Application of multibounce attenuated total reflectance fourier transform infrared spectroscopy and chemometrics for determination of aspartame in soft drinks.

Science.gov (United States)

Khurana, Harpreet Kaur; Cho, Il Kyu; Shim, Jae Yong; Li, Qing X; Jun, Soojin

2008-02-13

Aspartame is a low-calorie sweetener commonly used in soft drinks; however, the maximum usage dose is limited by the U.S. Food and Drug Administration. Fourier transform infrared (FTIR) spectroscopy with attenuated total reflectance sampling accessory and partial least-squares regression (PLS) was used for rapid determination of aspartame in soft drinks. On the basis of spectral characterization, the highest R2 value, and lowest PRESS value, the spectral region between 1600 and 1900 cm(-1) was selected for quantitative estimation of aspartame. The potential of FTIR spectroscopy for aspartame quantification was examined and validated by the conventional HPLC method. Using the FTIR method, aspartame contents in four selected carbonated diet soft drinks were found to average from 0.43 to 0.50 mg/mL with prediction errors ranging from 2.4 to 5.7% when compared with HPLC measurements. The developed method also showed a high degree of accuracy because real samples were used for calibration, thus minimizing potential interference errors. The FTIR method developed can be suitably used for routine quality control analysis of aspartame in the beverage-manufacturing sector.

Rainbow Fourier Transform

Science.gov (United States)

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).

Application of micro-attenuated total reflectance Fourier transform infrared spectroscopy to ink examination in signatures written with ballpoint pen on questioned documents.

Science.gov (United States)

Nam, Yun Sik; Park, Jin Sook; Lee, Yeonhee; Lee, Kang-Bong

2014-05-01

Questioned documents examined in a forensic laboratory sometimes contain signatures written with ballpoint pen inks; these signatures were examined to assess the feasibility of micro-attenuated total reflectance (ATR) Fourier transform infrared (FTIR) spectroscopy as a forensic tool. Micro-ATR FTIR spectra for signatures written with 63 ballpoint pens available commercially in Korea were obtained and used to construct an FTIR spectral database. A library-searching program was utilized to identify the manufacturer, blend, and model of each black ballpoint pen ink based upon their FTIR peak intensities, positions, and patterns in the spectral database. This FTIR technique was also successfully used in determining the sequence of homogeneous line intersections from the crossing lines of two ballpoint pen signatures. We have demonstrated with a set of sample documents that micro-ATR FTIR is a viable nondestructive analytical method that can be used to identify the origin of the ballpoint pen ink used to mark signatures. © 2014 American Academy of Forensic Sciences.

Fourier-transform imaging of cotton and botanical and field trash mixtures

Science.gov (United States)

Botanical and field cotton trash comingled with cotton lint can greatly reduce the marketability and quality of cotton. Trash can be found comingled with cotton lint during harvesting, ginning, and processing, thus this study is of interest. Attenuated Total Reflectance-Fourier Transform Infrared (A...

Characterization and quantitation of aprepitant drug substance polymorphs by attenuated total reflectance fourier transform infrared spectroscopy.

Science.gov (United States)

Helmy, Roy; Zhou, George X; Chen, Yadan W; Crocker, Louis; Wang, Tao; Wenslow, Robert M; Vailaya, Anant

2003-02-01

In this study, we report the use of attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FT-IR) for the identification and quantitation of two polymorphs of Aprepitant, a substance P antagonist for chemotherapy-induced emesis. Mixtures of the polymorph pair were prepared by weight and ATR-FT-IR spectra of the powdered samples were obtained over the wavelength range of 700-1500 cm(-1). Significant spectral differences between the two polymorphs at 1140 cm(-1) show that ATR-FT-IR can provide definitive identification of the polymorphs. To investigate the feasibility of ATR-FT-IR for quantitation of polymorphic forms of Aprepitant, a calibration plot was constructed with known mixtures of the two polymorphs by plotting the peak ratio of the second derivative of absorbance spectra against the weight percent of form II in the polymorphic mixture. Using this novel approach, 3 wt % of one crystal form could be detected in mixtures of the two polymorphs. The accuracy of ATR-FT-IR in determining polymorph purity of the drug substance was tested by comparing the results with those obtained by X-ray powder diffractometry (XRPD). Indeed, polymorphic purity results obtained by ATR-FT-IR were found to be in good agreement with the predictions made by XRPD and compared favorably with actual values in the known mixtures. The present study clearly demonstrates the potential of ATR-FT-IR as a quick, easy, and inexpensive alternative to XRPD for the determination of polymorphic identity and purity of solid drug substances. The technique is ideally suited for polymorph analysis, because it is precise, accurate, and requires minimal sample preparation.

Fourier transform NMR

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

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

Diffuse-reflectance fourier-transform mid-infrared spectroscopy as a method of characterizing changes in soil organic matter

Science.gov (United States)

Diffuse-Reflectance Fourier-Transform Mid-Infrared Spectroscopy (MidIR) can identify the presence of important organic functional groups in soil organic matter (SOM). Soils contain myriad organic and inorganic components that absorb in the MidIR so spectral interpretation needs to be validated in or...

A Catalytic Path for Electrolyte Reduction in Lithium-Ion Cells Revealed by in Situ Attenuated Total Reflection-Fourier Transform Infrared Spectroscopy

KAUST Repository

Shi, Feifei; Ross, Philip N.; Zhao, Hui; Liu, Gao; Somorjai, Gabor A.; Komvopoulos, Kyriakos

2015-01-01

© 2015 American Chemical Society. Although controlling the interfacial chemistry of electrodes in Li-ion batteries (LIBs) is crucial for maintaining the reversibility, electrolyte decomposition has not been fully understood. In this study, electrolyte decomposition on model electrode surfaces (Au and Sn) was investigated by in situ attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy. Simultaneously obtained ATR-FTIR spectra and cyclic voltammetry measurements show that lithium ethylene dicarbonate and lithium propionate form on the Au electrode at 0.6 V, whereas diethyl 2,5-dioxahexane dicarboxylate and lithium propionate form on the Sn electrode surface at 1.25 V. A noncatalytic reduction path on the Au surface and a catalytic reduction path on the Sn surface are introduced to explain the surface dependence of the overpotential and product selectivity. This represents a new concept for explaining electrolyte reactions on the anode of LIBs. The present investigation shows that catalysis plays a dominant role in the electrolyte decomposition process and has important implications in electrode surface modification and electrolyte recipe selection, which are critical factors for enhancing the efficiency, durability, and reliability of LIBs.

A Catalytic Path for Electrolyte Reduction in Lithium-Ion Cells Revealed by in Situ Attenuated Total Reflection-Fourier Transform Infrared Spectroscopy

KAUST Repository

Shi, Feifei

2015-03-11

© 2015 American Chemical Society. Although controlling the interfacial chemistry of electrodes in Li-ion batteries (LIBs) is crucial for maintaining the reversibility, electrolyte decomposition has not been fully understood. In this study, electrolyte decomposition on model electrode surfaces (Au and Sn) was investigated by in situ attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy. Simultaneously obtained ATR-FTIR spectra and cyclic voltammetry measurements show that lithium ethylene dicarbonate and lithium propionate form on the Au electrode at 0.6 V, whereas diethyl 2,5-dioxahexane dicarboxylate and lithium propionate form on the Sn electrode surface at 1.25 V. A noncatalytic reduction path on the Au surface and a catalytic reduction path on the Sn surface are introduced to explain the surface dependence of the overpotential and product selectivity. This represents a new concept for explaining electrolyte reactions on the anode of LIBs. The present investigation shows that catalysis plays a dominant role in the electrolyte decomposition process and has important implications in electrode surface modification and electrolyte recipe selection, which are critical factors for enhancing the efficiency, durability, and reliability of LIBs.

Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) for Rapid Determination of Microbial Cell Lipid Content: Correlation with Gas Chromatography-Mass Spectrometry (GC-MS).

Science.gov (United States)

Millan-Oropeza, Aaron; Rebois, Rolando; David, Michelle; Moussa, Fathi; Dazzi, Alexandre; Bleton, Jean; Virolle, Marie-Joelle; Deniset-Besseau, Ariane

2017-10-01

There is a growing interest worldwide for the production of renewable oil without mobilizing agriculture lands; fast and reliable methods are needed to identify highly oleaginous microorganisms of potential industrial interest. The aim of this study was to demonstrate the relevance of attenuated total reflection (ATR) spectroscopy to achieve this goal. To do so, the total lipid content of lyophilized samples of five Streptomyces strains with varying lipid content was assessed with two classical quantitative but time-consuming methods, gas chromatography-mass spectrometry (GC-MS) and ATR Fourier transform infrared (ATR FT-IR) spectroscopy in transmission mode with KBr pellets and the fast ATR method, often questioned for its lack of reliability. A linear correlation between these three methods was demonstrated allowing the establishment of equations to convert ATR values expressed as CO/amide I ratio, into micrograms of lipid per milligram of biomass. The ATR method proved to be as reliable and quantitative as the classical GC-MS and FT-IR in transmission mode methods but faster and more reproducible than the latter since it involves far less manipulation for sample preparation than the two others. Attenuated total reflection could be regarded as an efficient fast screening method to identify natural or genetically modified oleaginous microorganisms by the scientific community working in the field of bio-lipids.

Fractional finite Fourier transform.

Science.gov (United States)

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.

Measurement of conjugated linoleic acid (CLA) in CLA-rich soy oil by attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR).

Science.gov (United States)

Kadamne, Jeta V; Jain, Vishal P; Saleh, Mohammed; Proctor, Andrew

2009-11-25

Conjugated linoleic acid (CLA) isomers in oils are currently measured as fatty acid methyl esters by a gas chromatography-flame ionization detector (GC-FID) technique, which requires approximately 2 h to complete the analysis. Hence, we aim to develop a method to rapidly determine CLA isomers in CLA-rich soy oil. Soy oil with 0.38-25.11% total CLA was obtained by photo-isomerization of 96 soy oil samples for 24 h. A sample was withdrawn at 30 min intervals with repeated processing using a second batch of oil. Six replicates of GC-FID fatty acid analysis were conducted for each oil sample. The oil samples were scanned using attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR), and the spectrum was collected. Calibration models were developed using partial least-squares (PLS-1) regression using Unscrambler software. Models were validated using a full cross-validation technique and tested using samples that were not included in the calibration sample set. Measured and predicted total CLA, trans,trans CLA isomers, total mono trans CLA isomers, trans-10,cis-12 CLA, trans-9,cis-11 CLA and cis-10,trans-12 CLA, and cis-9,trans-11 CLA had cross-validated coefficients of determinations (R2v) of 0.97, 0.98, 0.97, 0.98, 0.97, and 0.99 and corresponding root-mean-square error of validation (RMSEV) of 1.14, 0.69, 0.27, 0.07, 0.14, and 0.07% CLA, respectively. The ATR-FTIR technique is a rapid and less expensive method for determining CLA isomers in linoleic acid photo-isomerized soy oil than GC-FID.

Fourier transform infrared spectra applications to chemical systems

CERN Document Server

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

Adsorption of water and butanol in silicalite-1 film studied with in situ attenuated total reflectance-Fourier transform infrared spectroscopy.

Science.gov (United States)

Farzaneh, Amirfarrokh; Zhou, Ming; Potapova, Elisaveta; Bacsik, Zoltán; Ohlin, Lindsay; Holmgren, Allan; Hedlund, Jonas; Grahn, Mattias

2015-05-05

Biobutanol produced by, e.g., acetone-butanol-ethanol (ABE) fermentation is a promising alternative to petroleum-based chemicals as, e.g., solvent and fuel. Recovery of butanol from dilute fermentation broths by hydrophobic membranes and adsorbents has been identified as a promising route. In this work, the adsorption of water and butanol vapor in a silicalite-1 film was studied using in situ attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy to better understand the adsorption properties of silicalite-1 membranes and adsorbents. Single-component adsorption isotherms were determined in the temperature range of 35-120 °C, and the Langmuir model was successfully fitted to the experimental data. The adsorption of butanol is very favorable compared to that of water. When the silicalite-1 film was exposed to a butanol/water vapor mixture with 15 mol % butanol (which is the vapor composition of an aqueous solution containing 2 wt % butanol, a typical concentration in an ABE fermentation broth, i.e., the composition of the gas obtained from gas stripping of an ABE broth) at 35 °C, the adsorption selectivity toward butanol was as high as 107. These results confirm that silicalite-1 quite selectively adsorbs hydrocarbons from vapor mixtures. To the best of our knowledge, this is the first comprehensive study on the adsorption of water and butanol in silicalite-1 from vapor phase.

A simple, sensitive and non-destructive technique for characterizing bovine dental enamel erosion: attenuated total reflection Fourier transform infrared spectroscopy.

Science.gov (United States)

Kim, In-Hye; Son, Jun Sik; Min, Bong Ki; Kim, Young Kyoung; Kim, Kyo-Han; Kwon, Tae-Yub

2016-03-30

Although many techniques are available to assess enamel erosion in vitro, a simple, non-destructive method with sufficient sensitivity for quantifying dental erosion is required. This study characterized the bovine dental enamel erosion induced by various acidic beverages in vitro using attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy. Deionized water (control) and 10 acidic beverages were selected to study erosion, and the pH and neutralizable acidity were measured. Bovine anterior teeth (110) were polished with up to 1 200-grit silicon carbide paper to produce flat enamel surfaces, which were then immersed in 20 mL of the beverages for 30 min at 37 °C. The degree of erosion was evaluated using ATR-FTIR spectroscopy and Vickers' microhardness measurements. The spectra obtained were interpreted in two ways that focused on the ν1, ν3 phosphate contour: the ratio of the height amplitude of ν3 PO4 to that of ν1 PO4 (Method 1) and the shift of the ν3 PO4 peak to a higher wavenumber (Method 2). The percentage changes in microhardness after the erosion treatments were primarily affected by the pH of the immersion media. Regression analyses revealed highly significant correlations between the surface hardness change and the degree of erosion, as detected by ATR-FTIR spectroscopy (Perosion.

