski, Wiktor; Zhukov, Igor
2006-01-01
Application of Fourier Transform for processing 3D NMR spectra with random sampling of evolution time space is presented. The 2D FT is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Signal to noise ratios and linewidths for different random distributions were investigated by simulations and experiments. The experimental examples include 3D HNCA, HNCACB and 15 N-edited NOESY-HSQC spectra of 13 C 15 N labeled ubiquitin sample. Obtained results revealed general applicability of proposed method and the significant improvement of resolution in comparison with conventional spectra recorded in the same time
Analysis of a thioether lubricant by infrared Fourier microemission spectrophotometry
Jones, W. R., Jr.; Morales, W.; Lauer, J. L.
1986-01-01
An infrared Fourier microemission spectrophotometer is used to obtain spectra (wavenumber range, 630 to 1230 0.1 cm) from microgram quantities of thioether lubricant samples deposited on aluminum foil. Infrared bands in the spectra are reproducible and could be identified as originating from aromatic species (1,3-disubstituted benzenes). Spectra from all samples (neat and formulated, used and unused) are very similar. Additives (an acid and a phosphinate) present in low concentration (0.10 percent) in the formulated fluid are not detected. This instrument appears to be a viable tool in helping to identify lubricant components separated by liquid chromatography.
Discrete Fourier Transform in a Complex Vector Space
Dean, Bruce H. (Inventor)
2015-01-01
An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.
Hochauflösende Fourier-Transform-Emissionsspektroskopie
Uibel, Christian
2000-01-01
Mittels hochauflösender Fourier-Transform-Infrarot-Emissionsspektroskopie wurden tiefliegende elektronische Anregungszustände der mittelschweren zweiatomigen Radikale As2, Sb2 und TeF untersucht. Dabei lag das Interesse vor allem bei den Emissionen nicht voll erlaubter Übergänge wie beispielsweise der 3Σ +u → 1Σ +g- bzw. (1u) → (0+g)-Übergänge bei den Stickstoff-Homologen. Dieses besondere Interesse an der genauen Analyse der 3Σ +u-Zustände liegt in ihrem metastab...
Magneto-sensor circuit efficiency incremented by Fourier-transformation
Talukdar, Abdul Hafiz Ibne; Useinov, Arthur; Hussain, Muhammad Mustafa
2011-01-01
In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.
Optical Two Dimensional Fourier Transform Spectroscopy of Layered Metal Dichalcogenides
Dey, P.; Paul, J.; Stevens, C. E.; Kovalyuk, Z. D.; Kudrynskyi, Z. R.; Romero, A. H.; Cantarero, A.; Hilton, D. J.; Shan, J.; Karaiskaj, D.; Z. D. Kovalyuk; Z. R. Kudrynskyi Collaboration; A. H. Romero Collaboration; A. Cantarero Collaboration; D. J. Hilton Collaboration; J. Shan Collaboration
2015-03-01
Nonlinear two-dimensional Fourier transform (2DFT) measurements were used to study the mechanism of excitonic dephasing and probe the electronic structure of the excitonic ground state in layered metal dichalcogenides. Temperature-dependent 2DFT measurements were performed to probe exciton-phonon interactions. Excitation density dependent 2DFT measurements reveal exciton-exciton and exciton-carrier scattering, and the lower limit for the homogeneous linewidth of excitons on positively and negatively doped samples. U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0012635.
Multi-band Image Registration Method Based on Fourier Transform
Institute of Scientific and Technical Information of China (English)
庹红娅; 刘允才
2004-01-01
This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features,they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.
An Interactive System For Fourier Analysis Of Artichoke Flower Shape.
Impedovo, Sebastiano; Fanelli, Anna M.; Ligouras, Panagiotis
1984-06-01
In this paper we present an interactive system which allows the Fourier analysis of the artichoke flower-head profile. The system consistsof a DEC pdp 11/34 computer with both a a track-following device and a Tektronix 4010/1 graphic and alpha numeric display on-line. Some experiments have been carried out taking into account some different parental types of artichoke flower-head samples. It is shown here that a narrow band of only eight harmonics is sufficient to classify different artichoke flower shapes.
A Fourier-based textural feature extraction procedure
Stromberg, W. D.; Farr, T. G.
1986-01-01
A procedure is presented to discriminate and characterize regions of uniform image texture. The procedure utilizes textural features consisting of pixel-by-pixel estimates of the relative emphases of annular regions of the Fourier transform. The utility and derivation of the features are described through presentation of a theoretical justification of the concept followed by a heuristic extension to a real environment. Two examples are provided that validate the technique on synthetic images and demonstrate its applicability to the discrimination of geologic texture in a radar image of a tropical vegetated area.
Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging
International Nuclear Information System (INIS)
Soloviev, Vadim Y.
2006-01-01
A novel adaptive mesh technique in the Fourier domain is introduced for problems in fluorescence lifetime imaging. A dynamical adaptation of the three-dimensional scheme based on the finite volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. Light propagation in the medium is modeled by the telegraph equation, while the lifetime reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the method are demonstrated by image reconstruction of two spherical fluorescent objects embedded in a tissue phantom
Magneto-sensor circuit efficiency incremented by Fourier-transformation
Talukdar, Abdul Hafiz Ibne
2011-10-01
In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.
An OTDM-To-WDM Converter Using Optical Fourier Transformation
Directory of Open Access Journals (Sweden)
Khin Su Myat Min
2015-08-01
Full Text Available We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements are expressed.
Directional short-time Fourier transform of distributions
Directory of Open Access Journals (Sweden)
Katerina Hadzi-Velkova Saneva
2016-04-01
Full Text Available Abstract In this paper we consider the directional short-time Fourier transform (DSTFT that was introduced and investigated in (Giv in J. Math. Anal. Appl. 399:100-107, 2013. We analyze the DSTFT and its transpose on test function spaces S ( R n $\\mathcal {S}(\\mathbb {R}^{n}$ and S ( Y 2 n $\\mathcal {S}(\\mathbb {Y}^{2n}$ , respectively, and prove the continuity theorems on these spaces. Then the obtained results are used to extend the DSTFT to spaces of distributions.
Hyperspectral imaging using the single-pixel Fourier transform technique
Jin, Senlin; Hui, Wangwei; Wang, Yunlong; Huang, Kaicheng; Shi, Qiushuai; Ying, Cuifeng; Liu, Dongqi; Ye, Qing; Zhou, Wenyuan; Tian, Jianguo
2017-03-01
Hyperspectral imaging technology is playing an increasingly important role in the fields of food analysis, medicine and biotechnology. To improve the speed of operation and increase the light throughput in a compact equipment structure, a Fourier transform hyperspectral imaging system based on a single-pixel technique is proposed in this study. Compared with current imaging spectrometry approaches, the proposed system has a wider spectral range (400-1100 nm), a better spectral resolution (1 nm) and requires fewer measurement data (a sample rate of 6.25%). The performance of this system was verified by its application to the non-destructive testing of potatoes.
Fourier transform infrared studies in solid egg white lysozyme
International Nuclear Information System (INIS)
Rivzi, T.Z.
1994-12-01
Fourier Transform Infrared (FTIR) Spectroscopy is the most recent addition to the arsenal of bioanalytical techniques capable of providing information about the secondary structure of proteins in a variety of environments. FTIR spectra have been obtained in solid egg white lysozyme. The spectra display the usual amide I, II and III bands. Secondary structural information obtained from the spectra after applying resolution enhancement techniques to the amide I band has been found consistent with the x-ray crystallographic data of the protein and also to the spectroscopic data of the protein in aqueous solution. (author). 17 refs, 6 figs, 2 tabs
Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions
Morelli, Eugene A.
2013-01-01
A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.
High-resolution extraction of particle size via Fourier Ptychography
Li, Shengfu; Zhao, Yu; Chen, Guanghua; Luo, Zhenxiong; Ye, Yan
2017-11-01
This paper proposes a method which can extract the particle size information with a resolution beyond λ/NA. This is achieved by applying Fourier Ptychographic (FP) ideas to the present problem. In a typical FP imaging platform, a 2D LED array is used as light sources for angle-varied illuminations, a series of low-resolution images was taken by a full sequential scan of the array of LEDs. Here, we demonstrate the particle size information is extracted by turning on each single LED on a circle. The simulated results show that the proposed method can reduce the total number of images, without loss of reliability in the results.
The discrete Fourier transform theory, algorithms and applications
Sundaraajan, D
2001-01-01
This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and
Capillary supercritical fluid chromatography - Fourier transform infrared spectrometry
International Nuclear Information System (INIS)
Olesik, S.V.; French, S.B.; Movotny, M.