Analysis of bacteria on steel surfaces using reflectance micro-Fourier transform infrared spectroscopy.

Science.gov (United States)

Ojeda, Jesús J; Romero-González, María E; Banwart, Steven A

2009-08-01

Reflectance micro-Fourier transform infrared (FT-IR) analysis has been applied to characterize biofilm formation of Aquabacterium commune, a common microorganism present on drinking water distribution systems, onto the increasingly popular pipe material stainless steel EN1.4307. The applicability of the reflectance micro-FT-IR technique for analyzing the bacterial functional groups is discussed, and the results are compared to spectra obtained using more conventional FT-IR techniques: transmission micro-FT-IR, attenuated transmitted reflectance (ATR), and KBr pellets. The differences between the infrared spectra of wet and dried bacteria, as well as free versus attached bacteria, are also discussed. The spectra obtained using reflectance micro-FT-IR spectroscopy were comparable to those obtained using other FT-IR techniques. The absence of sample preparation, the potential to analyze intact samples, and the ability to characterize opaque and thick samples without the need to transfer the bacterial samples to an infrared transparent medium or produce a pure culture were the main advantages of reflectance micro-FT-IR spectroscopy.

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 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

Fourier transforms principles and applications

CERN Document Server

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.

Application of multivariate chemometric techniques for simultaneous determination of five parameters of cottonseed oil by single bounce attenuated total reflectance Fourier transform infrared spectroscopy.

Science.gov (United States)

Talpur, M Younis; Kara, Huseyin; Sherazi, S T H; Ayyildiz, H Filiz; Topkafa, Mustafa; Arslan, Fatma Nur; Naz, Saba; Durmaz, Fatih; Sirajuddin

2014-11-01

Single bounce attenuated total reflectance (SB-ATR) Fourier transform infrared (FTIR) spectroscopy in conjunction with chemometrics was used for accurate determination of free fatty acid (FFA), peroxide value (PV), iodine value (IV), conjugated diene (CD) and conjugated triene (CT) of cottonseed oil (CSO) during potato chips frying. Partial least square (PLS), stepwise multiple linear regression (SMLR), principal component regression (PCR) and simple Beer׳s law (SBL) were applied to develop the calibrations for simultaneous evaluation of five stated parameters of cottonseed oil (CSO) during frying of French frozen potato chips at 170°C. Good regression coefficients (R(2)) were achieved for FFA, PV, IV, CD and CT with value of >0.992 by PLS, SMLR, PCR, and SBL. Root mean square error of prediction (RMSEP) was found to be less than 1.95% for all determinations. Result of the study indicated that SB-ATR FTIR in combination with multivariate chemometrics could be used for accurate and simultaneous determination of different parameters during the frying process without using any toxic organic solvent. Copyright © 2014 Elsevier B.V. All rights reserved.

Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

Science.gov (United States)

Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang

2016-03-01

An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS. © The Author(s) 2016.

Development of secondary cell wall in cotton fibers as examined with Fourier transform-infrared spectroscopy

Science.gov (United States)

Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...

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....

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)

Diffuse Reflectance Infrared Fourier Transform Study of NOx Adsorption on CGO10 Impregnated with K2O or BaO

DEFF Research Database (Denmark)

Traulsen, Marie Lund; Härelind Ingelsten, H.; Kammer Hansen, Kent

2012-01-01

In the present work Diffuse Reflectance Infrared Fourier Transform (DRIFT) spectroscopy is applied to study the adsorption of NOx at 300-500 °C in different atmospheres on gadolinium doped ceria (CGO), an important material in electrodes investigated for electrochemical NOx removal. Furthermore...

Attenuated total reflection-Fourier transform infrared imaging of large areas using inverted prism crystals and combining imaging and mapping.

Science.gov (United States)

Chan, K L Andrew; Kazarian, Sergei G

2008-10-01

Attenuated total reflection-Fourier transform infrared (ATR-FT-IR) imaging is a very useful tool for capturing chemical images of various materials due to the simple sample preparation and the ability to measure wet samples or samples in an aqueous environment. However, the size of the array detector used for image acquisition is often limited and there is usually a trade off between spatial resolution and the field of view (FOV). The combination of mapping and imaging can be used to acquire images with a larger FOV without sacrificing spatial resolution. Previous attempts have demonstrated this using an infrared microscope and a Germanium hemispherical ATR crystal to achieve images of up to 2.5 mm x 2.5 mm but with varying spatial resolution and depth of penetration across the imaged area. In this paper, we demonstrate a combination of mapping and imaging with a different approach using an external optics housing for large ATR accessories and inverted ATR prisms to achieve ATR-FT-IR images with a large FOV and reasonable spatial resolution. The results have shown that a FOV of 10 mm x 14 mm can be obtained with a spatial resolution of approximately 40-60 microm when using an accessory that gives no magnification. A FOV of 1.3 mm x 1.3 mm can be obtained with spatial resolution of approximately 15-20 microm when using a diamond ATR imaging accessory with 4x magnification. No significant change in image quality such as spatial resolution or depth of penetration has been observed across the whole FOV with this method and the measurement time was approximately 15 minutes for an image consisting of 16 image tiles.

Economical Appraisal of Total Aflatoxin Level in the Poultry Feeds by Fourier Transform Infrared Spectroscopy

International Nuclear Information System (INIS)

Sherazai, S.T.H.; Shar, Z.; Iqbal, M.; Sumbal, G.A.

2013-01-01

Single-bounce attenuated total reflectance (SB-ATR) Fourier transform infrared (FTIR) spectroscopy has been used for the quantitative determination of total aflatoxins in the broiler poultry feed. An FTIR calibration spanning the range 1-70 micro g/L aflatoxin standards in (70:30, v/v) methanol-water solvent system based on partial least square (PLS) model, developed by relating mid IR region between 3755-950 cm/ sub -1/. The excellent coefficient of various (using 0.998) was achieved with 1.49 relative mean square error of calibration (RMSEC). Aflatoxins from each of eight poultry feeds was extracted and the determined by the widely used commercially available Enzyme-linked Immunosorbent Assay (ELISA) procedure and the SB-ATR/FTIR method. The SB-ATR/FTIR aflatoxins predictions were related to those determined by the ELISA method by linear regression, producing an R value of 0.989 and a SD of +- 2.80 micro g/L. The result of the study clearly indicated that FT-IR spectroscopy due to its rapidity and simplicity along with data manipulation by advance computer software could be effectively used for routine determination of aflatoxins present in the poultry feeds at very low level. (author)

Fourier Transform Mass Spectrometry

Science.gov (United States)

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

Comparison of Fiber Optic and Conduit Attenuated Total Reflection (ATR) Fourier Transform Infrared (FT-IR) Setup for In-Line Fermentation Monitoring.

Science.gov (United States)

Koch, Cosima; Posch, Andreas E; Herwig, Christoph; Lendl, Bernhard

2016-12-01

The performance of a fiber optic and an optical conduit in-line attenuated total reflection mid-infrared (IR) probe during in situ monitoring of Penicillium chrysogenum fermentation were compared. The fiber optic probe was connected to a sealed, portable, Fourier transform infrared (FT-IR) process spectrometer via a plug-and-play interface. The optical conduit, on the other hand, was connected to a FT-IR process spectrometer via a knuckled probe with mirrors that had to be adjusted prior to each fermentation, which were purged with dry air. Penicillin V (PenV) and its precursor phenoxyacetic acid (POX) concentrations were determined by online high-performance liquid chromatography and the obtained concentrations were used as reference to build partial least squares regression models. Cross-validated root-mean-square errors of prediction were found to be 0.2 g L -1 (POX) and 0.19 g L -1 (PenV) for the fiber optic setup and 0.17 g L -1 (both POX and PenV) for the conduit setup. Higher noise-levels and spectrum-to-spectrum variations of the fiber optic setup lead to higher noise of estimated (i.e., unknown) POX and PenV concentrations than was found for the conduit setup. It seems that trade-off has to be made between ease of handling (fiber optic setup) and measurement accuracy (optical conduit setup) when choosing one of these systems for bioprocess monitoring. © The Author(s) 2016.

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

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.

Chemical fingerprinting of Arabidopsis using Fourier transform infrared (FT-IR) spectroscopic approaches.

Science.gov (United States)

Gorzsás, András; Sundberg, Björn

2014-01-01

Fourier transform infrared (FT-IR) spectroscopy is a fast, sensitive, inexpensive, and nondestructive technique for chemical profiling of plant materials. In this chapter we discuss the instrumental setup, the basic principles of analysis, and the possibilities for and limitations of obtaining qualitative and semiquantitative information by FT-IR spectroscopy. We provide detailed protocols for four fully customizable techniques: (1) Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS): a sensitive and high-throughput technique for powders; (2) attenuated total reflectance (ATR) spectroscopy: a technique that requires no sample preparation and can be used for solid samples as well as for cell cultures; (3) microspectroscopy using a single element (SE) detector: a technique used for analyzing sections at low spatial resolution; and (4) microspectroscopy using a focal plane array (FPA) detector: a technique for rapid chemical profiling of plant sections at cellular resolution. Sample preparation, measurement, and data analysis steps are listed for each of the techniques to help the user collect the best quality spectra and prepare them for subsequent multivariate analysis.

Preliminary investigations into macroscopic attenuated total reflection-fourier transform infrared imaging of intact spherical domains: spatial resolution and image distortion.

Science.gov (United States)

Everall, Neil J; Priestnall, Ian M; Clarke, Fiona; Jayes, Linda; Poulter, Graham; Coombs, David; George, Michael W

2009-03-01

This paper describes preliminary investigations into the spatial resolution of macro attenuated total reflection (ATR) Fourier transform infrared (FT-IR) imaging and the distortions that arise when imaging intact, convex domains, using spheres as an extreme example. The competing effects of shallow evanescent wave penetration and blurring due to finite spatial resolution meant that spheres within the range 20-140 microm all appeared to be approximately the same size ( approximately 30-35 microm) when imaged with a numerical aperture (NA) of approximately 0.2. A very simple model was developed that predicted this extreme insensitivity to particle size. On the basis of these studies, it is anticipated that ATR imaging at this NA will be insensitive to the size of intact highly convex objects. A higher numerical aperture device should give a better estimate of the size of small spheres, owing to superior spatial resolution, but large spheres should still appear undersized due to the shallow sampling depth. An estimate of the point spread function (PSF) was required in order to develop and apply the model. The PSF was measured by imaging a sharp interface; assuming an Airy profile, the PSF width (distance from central maximum to first minimum) was estimated to be approximately 20 and 30 microm for IR bands at 1600 and 1000 cm(-1), respectively. This work has two significant limitations. First, underestimation of domain size only arises when imaging intact convex objects; if surfaces are prepared that randomly and representatively section through domains, the images can be analyzed to calculate parameters such as domain size, area, and volume. Second, the model ignores reflection and refraction and assumes weak absorption; hence, the predicted intensity profiles are not expected to be accurate; they merely give a rough estimate of the apparent sphere size. Much further work is required to place the field of quantitative ATR-FT-IR imaging on a sound basis.

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

Science.gov (United States)

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…

The fractional Fourier transform and applications

Science.gov (United States)

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.

Quantitative measurements of fly ash, slag, and cement in limestone-based blends by Fourier transform infrared-attenuated total reflectance method

International Nuclear Information System (INIS)

Rebagay, T.V.; Dodd, D.A.; Claghorn, R.D.; Voogd, J.A.

1991-02-01

The disposal of the low-level radioactive liquids involves mixing the liquid waste with pozzolanic blend to form grout. Since the long-term performance of the grout depends on the composition of the blend, a rapid and reliable quantitative method to monitor blend compositions is needed. Earlier studies by Westinghouse Hanford Company demonstrated the utility of a Fourier transform infrared-attenuated total reflectance method for the analysis of cement blends. A sequential spectral subtraction technique was used to analyze the blend; however, its reproducibility depends on the operator's skill to perform spectral subtractions. A partial-least-squares (PLS) algorithm has replaced spectral subtraction. The PLS method is a statistical quantitative method suitable for analysis of multicomponent systems. Calibration blends are prepared by mixing the blend components in various proportions following a carefully designed calibration model. For the model, limestone content ranges from 30-50 wt%; blast furnace slag from 18-38 wt%; fly ash from 18-38 wt%; and cement from 0-16 wt%. Use of the large concentration range will enhance the chance that the calibration will be useful when target concentration change. The ability of the PLS method to predict limestone, slag, fly ash, and cement values in test blends was assessed. The prediction step of the PLS algorithm required only a few seconds to analyze the test spectra. The best and worst results for each component of the blends calculated by this method are shown in tables. The standard error of prediction of the true value is <2 wt% for limestone, <4 wt% for both fly ash and blast furnace slag, and <10 wt% for cement. 2 refs., 8 figs., 7 tabs

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)

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

Science.gov (United States)

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…

On fractional Fourier transform moments

NARCIS (Netherlands)

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

Electro-Optical Imaging Fourier-Transform Spectrometer

Science.gov (United States)

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.

A new twist to fourier transforms

CERN Document Server

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

An optical Fourier transform coprocessor with direct phase determination.

Science.gov (United States)

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.

Applications of Fourier transforms to generalized functions

CERN Document Server

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...