1984-01-01
One of the most demanding tasks asked of an analytical chemist today is to separate and identify the components of a nonvolatile complex mixture. An efficient separation technique combined with a universal detector that provides structural information, therefore, would be a great asset to analytical chemists. Capillary supercritical fluid chromatography (SFC) - Fourier transform infrared spectrometry (FTIR) shows great potential for being such a technique. SFC-FTIR shows great potential as a very powerful technique for separation and identification of thermally labile and nonvolatile compounds. Research is continuing in these labs to further optimize the technique. 2 refs
On the equisummability of Hermite and Fourier expansions
Indian Academy of Sciences (India)
is the Fourier transform on Rn. Let ب ; 2 Nn be the n-dimensional Hermite functions which are eigenfunctions of the Hermite operator H ¼ ہء jxj. 2 with the eigenvalue. ً2j j nق where j j ¼ 1 ءءء n. Let Pk be the orthogonal projection of L 2ًRnق onto the kth eigenspace spanned by ب ; j j ¼ k. More precisely,. Pk fًxق ¼. X j j¼k. Z.
Valuation of European Call Option via Inverse Fourier Transform
Directory of Open Access Journals (Sweden)
Rubenis Oskars
2017-12-01
Full Text Available Very few models allow expressing European call option price in closed form. Out of them, the famous Black- Scholes approach sets strong constraints - innovations should be normally distributed and independent. Availability of a corresponding characteristic function of log returns of underlying asset in analytical form allows pricing European call option by application of inverse Fourier transform. Characteristic function corresponds to Normal Inverse Gaussian (NIG probability density function. NIG distribution is obtained based on assumption that time series of log returns follows APARCH process. Thus, volatility clustering and leptokurtic nature of log returns are taken into account. The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used. To solve the problem, a dampened cumulative probability is introduced. As a computation tool Matlab framework is chosen because it contains many effective vectorization tools that greatly enhance code readability and maintenance. The characteristic function of Normal Inverse Gaussian distribution is taken and exercised with the chosen set of parameters. Finally, the call price dependence on strike price is obtained and rendered in XY plot. Valuation of European call option with analytical form of characteristic function allows further developing models with higher accuracy, as well as developing models for some exotic options.
Influences of overlap index on Fourier ptychography imaging
Wang, Honghong; Rong, Lu; Wang, Dayong; Zhang, Xu; Zhai, Changchao; Panezai, Spozmai; Wang, Yunxin; Zhao, Jie
2018-01-01
Fourier ptychography is a new type of synthetic aperture imaging technique based on phase retrieval method which can improve microscopeic imaging performance beyond the diffraction limit of the employed optical components by illuminating the object with oblique waves of different incident angles where the field of view remains unchanged. illumination angle and the overlap rate of spectrum will have a certain impact on the quality of reconstruction. In this paper, we study the effects of illumination angle and spectral overlap rate on the image quality of Fourier ptychography. The simulation results show that increasing the illumination angle and spectral overlap can improve the resolution, but there is a threshold for the key parameters of spectral overlap rate. The convergence rate decreases when the overlap rate exceeds 70%, and the reconstruction process is more time-consuming due to the high overlap rate. However the results of proposed study shows that an overlap of 60% is the optimal choice to acquire a high-quality recovery with high speed.
The gridding method for image reconstruction by Fourier transformation
International Nuclear Information System (INIS)
Schomberg, H.; Timmer, J.
1995-01-01
This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f. The method involves a window function w and proceeds in three steps. First, the convolution g = w * f is computed numerically on a Cartesian grid, using the available samples of f. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w * f is much less error prone than merely interpolating f. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Directory of Open Access Journals (Sweden)
Ovidiu Hâruţa
2011-02-01
Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage developmentof the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, mass center, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.
Elliptic Fourier analysis of crown shapes in Quercus petraea trees
Directory of Open Access Journals (Sweden)
Ovidiu Hâruţa
2011-06-01
Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage development of the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, centroid position, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.
Vector Radix 2 × 2 Sliding Fast Fourier Transform
Directory of Open Access Journals (Sweden)
Keun-Yung Byun
2016-01-01
Full Text Available The two-dimensional (2D discrete Fourier transform (DFT in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT algorithm based on the vector radix (VR 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.
Non-Harmonic Fourier Analysis for bladed wheels damage detection
Neri, P.; Peeters, B.