Implementation of quantum and classical discrete fractional Fourier transforms

Science.gov (United States)

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.

Science.gov (United States)

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.

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

Properties of the distributional finite Fourier transform

OpenAIRE

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 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)

Attenuated Total Reflectance-Fourier Transform Infrared Spectroscopy on Intact Dried Leaves of Sage (Salvia officinalis L.): Accelerated Chemotaxonomic Discrimination and Analysis of Essential Oil Composition.

Science.gov (United States)

Gudi, Gennadi; Krähmer, Andrea; Krüger, Hans; Schulz, Hartwig

2015-10-07

Sage (Salvia officinalis L.) is cultivated worldwide for its aromatic leaves, which are used as herbal spice, and for phytopharmaceutical applications. Fast analytical strategies for essential oil analysis, performed directly on plant material, would reduce the delay between sampling and analytical results. This would enhance product quality by improving technical control of cultivation. The attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) method described here provides a reliable calibration model for quantification of essential oil components [EOCs; R(2) = 0.96; root-mean-square error of cross-validation (RMSECV) = 0.249 mL 100 g(-1) of dry matter (DM); and range = 1.115-5.280 mL 100 g(-1) of DM] and main constituents [e.g., α-thujone/β-thujone; R(2) = 0.97/0.86; RMSECV = 0.0581/0.0856 mL 100 g(-1) of DM; and range = 0.010-1.252/0.005-0.893 mL 100 g(-1) of DM] directly on dried intact leaves of sage. Except for drying, no further sample preparation is required for ATR-FTIR, and the measurement time of less than 5 min per sample contrasts with the most common alternative of hydrodistillation followed by gas chromatography analysis, which can take several hours per sample.

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

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

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.

Quantitative evaluation of multiple adulterants in roasted coffee by Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS) and chemometrics.

Science.gov (United States)

Reis, Nádia; Franca, Adriana S; Oliveira, Leandro S

2013-10-15

The current study presents an application of Diffuse Reflectance Infrared Fourier Transform Spectroscopy for detection and quantification of fraudulent addition of commonly employed adulterants (spent coffee grounds, coffee husks, roasted corn and roasted barley) to roasted and ground coffee. Roasted coffee samples were intentionally blended with the adulterants (pure and mixed), with total adulteration levels ranging from 1% to 66% w/w. Partial Least Squares Regression (PLS) was used to relate the processed spectra to the mass fraction of adulterants and the model obtained provided reliable predictions of adulterations at levels as low as 1% w/w. A robust methodology was implemented that included the detection of outliers. High correlation coefficients (0.99 for calibration; 0.98 for validation) coupled with low degrees of error (1.23% for calibration; 2.67% for validation) confirmed that DRIFTS can be a valuable analytical tool for detection and quantification of adulteration in ground, roasted coffee. Copyright © 2013 Elsevier B.V. All rights reserved.

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

On the inverse windowed Fourier transform

OpenAIRE

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

Fourier Transform Infrared Radiation Spectroscopy Applied for Wood Rot Decay and Mould Fungi Growth Detection

OpenAIRE

Jelle, Bjørn Petter; Hovde, Per Jostein

2012-01-01

Material characterization may be carried out by the attenuated total reflectance (ATR) Fourier transform infrared (FTIR) radiation spectroscopical technique, which represents a powerful experimental tool. The ATR technique may be applied on both solid state materials, liquids, and gases with none or only minor sample preparations, also including materials which are nontransparent to IR radiation. This facilitation is made possible by pressing the sample directly onto various crystals, for exa...

(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

To See the World in a Grain of Sand: Recognizing the Origin of Sand Specimens by Diffuse Reflectance Infrared Fourier Transform Spectroscopy and Multivariate Exploratory Data Analysis

Science.gov (United States)

Pezzolo, Alessandra De Lorenzi

2011-01-01

The diffuse reflectance infrared Fourier transform (DRIFT) spectra of sand samples exhibit features reflecting their composition. Basic multivariate analysis (MVA) can be used to effectively sort subsets of homogeneous specimens collected from nearby locations, as well as pointing out similarities in composition among sands of different origins.…

Spectral Mining for Discriminating Blood Origins in the Presence of Substrate Interference via Attenuated Total Reflection Fourier Transform Infrared Spectroscopy: Postmortem or Antemortem Blood?

Science.gov (United States)

Takamura, Ayari; Watanabe, Ken; Akutsu, Tomoko; Ikegaya, Hiroshi; Ozawa, Takeaki

2017-09-19

Often in criminal investigations, discrimination of types of body fluid evidence is crucially important to ascertain how a crime was committed. Compared to current methods using biochemical techniques, vibrational spectroscopic approaches can provide versatile applicability to identify various body fluid types without sample invasion. However, their applicability is limited to pure body fluid samples because important signals from body fluids incorporated in a substrate are affected strongly by interference from substrate signals. Herein, we describe a novel approach to recover body fluid signals that are embedded in strong substrate interferences using attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy and an innovative multivariate spectral processing. This technique supported detection of covert features of body fluid signals, and then identified origins of body fluid stains on substrates. We discriminated between ATR FT-IR spectra of postmortem blood (PB) and those of antemortem blood (AB) by creating a multivariate statistics model. From ATR FT-IR spectra of PB and AB stains on interfering substrates (polyester, cotton, and denim), blood-originated signals were extracted by a weighted linear regression approach we developed originally using principal components of both blood and substrate spectra. The blood-originated signals were finally classified by the discriminant model, demonstrating high discriminant accuracy. The present method can identify body fluid evidence independently of the substrate type, which is expected to promote the application of vibrational spectroscopic techniques in forensic body fluid analysis.

Quantitative analysis of active compounds in pharmaceutical preparations by use of attenuated total-reflection Fourier transform mid-infrared spectrophotometry and the internal standard method.

Science.gov (United States)

Sastre Toraño, J; van Hattum, S H

2001-10-01

A new method is presented for the quantitative analysis of compounds in pharmaceutical preparations Fourier transform (FT) mid-infrared (MIR) spectroscopy with an attenuated total reflection (ATR) module. Reduction of the quantity of overlapping absorption bands, by interaction of the compound of interest with an appropriate solvent, and the employment of an internal standard (IS), makes MIR suitable for quantitative analysis. Vigabatrin, as active compound in vigabatrin 100-mg capsules, was used as a model compound for the development of the method. Vigabatrin was extracted from the capsule content with water after addition of a sodium thiosulfate IS solution. The extract was concentrated by volume reduction and applied to the FTMIR-ATR module. Concentrations of unknown samples were calculated from the ratio of the vigabatrin band area (1321-1610 cm(-1)) and the IS band area (883-1215 cm(-1)) using a calibration standard. The ratio of the area of the vigabatrin peak to that of the IS was linear with the concentration in the range of interest (90-110 mg, in twofold; n=2). The accuracy of the method in this range was 99.7-100.5% (n=5) with a variability of 0.4-1.3% (n=5). The comparison of the presented method with an HPLC assay showed similar results; the analysis of five vigabatrin 100-mg capsules resulted in a mean concentration of 102 mg with a variation of 2% with both methods.

On the windowed Fourier transform as an interpolation of the Gabor transform

NARCIS (Netherlands)

Bastiaans, M.J.; Prochßzka, A.; Uhlør, J.; Sovka, P.

1997-01-01

The windowed Fourier transform and its sampled version - the Gabor transform - are introduced. With the help of Gabor's signal expansion, an interpolation function is derived with which the windowed Fourier transform can be constructed from the Gabor transform. Using the Zak transform, it is shown

Classification and structural analysis of live and dead salmonella cells using fourier transform infrared (FT-IR) spectroscopy and principle component analysis (PCA)

Science.gov (United States)

Fourier Transform Infrared Spectroscopy (FT-IR) was used to detect Salmonella typhimurium and Salmonella enteritidis foodborne bacteria and distinguish between live and dead cells of both serotypes. Bacteria were loaded individually on the ZnSe Attenuated Total Reflection (ATR) crystal surface and s...

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)

Flow-through Fourier transform infrared sensor for total hydrocarbons determination in water.

Science.gov (United States)

Pérez-Palacios, David; Armenta, Sergio; Lendl, Bernhard

2009-09-01

A new flow-through Fourier transform infrared (FT-IR) sensor for oil in water analysis based on solid-phase spectroscopy on octadecyl (C18) silica particles has been developed. The C18 non-polar sorbent is placed inside the sensor and is able to retain hydrocarbons from water samples. The system does not require the use of chlorinated solvents, reducing the environmental impact, and the minimal sample handling stages serve to ensure sample integrity whilst reducing exposure of the analyst to any toxic hydrocarbons present within the samples. Fourier transform infrared (FT-IR) spectra were recorded by co-adding 32 scans at a resolution of 4 cm(-1) and the band located at 1462 cm(-1) due to the CH(2) bending was integrated from 1475 to 1450 cm(-1) using a baseline correction established between 1485 and 1440 cm(-1) using the areas as analytical signal. The technique, which provides a limit of detection (LOD) of 22 mg L(-1) and a precision expressed as relative standard deviation (RSD) lower than 5%, is considerably rapid and allows for a high level of automation.

Fourier transforms in radar and signal processing

CERN Document Server

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

Spectrums Transform Operators in Bases of Fourier and Walsh Functions

Directory of Open Access Journals (Sweden)

V. V. Syuzev

2017-01-01

components, allowed us to combine the nonzero coefficients in independent groups in each of the three cases of transformations. The original rules for group formation are formulated both for particular value of N, and in general terms.The formation rules of groups, group-by-group and common Parseval equalities were used to obtain descriptions of algorithms for mutual transformation of trigonometric Fourier spectrum into Hadamard, Paley and Hartmut spectra. An analytical record of these algorithms enables speaking of the Fourier kernels as of the new operators of spectra transformation. The computational complexity evaluation of operators showed the effectiveness of their use owing to more than three times reduction of the number of arithmetic operations as compared to the conventional method, i.e. direct calculation of the Walsh spectra. Because of this property the proposed operators become useful when solving the tasks of real-time discrete systems modeling.In the long run, there is a plan to solve a similar task for the mutual transformation of Walsh and Hartley spectra: both a Hartley basis system and a trigonometric system reflect the frequency structure of the signal that serves a useful purpose in terms of theory and practice.

Quantum arithmetic with the Quantum Fourier Transform

OpenAIRE

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.

Clifford Fourier transform on vector fields.

Science.gov (United States)

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.

Rapid, nondestructive estimation of surface polymer layer thickness using attenuated total reflection fourier transform infrared (ATR FT-IR) spectroscopy and synthetic spectra derived from optical principles.

Science.gov (United States)

Weinstock, B André; Guiney, Linda M; Loose, Christopher

2012-11-01

We have developed a rapid, nondestructive analytical method that estimates the thickness of a surface polymer layer with high precision but unknown accuracy using a single attenuated total reflection Fourier transform infrared (ATR FT-IR) measurement. Because the method is rapid, nondestructive, and requires no sample preparation, it is ideal as a process analytical technique. Prior to implementation, the ATR FT-IR spectrum of the substrate layer pure component and the ATR FT-IR and real refractive index spectra of the surface layer pure component must be known. From these three input spectra a synthetic mid-infrared spectral matrix of surface layers 0 nm to 10,000 nm thick on substrate is created de novo. A minimum statistical distance match between a process sample's ATR FT-IR spectrum and the synthetic spectral matrix provides the thickness of that sample. We show that this method can be used to successfully estimate the thickness of polysulfobetaine surface modification, a hydrated polymeric surface layer covalently bonded onto a polyetherurethane substrate. A database of 1850 sample spectra was examined. Spectrochemical matrix-effect unknowns, such as the nonuniform and molecularly novel polysulfobetaine-polyetherurethane interface, were found to be minimal. A partial least squares regression analysis of the database spectra versus their thicknesses as calculated by the method described yielded an estimate of precision of ±52 nm.

Fourier Transform Ultrasound Spectroscopy for the determination of wave propagation parameters.

Science.gov (United States)

Pal, Barnana

2017-01-01

The reported results for ultrasonic wave attenuation constant (α) in pure water show noticeable inconsistency in magnitude. A "Propagating-Wave" model analysis of the most popular pulse-echo technique indicates that this is a consequence of the inherent wave propagation characteristics in a bounded medium. In the present work Fourier Transform Ultrasound Spectroscopy (FTUS) is adopted to determine ultrasonic wave propagation parameters, the wave number (k) and attenuation constant (α) at 1MHz frequency in tri-distilled water at room temperature (25°C). Pulse-echo signals obtained under same experimental conditions regarding the exciting input signal and reflecting boundary wall of the water container for various lengths of water columns are captured. The Fast Fourier Transform (FFT) components of the echo signals are taken to compute k, α and r, the reflection constant at the boundary, using Oak Ridge and Oxford method. The results are compared with existing literature values. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

Science.gov (United States)

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

Fourier series, Fourier transform and their applications to mathematical physics

CERN Document Server

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 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

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

The morphing of geographical features by Fourier transformation.

Science.gov (United States)

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.

Fast inverse nonlinear Fourier transformation using exponential one-step methods : Darboux transformation

NARCIS (Netherlands)

Vaibhav, V.K.

2017-01-01

This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU(2) nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the

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.

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 Mass Spectrometry.

Science.gov (United States)

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)

Quantitative determination of polyphosphate in sediments using Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) spectroscopy and partial least squares regression.