2015-11-01
The interaction between bladed wheels and the fluid distributed by the stator vanes results in cyclic loading of the rotating components. Compressors and turbines wheels are subject to vibration and fatigue issues, especially when resonance conditions are excited. Even if resonance conditions can be often predicted and avoided, high cycle fatigue failures can occur, causing safety issues and economic loss. Rigorous maintenance programs are then needed, forcing the system to expensive shut-down. Blade crack detection methods are beneficial for condition-based maintenance. While contact measurement systems are not always usable in exercise conditions (e.g. high temperature), non-contact methods can be more suitable. One (or more) stator-fixed sensor can measure all the blades as they pass by, in order to detect the damaged ones. The main drawback in this situation is the short acquisition time available for each blade, which is shortened by the high rotational speed of the components. A traditional Discrete Fourier Transform (DFT) analysis would result in a poor frequency resolution. A Non-Harmonic Fourier Analysis (NHFA) can be executed with an arbitrary frequency resolution instead, allowing to obtain frequency information even with short-time data samples. This paper shows an analytical investigation of the NHFA method. A data processing algorithm is then proposed to obtain frequency shift information from short time samples. The performances of this algorithm are then studied by experimental and numerical tests.
Progress report of a static Fourier transform spectrometer breadboard
Rosak, A.; Tintó, F.
2017-11-01
MOLI instrument -for MOtionLess Interferometer- takes advantage of the new concept of static Fourier transform spectrometer. It is a high-resolution spectrometer working over a narrow bandwidth, which is adapted to a wide range of atmospheric sounding missions and compatible with micro-satellite platform. The core of this instrument is an echelette cube. Mirrors on the classical design are replaced by stepped mirrors -integrated into that interference cube- thus suppressing any moving part. The steps' directions being set over a perpendicular axis, the overlap of both stepped mirrors creates a cluster of so-called "echelettes", each one corresponding to a different optical path difference (OPD). Hence the Fourier transform of the incoming radiance is directly imaged on a CCD array in a single acquisition. The frequency domain of the measurements is selected by an interferential filter disposed on the incoming optical path. A rotating wheel equipped with several filters allows the successive measurement of spectra around some bands of interest, i.e. O2, CO2 and CO absorption bands.
Ultrafast and versatile spectroscopy by temporal Fourier transform
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.
2014-06-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.
Fourier-based automatic alignment for improved Visual Cryptography schemes.
Machizaud, Jacques; Chavel, Pierre; Fournel, Thierry
2011-11-07
In Visual Cryptography, several images, called "shadow images", that separately contain no information, are overlapped to reveal a shared secret message. We develop a method to digitally register one printed shadow image acquired by a camera with a purely digital shadow image, stored in memory. Using Fourier techniques derived from Fourier Optics concepts, the idea is to enhance and exploit the quasi periodicity of the shadow images, composed by a random distribution of black and white patterns on a periodic sampling grid. The advantage is to speed up the security control or the access time to the message, in particular in the cases of a small pixel size or of large numbers of pixels. Furthermore, the interest of visual cryptography can be increased by embedding the initial message in two shadow images that do not have identical mathematical supports, making manual registration impractical. Experimental results demonstrate the successful operation of the method, including the possibility to directly project the result onto the printed shadow image.
Soft x-ray microscope using Fourier transform holography
International Nuclear Information System (INIS)
McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H.
1989-01-01
A Fourier transform holographic microscope with an anticipated resolution of better than 100 nm has been built. Extensive testing of the apparatus has begun. Preliminary results include the recording of interference fringes using 3.6 nm x-rays. The microscope employs a charge-coupled device (CCD) detector array of 576 x 384 elements. The system is illuminated by soft x-rays from a high brightness undulator. The reference point source is formed by a Fresnel zone plate with a finest outer zone width of 50 nm. Sufficient temporal coherence for hologram formation is obtained by a spherical grating monochromator. The x-ray hologram intensities at the recording plane are to be collected, digitized and reconstructed by computer. Data acquisition is under CAMAC control, while image display and off-line processing takes place on a VAX graphics workstation. Computational models of Fourier transform hologram synthesis, and reconstruction in the presence of noise, have demonstrated the feasibility of numerical methods in two dimensions, and that three-dimensional information is potentially recoverable. 13 refs., 3 figs
Gas Measurement Using Static Fourier Transform Infrared Spectrometers.