Science.gov (United States)

Khoshmanesh, Aazam; Cook, Perran L M; Wood, Bayden R

2012-08-21

Phosphorus (P) is a major cause of eutrophication and subsequent loss of water quality in freshwater ecosystems. A major part of the flux of P to eutrophic lake sediments is organically bound or of biogenic origin. Despite the broad relevance of polyphosphate (Poly-P) in bioremediation and P release processes in the environment, its quantification is not yet well developed for sediment samples. Current methods possess significant disadvantages because of the difficulties associated with using a single extractant to extract a specific P compound without altering others. A fast and reliable method to estimate the quantitative contribution of microorganisms to sediment P release processes is needed, especially when an excessive P accumulation in the form of polyphosphate (Poly-P) occurs. Development of novel approaches for application of emerging spectroscopic techniques to complex environmental matrices such as sediments significantly contributes to the speciation models of P mobilization, biogeochemical nutrient cycling and development of nutrient models. In this study, for the first time Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) spectroscopy in combination with partial least squares (PLS) was used to quantify Poly-P in sediments. To reduce the high absorption matrix components in sediments such as silica, a physical extraction method was developed to separate sediment biological materials from abiotic particles. The aim was to achieve optimal separation of the biological materials from sediment abiotic particles with minimum chemical change in the sample matrix prior to ATR-FTIR analysis. Using a calibration set of 60 samples for the PLS prediction models in the Poly-P concentration range of 0-1 mg g(-1) d.w. (dry weight of sediment) (R(2) = 0.984 and root mean square error of prediction RMSEP = 0.041 at Factor-1) Poly-P could be detected at less than 50 μg g(-l) d.w. Using this technique, there is no solvent extraction or chemical

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)

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)

A discrete Fourier transform for virtual memory machines

Science.gov (United States)

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.

Comparison of Fourier transform and continuous wavelet transform to study echo-planar imaging flow maps

Energy Technology Data Exchange (ETDEWEB)

Rodriguez G, A.; Bowtell, R.; Mansfield, P. [Area de Procesamiento Digital de Senales e Imagenes Biomedicas. Universidad Autonoma Metropolitana Iztapalapa. Mexico D.F. 09340 Mexico (Mexico)

1998-12-31

Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)

Comparison of Fourier transform and continuous wavelet transform to study echo-planar imaging flow maps

International Nuclear Information System (INIS)

Rodriguez G, A.; Bowtell, R.; Mansfield, P.

1998-01-01

Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

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

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

International Nuclear Information System (INIS)

Fan Hongyi; Hao Ren; Lu Hailiang

2008-01-01

Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible

The application and improvement of Fourier transform spectrometer experiment

Science.gov (United States)

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.

Geometric Representations for Discrete Fourier Transforms

Science.gov (United States)

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.

Source Determination of Red Gel Pen Inks using Raman Spectroscopy and Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy combined with Pearson's Product Moment Correlation Coefficients and Principal Component Analysis.

Science.gov (United States)

Mohamad Asri, Muhammad Naeim; Mat Desa, Wan Nur Syuhaila; Ismail, Dzulkiflee

2018-01-01

The potential combination of two nondestructive techniques, that is, Raman spectroscopy (RS) and attenuated total reflectance-fourier transform infrared (ATR-FTIR) spectroscopy with Pearson's product moment correlation (PPMC) coefficient (r) and principal component analysis (PCA) to determine the actual source of red gel pen ink used to write a simulated threatening note, was examined. Eighteen (18) red gel pens purchased from Japan and Malaysia from November to December 2014 where one of the pens was used to write a simulated threatening note were analyzed using RS and ATR-FTIR spectroscopy, respectively. The spectra of all the red gel pen inks including the ink deposited on the simulated threatening note gathered from the RS and ATR-FTIR analyses were subjected to PPMC coefficient (r) calculation and principal component analysis (PCA). The coefficients r = 0.9985 and r = 0.9912 for pairwise combination of RS and ATR-FTIR spectra respectively and similarities in terms of PC1 and PC2 scores of one of the inks to the ink deposited on the simulated threatening note substantiated the feasibility of combining RS and ATR-FTIR spectroscopy with PPMC coefficient (r) and PCA for successful source determination of red gel pen inks. The development of pigment spectral library had allowed the ink deposited on the threatening note to be identified as XSL Poppy Red (CI Pigment Red 112). © 2017 American Academy of Forensic Sciences.

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

Science.gov (United States)

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",…

On integral and finite Fourier transforms of continuous q-Hermite polynomials

International Nuclear Information System (INIS)

Atakishiyeva, M. K.; Atakishiyev, N. M.

2009-01-01

We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

Limited-angle three-dimensional reconstructions using Fourier transform iterations and Radon transform iterations

International Nuclear Information System (INIS)

Tam, K.C.; Perez-Mendez, V.

1981-01-01

The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been analyzed in detail. it was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect which tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time

Limited-angle 3-D reconstructions using Fourier transform iterations and Radon transform iterations

International Nuclear Information System (INIS)

Tam, K.C.; Perez-Mendez, V.

1979-12-01

The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero was calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms was analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect that tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time. 8 figures, 2 tables

Applicability of a Diffuse Reflectance Infrared Fourier Transform handheld spectrometer to perform in situ analyses on Cultural Heritage materials.

Science.gov (United States)

Arrizabalaga, Iker; Gómez-Laserna, Olivia; Aramendia, Julene; Arana, Gorka; Madariaga, Juan Manuel

2014-08-14

This work studies the applicability of a Diffuse Reflectance Infrared Fourier Transform handheld device to perform in situ analyses on Cultural Heritage assets. This portable diffuse reflectance spectrometer has been used to characterise and diagnose the conservation state of (a) building materials of the Guevara Palace (15th century, Segura, Basque Country, Spain) and (b) different 19th century wallpapers manufactured by the Santa Isabel factory (Vitoria-Gasteiz, Basque Country, Spain) and by the well known Dufour and Leroy manufacturers (Paris, France), all of them belonging to the Torre de los Varona Castle (Villanañe, Basque Country, Spain). In all cases, in situ measurements were carried out and also a few samples were collected and measured in the laboratory by diffuse reflectance spectroscopy (DRIFT) in order to validate the information obtained by the handheld instrument. In the analyses performed in situ, distortions in the diffuse reflectance spectra can be observed due to the presence of specular reflection, showing the inverted bands caused by the Reststrahlen effect, in particular on those IR bands with the highest absorption coefficients. This paper concludes that the results obtained in situ by a diffuse reflectance handheld device are comparable to those obtained with laboratory diffuse reflectance spectroscopy equipment and proposes a few guidelines to acquire good spectra in the field, minimising the influence caused by the specular reflection. Copyright © 2014 Elsevier B.V. All rights reserved.

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

Science.gov (United States)

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.

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....

The Fourier Transform for Certain HyperKähler Fourfolds

NARCIS (Netherlands)

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

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

Science.gov (United States)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

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

Comparative study on γ energy spectrum denoise by fourier and wavelet transforms

International Nuclear Information System (INIS)

Shi Dongsheng; Di Yuming; Zhou Chunlin

2007-01-01

This paper introduces the basic principle of wavelet and Fourier transforms, applies wavelet transform method to denoise γ energy spectrum of 60 Co and compares it with Fourier transform method. The result of simulation with MATLAB software tool showed that as compared with traditional Fourier transform, wavelet transform has comparatively higher accuracy for γ energy spectrum denoising and is more feasible to γ energy spectrum denoising. (authors)

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

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 finite Fourier transform of classical polynomials

OpenAIRE

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.

Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) Spectroscopy as an Analytical Method to Investigate the Secondary Structure of a Model Protein Embedded in Solid Lipid Matrices.

Science.gov (United States)

Zeeshan, Farrukh; Tabbassum, Misbah; Jorgensen, Lene; Medlicott, Natalie J

2018-02-01

Protein drugs may encounter conformational perturbations during the formulation processing of lipid-based solid dosage forms. In aqueous protein solutions, attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy can investigate these conformational changes following the subtraction of spectral interference of solvent with protein amide I bands. However, in solid dosage forms, the possible spectral contribution of lipid carriers to protein amide I band may be an obstacle to determine conformational alterations. The objective of this study was to develop an ATR FT-IR spectroscopic method for the analysis of protein secondary structure embedded in solid lipid matrices. Bovine serum albumin (BSA) was chosen as a model protein, while Precirol AT05 (glycerol palmitostearate, melting point 58 ℃) was employed as the model lipid matrix. Bovine serum albumin was incorporated into lipid using physical mixing, melting and mixing, or wet granulation mixing methods. Attenuated total reflection FT-IR spectroscopy and size exclusion chromatography (SEC) were performed for the analysis of BSA secondary structure and its dissolution in aqueous media, respectively. The results showed significant interference of Precirol ATO5 with BSA amide I band which was subtracted up to 90% w/w lipid content to analyze BSA secondary structure. In addition, ATR FT-IR spectroscopy also detected thermally denatured BSA solid alone and in the presence of lipid matrix indicating its suitability for the detection of denatured protein solids in lipid matrices. Despite being in the solid state, conformational changes occurred to BSA upon incorporation into solid lipid matrices. However, the extent of these conformational alterations was found to be dependent on the mixing method employed as indicated by area overlap calculations. For instance, the melting and mixing method imparted negligible effect on BSA secondary structure, whereas the wet granulation mixing method promoted

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.

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 transforms and convolutions for the experimentalist

CERN Document Server

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

Characterization of ceramic matrix composite degradation using Fourier transform infrared spectroscopy

Science.gov (United States)

Henry, Christine; Criner, Amanda Keck; Imel, Megan; King, Derek

2018-04-01

Data collected with a handheld Fourier Transform Infrared (FTIR) device is analyzed and considered as a useful method for detecting and quantifying oxidation on the surface of ceramic matrix composite (CMC) materials. Experiments examine silicon carbide (SiC) coupons, looking for changes in chemical composition before and after thermal exposure. Using mathematical, physical and statistical models for FTIR reflectance data, this research seeks to quantify any detected spectral changes as an indicator of surface oxidation on the CMC coupon.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

Science.gov (United States)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

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)

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.

Beyond Fourier

Science.gov (United States)

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.

Fourier transform infrared spectra applications to chemical systems

CERN Document Server

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

Multichannel Dynamic Fourier-Transform IR Spectrometer

Science.gov (United States)

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.

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-based reconstruction via alternating direction total variation minimization in linear scan CT

International Nuclear Information System (INIS)

Cai, Ailong; Wang, Linyuan; Yan, Bin; Zhang, Hanming; Li, Lei; Xi, Xiaoqi; Li, Jianxin

2015-01-01

In this study, we consider a novel form of computed tomography (CT), that is, linear scan CT (LCT), which applies a straight line trajectory. Furthermore, an iterative algorithm is proposed for pseudo-polar Fourier reconstruction through total variation minimization (PPF-TVM). Considering that the sampled Fourier data are distributed in pseudo-polar coordinates, the reconstruction model minimizes the TV of the image subject to the constraint that the estimated 2D Fourier data for the image are consistent with the 1D Fourier transform of the projection data. PPF-TVM employs the alternating direction method (ADM) to develop a robust and efficient iteration scheme, which ensures stable convergence provided that appropriate parameter values are given. In the ADM scheme, PPF-TVM applies the pseudo-polar fast Fourier transform and its adjoint to iterate back and forth between the image and frequency domains. Thus, there is no interpolation in the Fourier domain, which makes the algorithm both fast and accurate. PPF-TVM is particularly useful for limited angle reconstruction in LCT and it appears to be robust against artifacts. The PPF-TVM algorithm was tested with the FORBILD head phantom and real data in comparisons with state-of-the-art algorithms. Simulation studies and real data verification suggest that PPF-TVM can reconstruct higher accuracy images with lower time consumption

Beyond Fourier.

Science.gov (United States)

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.

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

Vector frequency-comb Fourier-transform spectroscopy for characterizing metamaterials

International Nuclear Information System (INIS)

Ganz, T; Brehm, M; Von Ribbeck, H G; Keilmann, F; Van der Weide, D W

2008-01-01

We determine infrared transmission amplitude and phase spectra of metamaterial samples at well-defined incidence and polarization with a vector ('asymmetric') frequency-comb Fourier-transform spectrometer (c-FTS) that uses no moving elements. The metamaterials are free-standing metallic hole arrays; we study their resonances in the 7-13 μm and 100-1000 μm wavelength regions due both to interaction with bulk waves (Wood anomaly) and with leaky surface plasmon polaritons (near-unity transmittance, coupling features and dispersion). Such complex-valued transmission and reflection spectra could be used to compute a metamaterial's complex dielectric function directly, as well as its magnetic and magneto-optical permeability functions.

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

Science.gov (United States)

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

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.

Microscale Solubility Measurements of Matrix-Assisted Laser Desorption-Ionization (MALDI) Matrices Using Attenuated Total Reflection (ATR) Fourier Transform Infrared Spectroscopy (FT-IR) Coupled with Partial Least Squares (PLS) Analysis.

Science.gov (United States)

Gorre, Elsa; Owens, Kevin G

2016-11-01

In this work an attenuated total reflection Fourier transform infrared (FT-IR) absorption based method is used to measure the solubility of two matrix-assisted laser desorption-ionization (MALDI) matrices in a few pure solvents and mixtures of acetonitrile and water using low microliter amounts of solution. Results from a method that averages the values obtained from multiple calibration curves created by manual peak picking are compared to those predicted using a partial least squares (PLS) chemometrics approach. The PLS method provided solubility values that were in good agreement with the manual method with significantly greater ease of analysis. As a test, the solubility of adipic acid in acetone was measured using the two methods of analysis, and the values are in good agreement with solubility values reported in literature. The solubilities of the MALDI matrices α-cyano-4-hydroxy cinnamic acid (CHCA) and sinapinic acid (SA) were measured in a series of mixtures made from acetonitrile (ACN) and water; surprisingly, the results show a highly nonlinear trend. While both CHCA and SA show solubility values of less than 10 mg/mL in the pure solvents, the solubility value for SA increases to 56.3 mg/mL in a 75:25 v/v ACN:water mixture. This can have a significant effect on the matrix-to-analyte ratios in the MALDI experiment when sample protocols call for preparation of a saturated solution of the matrix in the chosen solvent system. © The Author(s) 2016.