Köhler, Michael H; Schardt, Michael; Rauscher, Markus S; Koch, Alexander W
2017-11-13
Online monitoring of gases in industrial processes is an ambitious task due to adverse conditions such as mechanical vibrations and temperature fluctuations. Whereas conventional Fourier transform infrared (FTIR) spectrometers use rather complex optical and mechanical designs to ensure stable operation, static FTIR spectrometers do not require moving parts and thus offer inherent stability at comparatively low costs. Therefore, we present a novel, compact gas measurement system using a static single-mirror Fourier transform spectrometer (sSMFTS). The system works in the mid-infrared range from 650 cm - 1 to 1250 cm - 1 and can be operated with a customized White cell, yielding optical path lengths of up to 120 cm for highly sensitive quantification of gas concentrations. To validate the system, we measure different concentrations of 1,1,1,2-Tetrafluoroethane (R134a) and perform a PLS regression analysis of the acquired infrared spectra. Thereby, the measured absorption spectra show good agreement with reference data. Since the system additionally permits measurement rates of up to 200 Hz and high signal-to-noise ratios, an application in process analysis appears promising.
X-ray stress measurement of ferritic steel using fourier analysis of Debye-Scherrer ring
International Nuclear Information System (INIS)
Fujimoto, Yohei; Sasaki, Toshihiko; Miyazaki, Toshiyuki
2015-01-01
In this study, X-ray stress measurements of ferritic steel based on Fourier analysis are conducted. Taira et al. developed the cosα method for X-ray stress measurements using a two-dimensional X-ray detector. Miyazaki et al. reported that the cosα method can be described more concisely by developing the Fourier series (the Fourier analysis method). The Fourier analysis method is expected to yield the stress measurement with an imperfect Debye-Scherrer ring and there is a possibility that the materials evaluation is different compared with the conventional method, that is, the sin 2 ψ method. In the Fourier analysis method, the strain measured by X-rays is developed as a Fourier series, and all the plane-stress components can be calculated from the Fourier series. In this study, the normal stress calculation was confirmed. In addition, the Fourier-analysis and cosα methods were used for X-ray stress measurements during a four-point bending test on a S45C test piece, and the effectiveness of the Fourier analysis method was confirmed. It was found that the experimental results from the Fourier analysis and cosα methods were nearly identical. In addition, the measurement accuracies of both the methods were equivalent. (author)
Zasova, L. V.; Moroz, V. I.; Formisano, V.; Ignatiev, N. I.; Khatuntsev, I. V.
2006-07-01
The infrared spectrometry of Venus in the range 6-45 μm allows one to sound the middle atmosphere of Venus in the altitude range 55-100 km and its cloud layer. This experiment was carried out onboard the Soviet automatic interplanetary Venera-15 station, where the Fourier spectrometer for this spectral range was installed. The measurements have shown that the main component of the cloud layer at all measured latitudes in the northern hemisphere is concentrated sulfuric acid (75-85%). The vertical profiles of temperature and aerosol were reconstructed in a self-consistent manner: the three-dimensional fields of temperature and zonal wind in the altitude range 55-100 km and aerosol at altitudes 55-70 km have been obtained, as well as vertical SO2 profiles and H2O concentration in the upper cloud layer. The solar-related waves at isobaric levels in the fields of temperature, zonal wind, and aerosol were investigated. This experiment has shown the efficiency of the method for investigation of the Venusian atmosphere. The Planetary Fourier Spectrometer has the spectral interval 0.9-45 μm and a spectral resolution of 1.8 cm-1. It will allow one to sound the middle atmosphere (55-100 km) of Venus and its cloud layer on the dayside, as well as the lower atmosphere and the planetary surface on the night side.
PFS: the Planetary Fourier Spectrometer for Mars Express
Formisano, V.; Grassi, D.; Orfei, R.; Biondi, D.; Mencarelli, E.; Mattana, A.; Nespoli, F.; Maturilli, A.; Giuranna, M.; Rossi, M.; Maggi, M.; Baldetti, P.; Chionchio, G.; Saggin, B.; Angrilli, F.; Bianchini, G.; Piccioni, G.; di Lellis, A.; Cerroni, P.; Capaccioni, F.; Capria, M. T.; Coradini, A.; Fonti, S.; Orofino, V.; Blanco, A.; Colangeli, L.; Palomba, E.; Esposito, F.; Patsaev, D.; Moroz, V.; Zasova, L.; Ignatiev, N.; Khatuntsev, I.; Moshkin, B.; Ekonomov, A.; Grigoriev, A.; Nechaev, V.; Kiselev, A.; Nikolsky, Y.; Gnedykh, V.; Titov, D.; Orleanski, P.; Rataj, M.; Malgoska, M.; Jurewicz, A.; Blecka, M. I.; Hirsh, H.; Arnold, G.; Lellouch, E.; Marten, A.; Encrenaz, T.; Lopez Moreno, J.; Atreya, S., Gobbi, P.
2004-08-01
The Planetary Fourier Spectrometer (PFS) for the Mars Express mission is optimised for atmospheric studies, covering the IR range of 1.2-45 μm in two channels. The apodised spectral resolution is 2 cm-1, while the sampling is 1 cm-1. The FOV is about 2° for the short wavelength (SW) channel and 4° for the long wavelength (LW) channel, corresponding to spatial resolutions of 10 km and 20 km, respectively, from an altitude of 300 km. PFS will also provide unique data on the surface-atmosphere interaction and the mineralogical composition of the surface. It will be the first Fourier spectrometer covering 1-5 μm to orbit the Earth or Mars. The experiment has real-time onboard Fast Fourier Transform (FFT) in order to select the spectral range of interest for data transmission to ground. Measurement of the 15-μm CO2 band is very important. Its profile gives, via a complex temperature-profile retrieval technique, the vertical pressure temperature relation, which is the basis of the global atmospheric study. The SW channel uses a PbSe detector cooled to 200-220K, while the LW channel is based on a pyroelectric (LiTaO3) device working at room temperature. The interferogram is measured at every 150 nm displacement step of the corner cube retroreflectors (corresponding to 600 nm optical path difference) via a laser diode monochromatic interferogram (a sine wave), with the zero crossings controlling the double pendulum motion. PFS will operate for about 1.5 h around the pericentre of the orbit. With a measurement every 10 s, 600 measurements per orbit will be acquired, corresponding to 224 Mbit. Onboard compression will reduce it to 125 Mbit or less, depending on the allocated data volume per day. An important requirement is to observe at all local times in order to include night-side vertical temperature profiles. Total instrument mass is 31.2 kg.
A high-resolution Fourier Transform Spectrometer for planetary spectroscopy
Cruikshank, D. P.; Sinton, W. M.
1973-01-01
The employment of a high-resolution Fourier Transform Spectrometer (FTS) is described for planetary and other astronomical spectroscopy in conjunction with the 88-inch telescope at Mauna Kea Observatory. The FTS system is designed for a broad range of uses, including double-beam laboratory spectroscopy, infrared gas chromatography, and nuclear magnetic resonance spectroscopy. The data system is well-suited to astronomical applications because of its great speed in acquiring and transforming data, and because of the enormous storage capability of the magnetic tape unit supplied with the system. The basic instrument is outlined 2nd some of the initial results from the first attempted use on the Mauna Kea 88-inch telescope are reported.
High-Throughput Screening Using Fourier-Transform Infrared Imaging
Directory of Open Access Journals (Sweden)
Erdem Sasmaz
2015-06-01
Full Text Available Efficient parallel screening of combinatorial libraries is one of the most challenging aspects of the high-throughput (HT heterogeneous catalysis workflow. Today, a number of methods have been used in HT catalyst studies, including various optical, mass-spectrometry, and gas-chromatography techniques. Of these, rapid-scanning Fourier-transform infrared (FTIR imaging is one of the fastest and most versatile screening techniques. Here, the new design of the 16-channel HT reactor is presented and test results for its accuracy and reproducibility are shown. The performance of the system was evaluated through the oxidation of CO over commercial Pd/Al2O3 and cobalt oxide nanoparticles synthesized with different reducer-reductant molar ratios, surfactant types, metal and surfactant concentrations, synthesis temperatures, and ramp rates.
A Fourier transform with speed improvements for microprocessor applications
Lokerson, D. C.; Rochelle, R.
1980-01-01
A fast Fourier transform algorithm for the RCA 1802microprocessor was developed for spacecraft instrument applications. The computations were tailored for the restrictions an eight bit machine imposes. The algorithm incorporates some aspects of Walsh function sequency to improve operational speed. This method uses a register to add a value proportional to the period of the band being processed before each computation is to be considered. If the result overflows into the DF register, the data sample is used in computation; otherwise computation is skipped. This operation is repeated for each of the 64 data samples. This technique is used for both sine and cosine portions of the computation. The processing uses eight bit data, but because of the many computations that can increase the size of the coefficient, floating point form is used. A method to reduce the alias problem in the lower bands is also described.
Using the fast fourier transform in binding free energy calculations.
Nguyen, Trung Hai; Zhou, Huan-Xiang; Minh, David D L
2018-04-30
According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Preservation of information in Fourier theory based deconvolved nuclear spectra
International Nuclear Information System (INIS)
Madan, V.K.; Gopalakrishnan, K.R.; Sharma, R.C.; Rattan, S.S.