Differentiation of Body Fluid Stains on Fabrics Using External Reflection Fourier Transform Infrared Spectroscopy (FT-IR) and Chemometrics.

Science.gov (United States)

Zapata, Félix; de la Ossa, Ma Ángeles Fernández; García-Ruiz, Carmen

2016-04-01

Body fluids are evidence of great forensic interest due to the DNA extracted from them, which allows genetic identification of people. This study focuses on the discrimination among semen, vaginal fluid, and urine stains (main fluids in sexual crimes) placed on different colored cotton fabrics by external reflection Fourier transform infrared spectroscopy (FT-IR) combined with chemometrics. Semen-vaginal fluid mixtures and potential false positive substances commonly found in daily life such as soaps, milk, juices, and lotions were also studied. Results demonstrated that the IR spectral signature obtained for each body fluid allowed its identification and the correct classification of unknown stains by means of principal component analysis (PCA) and soft independent modeling of class analogy (SIMCA). Interestingly, results proved that these IR spectra did not show any bands due to the color of the fabric and no substance of those present in daily life which were analyzed, provided a false positive. © The Author(s) 2016.

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 Fourier transform of tubular densities

KAUST Repository

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

Direct determination of sorbitol and sodium glutamate by attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) in the thermostabilizer employed in the production of yellow-fever vaccine.

Science.gov (United States)

de Castro, Eduardo da S G; Cassella, Ricardo J

2016-05-15

Reference methods for quality control of vaccines usually require treatment of the samples before analysis. These procedures are expensive, time-consuming, unhealthy and require careful manipulation of the sample, making them a potential source of analytical errors. This work proposes a novel method for the quality control of thermostabilizer samples of the yellow fever vaccine employing attenuated total reflectance Fourier transform infrared spectrometry (ATR-FTIR). The main advantage of the proposed method is the possibility of direct determination of the analytes (sodium glutamate and sorbitol) without any pretreatment of the samples. Operational parameters of the FTIR technique, such as the number of accumulated scans and nominal resolution, were evaluated. The best conditions for sodium glutamate were achieved when 64 scans were accumulated using a nominal resolution of 4 cm(-1). The measurements for sodium glutamate were performed at 1347 cm(-1) (baseline correction between 1322 and 1369 cm(-1)). In the case of sorbitol, the measurements were done at 890cm(-1) (baseline correction between 825 and 910 cm(-1)) using a nominal resolution of 2 cm(-1) with 32 accumulated scans. In both cases, the quantitative variable was the band height. Recovery tests were performed in order to evaluate the accuracy of the method and recovery percentages in the range 93-106% were obtained. Also, the methods were compared with reference methods and no statistical differences were observed. The limits of detection and quantification for sodium glutamate were 0.20 and 0.62% (m/v), respectively, whereas for sorbitol they were 1 and 3.3% (m/v), respectively. Copyright © 2016 Elsevier B.V. All rights reserved.

An analogue of a theorem of Titchmarsh for Walsh-Fourier transformations

International Nuclear Information System (INIS)

Golubov, B I

1998-01-01

Let f-hat c be the Fourier cosine transform of f. Then, as proved for functions of class L p (R + ) in Titchmarsh's book 'Introduction to the theory of Fourier integrals' (1937), the Hardy operator and the Hardy-Littlewood operator can be defined. In the present paper similar equalities are proved for functions of class L p (R + ), 1< p≤2, and the Walsh-Fourier transformation

Fourier transform infrared spectroscopy, a new method for rapid determination of total organic and inorganic carbon and biogenic silica concentration in lake sediments

DEFF Research Database (Denmark)

Rosén, Peter; Vogel, Hendrik; Cunningham, Laura

2010-01-01

We demonstrate the use of Fourier transform infrared spectroscopy (FTIRS) to make quantitative measures of total organic carbon (TOC), total inorganic carbon (TIC) and biogenic silica (BSi) concentrations in sediment. FTIRS is a fast and cost-effective technique and only small sediment samples...... varied between r = 0.84-0.99 for TOC, r = 0.85-0.99 for TIC, and r = 0.68-0.94 for BSi. Because FTIR spectra contain information on a large number of both inorganic and organic components, there is great potential for FTIRS to become an important tool in paleolimnology....

Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform

Directory of Open Access Journals (Sweden)

Zohreh Moghareh Abed

2010-01-01

Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.

Electro-optic imaging Fourier transform spectrometer

Science.gov (United States)

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.

Large quantum Fourier transforms are never exactly realized by braiding conformal blocks

International Nuclear Information System (INIS)

Freedman, Michael H.; Wang, Zhenghan

2007-01-01

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {U(2), controlled-NOT}, the discrete Fourier transforms F N =(ω ij ) NxN , i,j=0,1,...,N-1, ω=e 2πi at ∼sol∼ at N , can be realized exactly by quantum circuits of size O(n 2 ), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F N and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks

Segment density profiles of polyelectrolyte brushes determined by Fourier transform ellipsometry

Science.gov (United States)

Biesalski, Markus; Rühe, Jürgen; Johannsmann, Diethelm

1999-10-01

We describe a method for the explicit determination of the segment density profile φ(z) of surface-attached polymer brushes with multiple angle of incidence null-ellipsometry. Because the refractive index contrast between the brush layer and the solvent is weak, multiple reflections are of minor influence and the ellipsometric spectrum is closely related to the Fourier transform of the refractive index profile, thereby allowing for explicit inversion of the ellipsometric data. We chose surface-attached monolayers of polymethacrylic acid (PMAA), a weak polyelectrolyte, as a model system and determined the segment density profile of this system as a function of the pH value of the surrounding medium by the Fourier method. Complementary to the Fourier analysis, fits with error functions are given as well. The brushes were prepared on the bases of high refractive index prisms with the "grafting-from" technique. In water, the brushes swell by more than a factor of 30. The swelling increases with increasing pH because of a growing fraction of dissociated acidic groups leading to a larger electrostatic repulsion.

Gas sensing properties and in situ diffuse reflectance infrared Fourier transform spectroscopy study of trichloroethylene adsorption and reactions on SnO2 films

Science.gov (United States)

Zhang, Zhenxin; Huang, Kaijin; Yuan, Fangli; Xie, Changsheng

2014-05-01

The detection of trichloroethylene has attracted much attention because it has an important effect on human health. The sensitivity of the SnO2 flat-type coplanar gas sensor arrays to 100 ppm trichloroethylene in air was investigated. The adsorption and surface reactions of trichloroethylene were investigated at 100-200 °C by in-situ diffuse reflection Fourier transform infrared spectroscopy (DIRFTS) on SnO2 films. Molecularly adsorbed trichloroethylene, dichloroacetyl chloride (DCAC), phosgene, HCl, CO, H2O, CHCl3, Cl2 and CO2 surface species are formed during trichloroethylene adsorption at 100-200 °C. A possible mechanism of the reaction process is discussed.

The RC Circuit: An Approach with Fourier Transforms In this article ...

Indian Academy of Sciences (India)

CLASSROOM. Mitrajyoti Ghosh. 83, Mitrapara 2nd Lane, Harinavi,. Kolkata 700148, West Bengal,. India. Email: mijospeakingnow@gmail.com. The RC Circuit: An Approach with Fourier Transforms. In this article we shall mathematically analyse the Resistor-. Capacitor (RC) circuit with the help of Fourier transforms. (FT).

Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) Spectroscopy as a Forensic Method to Determine the Composition of Inks Used to Print the United States One-cent Blue Benjamin Franklin Postage Stamps of the 19th Century.

Science.gov (United States)

Brittain, Harry G

2016-01-01

Through the combined use of infrared (IR) absorption spectroscopy and attenuated total reflectance (ATR) sampling, the composition of inks used to print the many different types of one-cent Benjamin Franklin stamps of the 19th century has been established. This information permits a historical evaluation of the formulations used at various times, and also facilitates the differentiation of the various stamps from each other. In two instances, the ink composition permits the unambiguous identification of stamps whose appearance is identical, and which (until now) have only been differentiated through estimates of the degree of hardness or softness of the stamp paper, or through the presence or absence of a watermark in the paper. In these instances, the use of ATR Fourier transform infrared spectroscopy (FT-IR) spectroscopy effectively renders irrelevant two 100-year-old practices of stamp identification. Furthermore, since the use of ATR sampling makes it possible to obtain the spectrum of a stamp still attached to its cover, it is no longer necessary to identify these blue Franklin stamps using their cancellation dates. © The Author(s) 2015.

Fourier transform of delayed fluorescence as an indicator of herbicide concentration.

Science.gov (United States)

Guo, Ya; Tan, Jinglu

2014-12-21

It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

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.

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 transform spectra of quantum dots

Science.gov (United States)

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.

Surface analysis by Fourier-transform infrared (FTIR) spectroscopy

International Nuclear Information System (INIS)

Powell, G.L.; Smyrl, N.R.; Fuller, E.L.

1981-01-01

A diffuse-reflectance capability for the Fourier transform infrared spectrometer at the Y-12 Plant Laboratory has been implemented. A sample cell with a 25 to 400 0 C temperature-controlled sample stage and an ultrahigh-vacuum-to-atmospheric pressure gas-handling capability has been developed. Absorbance of light from the spectrometer beam, resulting from the beam being scattered from a powder sample, can be measured. This capability of detecting molecular species on and in powders is to be used to study chemisorption on actinide and rare-earth metals, alloys, and compounds. Cell design is described along with experiments demonstrating its performance in detecting moisture absorption on uranium oxide, moisture and carbon dioxide absorption on the lithium hydride/hydroxide system, and carbon dioxide absorption on potassium borohydride. 13 figures

Fourier-transform optical microsystems

Science.gov (United States)

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.

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 ...

The short time Fourier transform and local signals

Science.gov (United States)

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.

Discrete Fourier Transform Analysis in a Complex Vector Space

Science.gov (United States)

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.

Study on sampling of continuous linear system based on generalized Fourier transform

Science.gov (United States)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

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)

Application of fourier-transform infrared (ft-ir) spectroscopy for determination of total phenolics of freeze dried lemon juices

International Nuclear Information System (INIS)

Sherazi, S.T.H.; Bhutto, A.A.; Mehesar, S.A.

2017-01-01

A cost effective and environmentally safe analytical method for rapid assessment of total phenolic content (TPC) in freeze dried lemon juice samples was developed using transmission Fourier-transform infrared spectroscopy (FT-IR) in conjunction with chemometric techniques. Two types of calibrations i.e. simple Beer's law and partial least square (PLS) were applied to investigate most accurate calibration model based on region from1420 to 1330 cm-1. The better analytical performance was obtained by PLS technique coefficient of determination (R2), root mean square error of calibration (RMSEC) with the value of 0.999 and 0.00864, respectively. The results of TPC in freeze dried lemon juice samples obtained by transmission FT-IR were compared with TPC observed by Folin-Ciocalteu (FC) assay and found to be comparable. Outcomes of the present study indicate that transmission FT-IR spectroscopic approach could be used as an alternative approach in place of Folin-Ciocalteu (FC) assay which is expensive and time-consuming conventional chemical methods for determination of the total phenolic content of lemon fruits. (author)

Fourier transforms in spectroscopy

CERN Document Server

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

Study of Surface Wettability Change of Unconsolidated Sand Using Diffuse Reflectance Infrared Fourier Transform Spectroscopy and Thermogravimetric Analysis.

Science.gov (United States)

Gómora-Herrera, Diana; Navarrete Bolaños, Juan; Lijanova, Irina V; Olivares-Xometl, Octavio; Likhanova, Natalya V

2018-04-01

The effects exerted by the adsorption of vapors of a non-polar compound (deuterated benzene) and a polar compound (water) on the surface of Ottawa sand and a sample of reservoir sand (Channel), which was previously impregnated with silicon oil or two kinds of surfactants, (2-hydroxyethyl) trimethylammonium oleate (HETAO) and (2-hydroxyethyl)trimethylammonium azelate (HETAA), were studied by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and thermogravimetric analysis (TGA). The surface chemistry of the sandstone rocks was elucidated by X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDX). Terminal surface groups such as hydroxyls can strongly adsorb molecules that interact with these surface groups (surfactants), resulting in a wettability change. The wettability change effect suffered by the surface after treating it with surfactants was possible to be detected by the DRIFTS technique, wherein it was observed that the surface became more hydrophobic after being treated with silicon oil and HETAO; the surface became more hydrophilic after treating it with HETAA.

Decay of the Fourier transform analytic and geometric aspects

CERN Document Server

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.

Accelerating the Non-equispaced Fast Fourier Transform on Commodity Graphics Hardware

DEFF Research Database (Denmark)

Sørensen, Thomas Sangild; Schaeffter, Tobias; Noe, Karsten Østergaard

2008-01-01

We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe the performa......We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe...

Functional differential equations for the q-Fourier transform of q-Gaussians

International Nuclear Information System (INIS)

Umarov, S; Queiros, S M Duarte

2010-01-01

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 ≤ q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Functional differential equations for the q-Fourier transform of q-Gaussians

Energy Technology Data Exchange (ETDEWEB)

Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)

2010-02-05

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Analysis of the Interference Modulation Depth in the Fourier Transform Spectrometer

Directory of Open Access Journals (Sweden)

Rilong Liu

2015-01-01

Full Text Available Based on the principle of the Michelson interferometer, the paper briefly describes the theoretical significance and calculates and deduces three expressions of the interference modulation depth. The influence of the surface shape error of plane mirror on modulation depth is analyzed, and the tolerance of error is also pointed out. Moreover, the dependence of modulation depth on the reflectance change of beam splitter interface is also analyzed, and the curve is given. It is concluded that this paper is of general significance for the Fourier transform spectrometer based on the principle of the Michelson two-beam interference.

Topography description of thin films by optical Fourier Transform

International Nuclear Information System (INIS)

Jaglarz, Janusz

2008-01-01

In this work, the main problems concerning the scattering of light by real surfaces and films are presented in view of results obtained with the bidirectional reflection distribution function (BRDF) method and optical profilometry (OP). The BRDF and OP studies, being complementary to the atomic force microscopy (AFM), allow one to get information about surface topography. From the optical data, the surface power spectral density (PSD) functions for absorbing and transparent rough films have been found. Both functions have been evaluated from the Fourier transform (FT) of the surface profiles. The usefulness of BRDF-and OP methods in characterization of real surfaces is demonstrated when analyzing the optical data obtained for metallic TiN-and organic PVK thin films deposited on various substrates

Topography description of thin films by optical Fourier Transform

Energy Technology Data Exchange (ETDEWEB)

Jaglarz, Janusz [Institute of Physics, Cracow University of Technology, ul. Podchoraz.ych 1, 30-084 Krakow (Poland)], E-mail: pujaglar@cyfronet.krakow.pl

2008-09-30

In this work, the main problems concerning the scattering of light by real surfaces and films are presented in view of results obtained with the bidirectional reflection distribution function (BRDF) method and optical profilometry (OP). The BRDF and OP studies, being complementary to the atomic force microscopy (AFM), allow one to get information about surface topography. From the optical data, the surface power spectral density (PSD) functions for absorbing and transparent rough films have been found. Both functions have been evaluated from the Fourier transform (FT) of the surface profiles. The usefulness of BRDF-and OP methods in characterization of real surfaces is demonstrated when analyzing the optical data obtained for metallic TiN-and organic PVK thin films deposited on various substrates.

Investigation on H-containing shallow trap of hydrogenated TiO2 with in situ Fourier transform infrared diffuse reflection spectroscopy.

Science.gov (United States)

Han, Bing; Hang Hu, Yun

2017-07-28

A novel technique, high temperature high pressure in situ Fourier transform infrared diffuse reflection spectroscopy, was successfully used to investigate the formation and stability of shallow trap states in P25 TiO 2 nanoparticles. Two types of shallow traps (with and without H atoms) were identified. The H-containing shallow trap can be easily generated by heating in H 2 atmosphere. However, the trap is unstable in vacuum at 600 °C. In contrast, the H-free shallow trap, which can be formed by heating in vacuum, is stable even at 600 °C. The energy gaps between shallow trap states and the conduction band are 0.09 eV for H-containing shallow trap and 0.13 eV for H-free shallow trap, indicating that the H-containing shallow trap state is closer to the conduction band than that without H.

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

International Nuclear Information System (INIS)

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-01-01

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

Two-dimensional fourier transform spectrometer

Science.gov (United States)

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.

An introduction to Laplace transforms and Fourier series

CERN Document Server

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 ...

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)

The Fourier transform of tubular densities

KAUST Repository

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.

On the moments of the Wigner distribution and the fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Veen, J.P.

2000-01-01

A Fourier transformation maps a one-dimensional time signal into a one-dimensional frequency function, the signal spectrum. Although the Fourier transform provides the signal's spectral content, it fails to indicate the time location of the spectral components, which is important, for example, when

Techniques for Handling and Removal of Spectral Channels in Fourier Transform Synchrotron-Based Spectra

International Nuclear Information System (INIS)

Ibrahim, Amr; Predoi-Cross, Adriana; Teillet, Philippe M.

2010-01-01

Channel spectra are a big problem for those attempting to use synchrotron-based Fourier transform spectra for spectral lineshape studies. Due to the layout of the optical system at the CLS far-infrared beamline, the synchrotron beam undergoes unavoidable multiple reflections on the steering mirrors, beam splitter, several sets of windows, and filters. We present a method for eliminating channel spectra and compare the results of our technique with other methods available in the literature.

The total column of CO2 and CH4 measured with a compact Fourier transform spectrometer at NASA Armstrong Flight Research Center and Railroad Valley, Nevada, USA

Science.gov (United States)

Kawakami, S.; Shiomi, K.; Suto, H.; Kuze, A.; Hillyard, P. W.; Tanaka, T.; Podolske, J. R.; Iraci, L. T.; Albertson, R. T.

2014-12-01

The total columns of carbon dioxide (XCO2) and methane (XCH4) were measured with a compact Fourier transform spectrometer (FTS) at NASA Armstrong Flight Research Center (AFRC) and Railroad Valley, Nevada, USA (RRV) during a vicarious calibration campaign in June 2014. The campaign was performed to estimate changes in the radiometric response of the Thermal and Near Infrared Sensor for carbon Observations Fourier Transform Spectrometer (TANSO-FTS) and the Cloud and Aerosol Imager (TANSO-CAI) aboard Greenhouse gases Observing SATellite (GOSAT). TANSO-FTS measures spectra of radiance scattered by the Earth surface with high- and medium-gain depending on the surface reflectance. At high reflectance areas, such as deserts over north Africa and Australia, TANSO-FTS collects spectra with medium-gain. There was differences on atmospheric pressure and XCO2 retrieved from spectra obtained between high-gain and medium-gain. Because the retrieved products are useful for evaluating the difference of spectral qualities between high- and medium-gain, this work is an attempt to collect validation data for spectra with medium-gain of TANSO-FTS at remote and desert area with a compact and medium-spectral resolution instrument. As a compact FTS, EM27/SUN was used. It was manufactured and newly released on April 1, 2014 by Bruker. It is robust and operable in a high temperature environment. It was housed in a steel box to protect from dust and rain and powered by Solar panels. It can be operated by such a remote and desert area, like a RRV. Over AFRC and RRV, vertical profiles of CO2 and CH4 were measured using the Alpha Jet research aircraft as part of the Alpha Jet Atmospheric eXperiment (AJAX) of ARC, NASA. The values were calibrated to standard gases. To make the results comparable to WMO (World Meteorological Organization) standards, the retrieved XCO2 and XCH4 values are divided by a calibration factor. This values were determined by comparisons with in situ profiles measured by

TMS320C25 Digital Signal Processor For 2-Dimensional Fast Fourier Transform Computation

International Nuclear Information System (INIS)

Ardisasmita, M. Syamsa

1996-01-01

The Fourier transform is one of the most important mathematical tool in signal processing and analysis, which converts information from the time/spatial domain into the frequency domain. Even with implementation of the Fast Fourier Transform algorithms in imaging data, the discrete Fourier transform execution consume a lot of time. Digital signal processors are designed specifically to perform computation intensive digital signal processing algorithms. By taking advantage of the advanced architecture. parallel processing, and dedicated digital signal processing (DSP) instruction sets. This device can execute million of DSP operations per second. The device architecture, characteristics and feature suitable for fast Fourier transform application and speed-up are discussed

Single-particle characterization of summertime Antarctic aerosols collected at King George Island using quantitative energy-dispersive electron probe X-ray microanalysis and attenuated total reflection Fourier transform-infrared imaging techniques.

Science.gov (United States)

Maskey, Shila; Geng, Hong; Song, Young-Chul; Hwang, Heejin; Yoon, Young-Jun; Ahn, Kang-Ho; Ro, Chul-Un

2011-08-01

Single-particle characterization of Antarctic aerosols was performed to investigate the impact of marine biogenic sulfur species on the chemical compositions of sea-salt aerosols in the polar atmosphere. Quantitative energy-dispersive electron probe X-ray microanalysis was used to characterize 2900 individual particles in 10 sets of aerosol samples collected between March 12 and 16, 2009 at King Sejong Station, a Korean scientific research station located at King George Island in the Antarctic. Two size modes of particles, i.e., PM(2.5-10) and PM(1.0-2.5), were analyzed, and four types of particles were identified, with sulfur-containing sea-salt particles being the most abundant, followed by genuine sea-salt particles without sulfur species, iron-containing particles, and other species including CaCO(3)/CaMg(CO(3))(2), organic carbon, and aluminosilicates. When a sulfur-containing sea-salt particle showed an atomic concentration ratio of sulfur to sodium of >0.083 (seawater ratio), it is regarded as containing nonsea-salt sulfate (nss-SO(4)(2-)) and/or methanesulfonate (CH(3)SO(3)(-)), which was supported by attenuated total reflection Fourier transform-infrared imaging measurements. These internal mixture particles of sea-salt/CH(3)SO(3)(-)/SO(4)(2-) were very frequently encountered. As nitrate-containing particles were not encountered, and the air-masses for all of the samples originated from the Pacific Ocean (based on 5-day backward trajectories), the oxidation of dimethylsulfide (DMS) emitted from phytoplanktons in the ocean is most likely to be responsible for the formation of the mixed sea-salt/CH(3)SO(3)(-)/SO(4)(2-) particles.

The use of Fourier eigen transform to the boundary element method for transient elastodynamic problems

International Nuclear Information System (INIS)

Ji, X.; Chen, Y.M.

1989-01-01

The boundary element method (BEM) is developed from the boundary integral equation method and the discretization techniques. Compared with other numerical method, BEM has been shown to be a versatile and efficient method for a wide variety of engineering problems, including the wave propagation in elastic media. The first formulation and solution of the transient elastodynamic problem by combining BEM and Laplace transform is due to Cruse. Further improvement was achieved by introducing Durbin's method instead of Papoulis method of numerical Laplace inverse transform. However, a great deal of computer time is still needed for the inverse transformation. The alternative integral transform approach is BEM combining with Fourier transform. The numerical Fourier inverse transformation is also computer time consuming, even if the fast Fourier transform is used. In the present paper, the authors use BEM combining with Fourier transform and Fourier eigen transform (FET). The new approach is very attractive in saving on computer time. This paper illustrates the application of FET to BEM of 2-dimensional transient elastodynamic problem. The example of a half plane subjected to a discontinuous boundary load is solved on ELXSI 6400 computer. The CPU time is less than one minute. If Laplace or Fourier transform is adopted, the CPU time will be more than 10 minutes

Reduction and coding of synthetic aperture radar data with Fourier transforms

Science.gov (United States)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

Imaging properties of the mesooptical Fourier transform microscope for nuclear research emulsion

International Nuclear Information System (INIS)

Bencze, Gy.L.; Soroko, L.M.

1987-01-01

The optical signal transformation in the Mesooptical Fourier Transform Microscope (MFTM) for nuclear emulsion is treated in terms of Fourier Optics. A continuous conversion of the traditional optical microscope into the MFTM is followed. The images of dot-like and straight line objects given by the MFTM are discussed

Application of Fourier transforms for microwave radiometric inversions

Science.gov (United States)

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.

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)

Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation

NARCIS (Netherlands)

Bastiaans, M.J.; Leest, van A.J.

1998-01-01

Transformations of Gabor lattices are associated with operations on the window functions that arise in Gabor theory. In particular it is shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays

Reconstruction of on-axis lensless Fourier transform digital hologram with the screen division method

Science.gov (United States)

Jiang, Hongzhen; Liu, Xu; Liu, Yong; Li, Dong; Chen, Zhu; Zheng, Fanglan; Yu, Deqiang

2017-10-01

An effective approach for reconstructing on-axis lensless Fourier Transform digital hologram by using the screen division method is proposed. Firstly, the on-axis Fourier Transform digital hologram is divided into sub-holograms. Then the reconstruction result of every sub-hologram is obtained according to the position of corresponding sub-hologram in the hologram reconstruction plane with Fourier transform operation. Finally, the reconstruction image of on-axis Fourier Transform digital hologram can be acquired by the superposition of the reconstruction result of sub-holograms. Compared with the traditional reconstruction method with the phase shifting technology, in which multiple digital holograms are required to record for obtaining the reconstruction image, this method can obtain the reconstruction image with only one digital hologram and therefore greatly simplify the recording and reconstruction process of on-axis lensless Fourier Transform digital holography. The effectiveness of the proposed method is well proved with the experimental results and it will have potential application foreground in the holographic measurement and display field.

Fourier transform infrared spectroscopy for Kona coffee authentication.

Science.gov (United States)

Wang, Jun; Jun, Soojin; Bittenbender, H C; Gautz, Loren; Li, Qing X

2009-06-01

Kona coffee, the variety of "Kona typica" grown in the north and south districts of Kona-Island, carries a unique stamp of the region of Big Island of Hawaii, U.S.A. The excellent quality of Kona coffee makes it among the best coffee products in the world. Fourier transform infrared (FTIR) spectroscopy integrated with an attenuated total reflectance (ATR) accessory and multivariate analysis was used for qualitative and quantitative analysis of ground and brewed Kona coffee and blends made with Kona coffee. The calibration set of Kona coffee consisted of 10 different blends of Kona-grown original coffee mixture from 14 different farms in Hawaii and a non-Kona-grown original coffee mixture from 3 different sampling sites in Hawaii. Derivative transformations (1st and 2nd), mathematical enhancements such as mean centering and variance scaling, multivariate regressions by partial least square (PLS), and principal components regression (PCR) were implemented to develop and enhance the calibration model. The calibration model was successfully validated using 9 synthetic blend sets of 100% Kona coffee mixture and its adulterant, 100% non-Kona coffee mixture. There were distinct peak variations of ground and brewed coffee blends in the spectral "fingerprint" region between 800 and 1900 cm(-1). The PLS-2nd derivative calibration model based on brewed Kona coffee with mean centering data processing showed the highest degree of accuracy with the lowest standard error of calibration value of 0.81 and the highest R(2) value of 0.999. The model was further validated by quantitative analysis of commercial Kona coffee blends. Results demonstrate that FTIR can be a rapid alternative to authenticate Kona coffee, which only needs very quick and simple sample preparations.

Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data

Directory of Open Access Journals (Sweden)

Darian M. Onchiș

2011-09-01

Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

Science.gov (United States)

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane

Science.gov (United States)

Huang, Lin; Lenells, Jonatan

2018-03-01

Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions a , b , A , B. The functions a (k) and b (k) are defined via a nonlinear Fourier transform of the initial data, whereas A (k) and B (k) are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques.

Reduced Order Fractional Fourier Transform A New Variant to Fractional Signal Processing Definition and Properties

OpenAIRE

Kumar, Sanjay

2018-01-01

In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also derived and it is shown mathematically that when the rotation angle of Reduced Order Fractional Fourier Transform approaches 90 degrees, the propos...

Some notes concerning the fourier transformation of auto-correlation functions; Quelques notes sur la transformee de fourier des fonctions d'autocorrelation

Energy Technology Data Exchange (ETDEWEB)

Froelicher, B; Dalfes, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1968-07-01

A study is made of the passage of the auto-correlation function to the frequency spectrum by a numerical Fourier transformation. Two principal characteristics of auto-correlation functions, the time between two points and the total time, are related to two oscillations which appear in the frequency spectrum and which deform it. Various methods are proposed for reducing the effect of these two parasitic oscillations and for re-obtaining the real spectrum. (authors) [French] On etudie le passage de la fonction d'autocorrelation au spectre de frequence par transformee de Fourier numerique. Deux caracteristiques principales des fonctions d'autocorrelation, la duree entre points et la duree totale sont reliees a deux oscillations qui apparaissent dans le spectre de frequence et le deforment. Diverses methodes sont proposees pour reduire l'effet de ces deux oscillations parasites, et retrouver le spectre reel. (auteurs)

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)

Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

International Nuclear Information System (INIS)

Miao, J.; Sayre, D.; Chapman, H.N.

1998-01-01

It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2x in each dimension (i.e., oversampling by 4x for 2D and 8x for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop. copyright 1998 Optical Society of America

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

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

Pi, Fourier Transform and Ludolph van Ceulen

NARCIS (Netherlands)

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

DWDM-TO-OTDM Conversion by Time-Domain Optical Fourier Transformation

DEFF Research Database (Denmark)

Mulvad, Hans Christian Hansen; Hu, Hao; Galili, Michael

2011-01-01

We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated.......We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated....

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

International Nuclear Information System (INIS)

Jin Zhao; Zhang Han-Ming; Yan Bin; Li Lei; Wang Lin-Yuan; Cai Ai-Long

2016-01-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. (paper)

Application of finite Fourier transformation for the solution of the diffusion equation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1991-01-01

The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

Science.gov (United States)

Park, J. H.

1984-01-01

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

Science.gov (United States)

Morelli, Eugene A.

1997-01-01

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

Method of local pointed function reduction of original shape in Fourier transformation

International Nuclear Information System (INIS)

Dosch, H.; Slavyanov, S.Yu.

2002-01-01

The method for analytical reduction of the original shape in the one-dimensional Fourier transformation by the fourier image modulus is proposed. The basic concept of the method consists in the presentation of the model shape in the form of the local peak functions sum. The eigenfunctions, generated by the linear differential equations with the polynomial coefficients, are selected as the latter ones. This provides for the possibility of managing the Fourier transformation without numerical integration. This reduces the reverse task to the nonlinear regression with a small number of the evaluated parameters and to the numerical or asymptotic study on the model peak functions - the eigenfunctions of the differential tasks and their fourier images [ru

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.)

Toward a soft x-ray Fourier-transform spectrometer

International Nuclear Information System (INIS)

Howells, M.R.; Frank, K.; Hussain, Z.; Moler, E.J.; Reich, T.; Moeller, D.

1993-01-01

The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range ±1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

Science.gov (United States)

Holmes, J. J.; Balanis, C. A.

1974-01-01

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 equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were 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 were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.

Fourier-transform infrared spectroscopy for rapid screening and live-cell monitoring: application to nanotoxicology.

Science.gov (United States)

Sundaram, S K; Sacksteder, Colette A; Weber, Thomas J; Riley, Brian J; Addleman, R Shane; Harrer, Bruce J; Peterman, John W

2013-01-01

A significant challenge to realize the full potential of nanotechnology for therapeutic and diagnostic applications is to understand and evaluate how live cells interact with an external stimulus, such as a nanosized particle, and the toxicity and broad risk associated with these stimuli. It is difficult to capture the complexity and dynamics of these interactions by following omics-based approaches exclusively, which can be expensive and time-consuming. Attenuated total reflectance-Fourier transform infrared spectroscopy is well suited to provide noninvasive live-cell monitoring of cellular responses to potentially toxic nanosized particles or other stimuli. This alternative approach provides the ability to carry out rapid toxicity screenings and nondisruptive monitoring of live-cell cultures. We review the technical basis of the approach, the instrument configuration and interface with the biological media, the various effects that impact the data, subsequent data analysis and toxicity, and present some preliminary results on live-cell monitoring.

Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

Science.gov (United States)

Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

2016-10-01

The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

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...

Discrete Fourier Transform in a Complex Vector Space

Science.gov (United States)

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.

Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.

Science.gov (United States)

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.

Properly used ''aliasing'' can give better resolution from fewer points in Fourier transform spectroscopy

Science.gov (United States)

D'Astous, Y.; Blanchard, M.

1982-05-01

In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)

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 ...

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)

Fourier transforms on a semisimple symmetric space

NARCIS (Netherlands)

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

NARCIS (Netherlands)

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

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

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 ...

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 ...

S-duality as Fourier transform for arbitrary ϵ1, ϵ2

International Nuclear Information System (INIS)

N Nemkov

2014-01-01

The Alday–Gaiotto–Tachikawa relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that, for the four-point conformal block, the modular transform up to the non-perturbative contributions can be written in the form of the ordinary Fourier transform when β ≡ −ϵ 1 /ϵ 2 = 1. Here I extend this conjecture to general values of ϵ 1 , ϵ 2 . Namely, I argue that, for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters ϵ 1 , ϵ 2 . The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant g 2 ≡ −ϵ 1 ϵ 2 and hypermultiplet masses. (paper)

The Pegg–Barnett phase operator and the discrete Fourier transform

International Nuclear Information System (INIS)

Perez-Leija, Armando; Szameit, Alexander; Andrade-Morales, Luis A; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2016-01-01

In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg–Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London–Susskind–Glogower phase operator, whose natural logarithm gives rise to the Pegg–Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties. (invited comment)

Fourier Transform Spectrometer System

Science.gov (United States)

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.

The su(2)α Hahn oscillator and a discrete Fourier-Hahn transform

International Nuclear Information System (INIS)

Jafarov, E I; Stoilova, N I; Van der Jeugt, J

2011-01-01

We define the quadratic algebra su(2) α which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2) α . We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2) α . It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this so-called discrete Fourier-Hahn transform is computed explicitly. The matrix of this discrete Fourier-Hahn transform has many interesting properties, similar to those of the traditional discrete Fourier transform. (paper)

[Continuum based fast Fourier transform processing of infrared spectrum].

Science.gov (United States)

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.

Quantum Fourier Transform Over Galois Rings

OpenAIRE

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 Methods. Chapter 4

Science.gov (United States)

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..

Application of the fractional Fourier transform to image reconstruction in MRI.

Science.gov (United States)

Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

2012-07-01

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

Time-Domain Optical Fourier Transformation for OTDM-DWDM and DWDM-OTDM Conversion

DEFF Research Database (Denmark)

Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael

2011-01-01

Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats.......Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats....

Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy*

OpenAIRE

Liu, Yan-de; Ying, Yi-bin; Fu, Xia-ping

2005-01-01

To develop nondestructive acidity prediction for intact Fuji apples, the potential of Fourier transform near infrared (FT-NIR) method with fiber optics in interactance mode was investigated. Interactance in the 800 nm to 2619 nm region was measured for intact apples, harvested from early to late maturity stages. Spectral data were analyzed by two multivariate calibration techniques including partial least squares (PLS) and principal component regression (PCR) methods. A total of 120 Fuji appl...

Ultrafast and versatile spectroscopy by temporal Fourier transform

Science.gov (United States)

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 transform digital holographic adaptive optics imaging system

Science.gov (United States)

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

The Fourier transform for certain hyperkähler fourfolds

CERN Document Server

Shen, Mingmin

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 \\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 Hyperkähler 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.

Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

International Nuclear Information System (INIS)

Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P

2011-01-01

According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.

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...

SPICA/SAFARI fourier transform spectrometer mechanism evolutionary design

NARCIS (Netherlands)

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

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

Multi-Beam Radio Frequency (RF) Aperture Arrays Using Multiplierless Approximate Fast Fourier Transform (FFT)

Science.gov (United States)

2017-08-01

Fourier transform, discrete Fourier transform, digital array processing , antenna beamformers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF...125 3.7 Simulation of 2-D Beams Cross Sections .................................................................... 125 3.7.1 8...unlimited. List of Figures Figure Page Figure 1: N-beam Array Processing System using a Linear Array

Fourier transform ion cyclotron resonance mass spectrometry

Science.gov (United States)

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.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

Science.gov (United States)

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

A Fourier-Transform Infrared Study of Biochar Aging in Soils

Science.gov (United States)

Singh, B.; Fang, Y.; Johnston, C.T.

2018-01-01

We used diffuse reflectance Fourier-transform infrared (DR-FTIR) spectroscopy, X-ray diffraction (XRD), and chemical and isotopic analyses to characterize the light fraction of four contrasting soils (control and biocharamended soils) to determine changes in biochar properties after aging. Two Eucalyptus saligna Sm. wood biochars, produced at 450°C (B450) and 550°C (B550), were incubated separately in each of the four soils for up to 12 mo at 20, 40, and 60°C. Total C and isotopic (δ13C) methods were used to quantify the amounts of biochar C and native C mineralized during incubation. The DR-FTIR spectra of the light fraction showed distinct absorption bands representing native soil organic C, biochar C, and mineral constituents present in the soils; the mineral bands were consistent with XRD data of the clay fraction of the four soils. Analysis of the DR-FTIR spectra in the ν(C–H) bands showed that the ratio of the aromatic ν(C–H) bands systematically increased relative to the aliphatic ν(C–H) bands with increasing mineralization of biochar C in the B550 amended soils, and this relationship was unique for each soil type. In contrast, this relationship was not observed for the B450 amended soils that contained a relatively smaller proportion of aromatic C. PMID:29657354

Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform

International Nuclear Information System (INIS)

Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet; Torres, Yezid

2014-01-01

We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations. (paper)

Machine learning (ML)-guided OPC using basis functions of polar Fourier transform

Science.gov (United States)

Choi, Suhyeong; Shim, Seongbo; Shin, Youngsoo

2016-03-01

With shrinking feature size, runtime has become a limitation of model-based OPC (MB-OPC). A few machine learning-guided OPC (ML-OPC) have been studied as candidates for next-generation OPC, but they all employ too many parameters (e.g. local densities), which set their own limitations. We propose to use basis functions of polar Fourier transform (PFT) as parameters of ML-OPC. Since PFT functions are orthogonal each other and well reflect light phenomena, the number of parameters can significantly be reduced without loss of OPC accuracy. Experiments demonstrate that our new ML-OPC achieves 80% reduction in OPC time and 35% reduction in the error of predicted mask bias when compared to conventional ML-OPC.

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 ...

Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes

KAUST Repository

Lin, Sian-Jheng; Al-Naffouri, Tareq Y.; Han, Yunghsiang S.; Chung, Wei-Ho

2016-01-01

In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h

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.

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

Science.gov (United States)

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

Fourier transform wavefront control with adaptive prediction of the atmosphere.

Science.gov (United States)

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-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.

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

From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation

NARCIS (Netherlands)

Bastiaans, M.J.; Leest, van A.J.

1998-01-01

Transformations of Gabor lattices have been associated with operations on the window functions that arise in Gabor theory. In particular it has been shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function,

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

Science.gov (United States)

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity

NARCIS (Netherlands)

Atakishiyeva, M.K.; Atakishiyev, N.M.; Koornwinder, T.H.

2009-01-01

It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.

Hochauflösende Fourier-Transform-Emissionsspektroskopie

OpenAIRE

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...

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 ...

FREQUENCY COMPONENT EXTRACTION OF HEARTBEAT CUES WITH SHORT TIME FOURIER TRANSFORM (STFT

Directory of Open Access Journals (Sweden)

Sumarna Sumarna

2017-01-01

  Electro-acoustic human heartbeat detector have been made with the main parts : (a stetoscope (piece chest, (b mic condenser, (c transistor amplifier, and (d cues analysis program with MATLAB. The frequency components that contained in heartbeat. cues have also been extracted with Short Time Fourier Transform (STFT from 9 volunteers. The results of the analysis showed that heart rate appeared in every cue frequency spectrum with their harmony. The steps of the research were including detector instrument design, test and instrument repair, cues heartbeat recording with Sound Forge 10 program and stored in wav file ; cues breaking at the start and the end, and extraction/cues analysis using MATLAB. The MATLAB program included filter (bandpass filter with bandwidth between 0.01 – 110 Hz, cues breaking with hamming window and every part was calculated using Fourier Transform (STFT mechanism and the result were shown in frequency spectrum graph.   Keywords: frequency components extraction, heartbeat cues, Short Time Fourier Transform

Step-scan Fourier transform infrared (FTIR) spectrometer for investigating chemical reactions of energy-related materials. Final report, April 1, 1995--March 31, 1997

Energy Technology Data Exchange (ETDEWEB)

Eyring, E.M.