1995-01-01
Nuclear spectroscopy is extremely useful to the internal radiation dosimetry for the estimation of body burden due to gamma emitters. Analysis of nuclear spectra is concerned with the extraction of qualitative and quantitative information embedded in the spectra. A spectral deconvolution method based on Fourier theory is probably the simplest method of deconvolving nuclear spectra. It is proved mathematically that the deconvolution method preserves the qualitative information. It is shown by using simulated spectra and an observed gamma ray spectrum that the method preserves the quantitative information. This may provide a novel approach of information extraction from a deconvolved spectrum. The paper discusses the methodology, mathematical analysis, and the results obtained by deconvolving spectra. (author). 6 refs., 2 tabs
Optical polarimeter based on Fourier analysis and electronic control
International Nuclear Information System (INIS)
Vilardy, J; Salas, V.; Torres, C.
2016-01-01
In this paper, we show the design and implementation of an optical polarimeter using electronic control and the Fourier analysis. The polarimeter prototype will be used as a main tool for the students of the Universidad Popular del Cesar that belong to the following university programs: Electronics engineering (optoelectronics area), Math and Physics degree and the Master in Physics Sciences, in order to learning the theory and experimental aspects of the state of optical polarization via the Stokes vector measurement. Using the electronic polarimeter proposed in this paper, the students will be able to observe (in an optical bench) and understand the different interactions of the states of optical polarization when the optical waves pass through to the polarizers and retarder waves plates. The electronic polarimeter has a software that captures the optical intensity measurement and evaluates the Stokes vector. (Author)
Collision-induced dissociation with Fourier transform mass spectrometry
International Nuclear Information System (INIS)
Cody, R.B.; Burnier, R.C.; Freiser, B.S.
1982-01-01
Collision-induced dissociations (CID) is demonstrated on a number of primary and secondary ions using a Nicolet prototype Fourier transform mass spectrometer (FT-MS). Like the triple quadrupole technique, CID using FT-MS is a relatively low energy and efficient process. The ability to study a wide range of ion-molecule reaction products is exemplified by results on proton-bound dimers and transition metal containing ionic species. Variation of collision energy by varying the RF irradiation level can provide information about product distributions as a function of energy as well as yield ion structural information. Like the triple quadrupole technique, no slits are employed and virtually all of the fragment ions formed by the CID process may be detected. Unlike all previous mass spectrometric techniques for studying CID, a tandem instrument is not required, and different experiments are performed by making software modifications rather than hardware modifications
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses
Lim, Lucy; Yan, Fangzhi; Bach, Stephen; Pihakari, Katianna; Klein, David
2016-01-01
Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS) has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices. PMID:26784175
Seismic Shear Energy Reflection By Radon-Fourier Transform
Directory of Open Access Journals (Sweden)
Malik Umairia
2016-01-01
Full Text Available Seismic waves split in an anisotropic medium, instead of rotating horizontal component to principal direction, Radon-Fourier is derived to observe the signature of shear wave reflection. Synthetic model with fracture is built and discretized using finite difference scheme for spatial and time domain. Common depth point (CDP with single shot gives traces and automatic gain is preprocessed before Radon Transform (RT, a filtering technique gives radon domain. It makes easier to observe fractures at specific incidence and improves its quality in some way by removing the noise. A comparison of synthetic data and BF-data is performed on the basis of root means square error (RMS values. The RMS error is minimum at the 10th trace in radon domain.
Closed form fourier-based transmit beamforming for MIMO radar
Lipor, John J.
2014-05-01
In multiple-input multiple-output (MIMO) radar setting, it is often desirable to design correlated waveforms such that power is transmitted only to a given set of locations, a process known as beampattern design. To design desired beam-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform and Toeplitz matrix. The resulting covariance matrix fulfills the practical constraints and performance is similar to that of iterative methods. Next, we present a radar architecture for the desired beampattern that does not require the synthesis of covariance matrix nor the design of correlated waveforms. © 2014 IEEE.
A rheumatoid arthritis study by Fourier transform infrared spectroscopy
Carvalho, Carolina S.; Silva, Ana Carla A.; Santos, Tatiano J. P. S.; Martin, Airton A.; dos Santos Fernandes, Ana Célia; Andrade, Luís E.; Raniero, Leandro
2012-01-01
Rheumatoid arthritis is a systemic inflammatory disease of unknown causes and a new methods to identify it in early stages are needed. The main purpose of this work is the biochemical differentiation of sera between normal and RA patients, through the establishment of a statistical method that can be appropriately used for serological analysis. The human sera from 39 healthy donors and 39 rheumatics donors were collected and analyzed by Fourier Transform Infrared Spectroscopy. The results show significant spectral variations with p<0.05 in regions corresponding to protein, lipids and immunoglobulins. The technique of latex particles, coated with human IgG and monoclonal anti-CRP by indirect agglutination known as FR and CRP, was performed to confirm possible false-negative results within the groups, facilitating the statistical interpretation and validation of the technique.
Fourier transforms in NMR, optical, and mass spectrometry
International Nuclear Information System (INIS)
Marshall, A.G.; Verdun, F.R.; Ohio State Univ., Columbus, OH
1990-01-01
This book is a teaching and reference text for Fourier transform methods as they are applied in spectroscopy. It offers a unified treatment of the three most popular types of FT/spectroscopy. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g., use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance versus off-resonance response; interpolation; ultimate accuracy of discrete representation of an analog signal; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc. (author). refs.; figs.; tabs
Quantum Fourier transform, Heisenberg groups and quasi-probability distributions
International Nuclear Information System (INIS)
Patra, Manas K; Braunstein, Samuel L
2011-01-01
This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl-Gabor-Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.
Closed fringe demodulation using phase decomposition by Fourier basis functions.
Kulkarni, Rishikesh; Rastogi, Pramod
2016-06-01
We report a new technique for the demodulation of a closed fringe pattern by representing the phase as a weighted linear combination of a certain number of linearly independent Fourier basis functions in a given row/column at a time. A state space model is developed with the weights of the basis functions as the elements of the state vector. The iterative extended Kalman filter is effectively utilized for the robust estimation of the weights. A coarse estimate of the fringe density based on the fringe frequency map is used to determine the initial row/column to start with and subsequently the optimal number of basis functions. The performance of the proposed method is evaluated with several noisy fringe patterns. Experimental results are also reported to support the practical applicability of the proposed method.
Instantaneous lineshape analysis of Fourier domain mode-locked lasers.
Todor, Sebastian; Biedermann, Benjamin; Wieser, Wolfgang; Huber, Robert; Jirauschek, Christian
2011-04-25
We present a theoretical and experimental analysis of the instantaneous lineshape of Fourier domain mode-locked (FDML) lasers, yielding good agreement. The simulations are performed employing a recently introduced model for FDML operation. Linewidths around 10 GHz are found, which is significantly below the sweep filter bandwidth. The effect of detuning between the sweep filter drive frequency and cavity roundtrip time is studied revealing features that cannot be resolved in the experiment, and shifting of the instantaneous power spectrum against the sweep filter center frequency is analyzed. We show that, in contrast to most other semiconductor based lasers, the instantaneous linewidth is governed neither by external noise sources nor by amplified spontaneous emission, but it is directly determined by the complex FDML dynamics.
Live face detection based on the analysis of Fourier spectra
Li, Jiangwei; Wang, Yunhong; Tan, Tieniu; Jain, Anil K.
2004-08-01
Biometrics is a rapidly developing technology that is to identify a person based on his or her physiological or behavioral characteristics. To ensure the correction of authentication, the biometric system must be able to detect and reject the use of a copy of a biometric instead of the live biometric. This function is usually termed "liveness detection". This paper describes a new method for live face detection. Using structure and movement information of live face, an effective live face detection algorithm is presented. Compared to existing approaches, which concentrate on the measurement of 3D depth information, this method is based on the analysis of Fourier spectra of a single face image or face image sequences. Experimental results show that the proposed method has an encouraging performance.
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses
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Lucy Lim
2016-01-01
Full Text Available Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices.
Analysis of cigarette smoke by Fourier transform infrared spectrometry
Energy Technology Data Exchange (ETDEWEB)
Maddox, W.L. (Oak Ridge National Lab., TN); Mamantov, G.
1977-02-01
The application of Fourier transform infrared spectrometry (FT-IR) to the quantitative determination of several components in the gas phase of whole, dilute tobacco smoke was demonstrated. The 18-cm absorption cell was part of a cigarette smoking system similar to the intermittent inhalation exposure devices used in smoking and health research with rodents. Concentrations were measured for carbon monoxide, carbon dioxide, methane, ethylene, and methanol in 7 to 22% smoke. The precision of a measurement in 22% smoke ranged from 3% for carbon dioxide to 34% for ethylene. Absorbances measured for isoprene and hydrogen cyanide followed expected concentrations in different cigarette smokes. It was shown that the concentrations of these components remain constant during a 30-s hold-up following each puff on the cigarettes.