1997-11-04

Two step-scan Fourier transform infrared (FTIR) spectrometers were purchased with URI-DOE funds by the University of Utah. These infrared spectrometers have been used to carry out the following investigations: the determination of strength of adsorption of organic molecules at the liquid-solid interface of coated attenuated total reflectance (ATR) elements, the kinetic study of the photoinitiated polymerization of a dental resin, the exploration of the kinetics of photochemical reactions of organic molecules in solution, and the development of a stopped-flow FTIR interface for measuring rates and mechanisms of reactions in solution that are not photoinitiated and do not have convenient ultraviolet-visible spectral features.

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.

Science.gov (United States)

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.

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.

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

Application of the fourier and wavelet transforms in noise reduction of the out of the ordinary data

International Nuclear Information System (INIS)

Tafreshi, M. A.; Sadeghi, Y.

2006-01-01

In this article the noise reduction of the experimental data by the Fourier and the wavelet transforms has been investigated. Using both simulated and experimental data (from the plasma focus facility, Dena), the sensitive features of the application of the Fourier transform are visualized and discussed. Then, the main idea of the wavelet transform and the results of the noise reduction with this transform are presented. Due to this investigation, for the cases such as the current derivative of the Dena facility, where the reliability of the Fourier transform can be doubtful, the wavelet transform can be considered as a more accurate alternative approach

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

Science.gov (United States)

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Fourier Transform Infrared Radiation Spectroscopy Applied for Wood Rot Decay and Mould Fungi Growth Detection

Directory of Open Access Journals (Sweden)

Bjørn Petter Jelle

2012-01-01

Full Text Available Material characterization may be carried out by the attenuated total reflectance (ATR Fourier transform infrared (FTIR radiation spectroscopical technique, which represents a powerful experimental tool. The ATR technique may be applied on both solid state materials, liquids, and gases with none or only minor sample preparations, also including materials which are nontransparent to IR radiation. This facilitation is made possible by pressing the sample directly onto various crystals, for example, diamond, with high refractive indices, in a special reflectance setup. Thus ATR saves time and enables the study of materials in a pristine condition, that is, the comprehensive sample preparation by pressing thin KBr pellets in traditional FTIR transmittance spectroscopy is hence avoided. Materials and their ageing processes, both ageing by natural and accelerated climate exposure, decomposition and formation of chemical bonds and products, may be studied in an ATR-FTIR analysis. In this work, the ATR-FTIR technique is utilized to detect wood rot decay and mould fungi growth on various building material substrates. An experimental challenge and aim is to be able to detect the wood rot decay and mould fungi growth at early stages when it is barely visible to the naked eye. Another goal is to be able to distinguish between various species of fungi and wood rot.

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....

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.

The Fractional Fourier Transform and Its Application to Energy Localization Problems

Directory of Open Access Journals (Sweden)

ter Morsche Hennie G

2003-01-01

Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.

OTDM-WDM Conversion Based on Time-Domain Optical Fourier Transformation with Spectral Compression

DEFF Research Database (Denmark)

Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael

2011-01-01

We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown.......We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown....

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...

A validated Fourier transform infrared spectroscopy method for quantification of total lactones in Inula racemosa and Andrographis paniculata.

Science.gov (United States)

Shivali, Garg; Praful, Lahorkar; Vijay, Gadgil

2012-01-01

Fourier transform infrared (FT-IR) spectroscopy is a technique widely used for detection and quantification of various chemical moieties. This paper describes the use of the FT-IR spectroscopy technique for the quantification of total lactones present in Inula racemosa and Andrographis paniculata. To validate the FT-IR spectroscopy method for quantification of total lactones in I. racemosa and A. paniculata. Dried and powdered I. racemosa roots and A. paniculata plant were extracted with ethanol and dried to remove ethanol completely. The ethanol extract was analysed in a KBr pellet by FT-IR spectroscopy. The FT-IR spectroscopy method was validated and compared with a known spectrophotometric method for quantification of lactones in A. paniculata. By FT-IR spectroscopy, the amount of total lactones was found to be 2.12 ± 0.47% (n = 3) in I. racemosa and 8.65 ± 0.51% (n = 3) in A. paniculata. The method showed comparable results with a known spectrophotometric method used for quantification of such lactones: 8.42 ± 0.36% (n = 3) in A. paniculata. Limits of detection and quantification for isoallantolactone were 1 µg and 10 µg respectively; for andrographolide they were 1.5 µg and 15 µg respectively. Recoveries were over 98%, with good intra- and interday repeatability: RSD ≤ 2%. The FT-IR spectroscopy method proved linear, accurate, precise and specific, with low limits of detection and quantification, for estimation of total lactones, and is less tedious than the UV spectrophotometric method for the compounds tested. This validated FT-IR spectroscopy method is readily applicable for the quality control of I. racemosa and A. paniculata. Copyright © 2011 John Wiley & Sons, Ltd.

Pulse shaping using the optical Fourier transform technique - for ultra-high-speed signal processing

DEFF Research Database (Denmark)

Palushani, Evarist; Oxenløwe, Leif Katsuo; Galili, Michael

2009-01-01

This paper reports on the generation of a 1.6 ps FWHM flat-top pulse using the optical Fourier transform technique. The pulse is validated in a 320 Gbit/s demultiplexing experiment.......This paper reports on the generation of a 1.6 ps FWHM flat-top pulse using the optical Fourier transform technique. The pulse is validated in a 320 Gbit/s demultiplexing experiment....

Quaternion Fourier transforms for signal and image processing

CERN Document Server

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.

Simple surface structure determination from Fourier transforms of angle-resolved photoemission extended fine structure

Energy Technology Data Exchange (ETDEWEB)

Zheng, Y. [Pennsylvania State Univ., University Park, PA (United States)]|[Lawrence Berkeley Lab., CA (United States); Shirley, D.A. [Pennsylvania State Univ., University Park, PA (United States)

1995-02-01

The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.

Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

Science.gov (United States)

Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

2018-02-01

Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

Dual-polarization nonlinear Fourier transform-based optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone; Perego, A. M.; da Silva, Edson Porto

2018-01-01

communication could potentially overcome these limitations. It relies on a mathematical technique called “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical...

Fourier transform infrared spectroscopy in physics laboratory courses

International Nuclear Information System (INIS)

Möllmann, K-P; Vollmer, M

2013-01-01

Infrared spectrometry is one of the most important tools in the field of spectroscopic analysis. This is due to the high information content of spectra in the so-called spectroscopic fingerprint region, which enables measurement not only of gases, but also of liquids and solids. Today, infrared spectroscopy is almost completely dominated by Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy is able to detect minute quantities in the ppm and ppb ranges, and the respective analyses are now standard tools in science as well as industry. Therefore FTIR spectroscopy should be taught within the standard curriculum at university to physicists and engineers. Here we present respective undergraduate laboratory experiments designed for students at the end of their third year. Experiments deal first with understanding the spectrometer and second with recording and analysing spectra. On the one hand, transmission spectra of gases are treated which relate to environmental analytics (being probably the most prominent and well-known examples), and on the other hand, the focus is on the transmission and reflection spectra of solids. In particular, silicon wafers are studied—as is regularly done in the microelectronics industry—in order to characterize their thickness, oxygen content and phonon modes. (paper)

Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

International Nuclear Information System (INIS)

Aerts, Diederik; Czachor, Marek; Kuna, Maciej

2016-01-01

Highlights: • Fractal arithmetic allows to define Fourier transforms on Cantor-like sets. • General construction is illustrated on the example of a sawtooth signal. • The formalism is much simpler than the approaches discussed so far in the literature. - Abstract: Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation

International Nuclear Information System (INIS)

Aldea, N; Pintea, S; Rednic, V; Matei, F; Hu Tiandou; Xie Yaning

2009-01-01

The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe 3 O 4 core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.

Fourier transforms in the complex domain

CERN Document Server

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 Münz and Szász 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,

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

Science.gov (United States)

Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

2009-05-01

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

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.

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

Science.gov (United States)

Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

2017-09-01

Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

Time dependent and asymptotic neutron number probability distribution calculation using discrete Fourier transform

International Nuclear Information System (INIS)

Humbert, Ph.

2005-01-01

In this paper we consider the probability distribution of neutrons in a multiplying assembly. The problem is studied using a space independent one group neutron point reactor model without delayed neutrons. We recall the generating function methodology and analytical results obtained by G.I. Bell when the c 2 approximation is used and we present numerical solutions in the general case, without this approximation. The neutron source induced distribution is calculated using the single initial neutron distribution which satisfies a master (Kolmogorov backward) equation. This equation is solved using the generating function method. The generating function satisfies a differential equation and the probability distribution is derived by inversion of the generating function. Numerical results are obtained using the same methodology where the generating function is the Fourier transform of the probability distribution. Discrete Fourier transforms are used to calculate the discrete time dependent distributions and continuous Fourier transforms are used to calculate the asymptotic continuous probability distributions. Numerical applications are presented to illustrate the method. (author)

Baseline correction combined partial least squares algorithm and its application in on-line Fourier transform infrared quantitative analysis.

Science.gov (United States)

Peng, Jiangtao; Peng, Silong; Xie, Qiong; Wei, Jiping

2011-04-01

In order to eliminate the lower order polynomial interferences, a new quantitative calibration algorithm "Baseline Correction Combined Partial Least Squares (BCC-PLS)", which combines baseline correction and conventional PLS, is proposed. By embedding baseline correction constraints into PLS weights selection, the proposed calibration algorithm overcomes the uncertainty in baseline correction and can meet the requirement of on-line attenuated total reflectance Fourier transform infrared (ATR-FTIR) quantitative analysis. The effectiveness of the algorithm is evaluated by the analysis of glucose and marzipan ATR-FTIR spectra. BCC-PLS algorithm shows improved prediction performance over PLS. The root mean square error of cross-validation (RMSECV) on marzipan spectra for the prediction of the moisture is found to be 0.53%, w/w (range 7-19%). The sugar content is predicted with a RMSECV of 2.04%, w/w (range 33-68%). Copyright © 2011 Elsevier B.V. All rights reserved.

High-resolution magnetic-domain imaging by Fourier transform holography at 21 nm wavelength

International Nuclear Information System (INIS)

Schaffert, Stefan; Pfau, Bastian; Günther, Christian M; Schneider, Michael; Korff Schmising, Clemens von; Eisebitt, Stefan; Geilhufe, Jan

2013-01-01

Exploiting x-ray magnetic circular dichroism at the L-edges of 3d transition metals, Fourier transform holography has become a standard technique to investigate magnetic samples with sub-100 nm spatial resolution. Here, magnetic imaging in the 21 nm wavelength regime using M-edge circular dichroism is demonstrated. Ultrafast pulses in this wavelength regime are increasingly available from both laser- and accelerator-driven soft x-ray sources. We explain the adaptations concerning sample preparation and data evaluation compared to conventional holography in the 1 nm wavelength range. We find the correction of the Fourier transform hologram to in-plane Fourier components to be critical for high-quality reconstruction and demonstrate 70 nm spatial resolution in magnetization imaging with this approach. (paper)

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

Energy Technology Data Exchange (ETDEWEB)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net [NASA Ames Research Center, Astrobiology and Space Science Division, Moffett Field, CA 94035 (United States)

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

International Nuclear Information System (INIS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules

International Nuclear Information System (INIS)

Dong Ping; Yang Ming; Cao Zhuoliang

2008-01-01

In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system

All-optical signal processing of OTDM and OFDM signals based on time-domain Optical Fourier Transformation

DEFF Research Database (Denmark)

Clausen, Anders; Guan, Pengyu; Mulvad, Hans Christian Hansen

2014-01-01

All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented.......All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented....

Analysis of gamma-ray spectra by using fast Fourier transform

International Nuclear Information System (INIS)

Tominaga, Shoji; Nagata, Shojiro; Nayatani, Yoshinobu; Ueda, Isamu; Sasaki, Satoshi.

1977-01-01

In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform devised. The validity of the method was confirmed by a computer simulation for spectra of a NaI detector. The method uses the fact that spectral data can be represented by Fourier series with reduced number of terms. The estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features in the method and a general problem to be solved in a response matrix method are described. (auth.)

Use of fast Fourier transform in gamma-ray spectral analysis

International Nuclear Information System (INIS)

Tominaga, Shoji; Nayatani, Yoshinobu; Nagata, Shojiro; Sasaki, Takashi; Ueda, Isamu.

1978-01-01

In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform has been devised. The validity of the method has been confirmed by computer simulation for spectra of a NaI detector. First, it is shown that spectral data can be represented by Fourier series with a reduced number of terms. Then the estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features of the method and a general problem to be solved in relation to a response matrix method are described. (author)

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.

Multivariate analysis of attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopic data to confirm phase partitioning in methacrylate-based dentin adhesive.

Science.gov (United States)

Ye, Qiang; Parthasarathy, Ranganathan; Abedin, Farhana; Laurence, Jennifer S; Misra, Anil; Spencer, Paulette

2013-12-01

Water is ubiquitous in the mouths of healthy individuals and is a major interfering factor in the development of a durable seal between the tooth and composite restoration. Water leads to the formation of a variety of defects in dentin adhesives; these defects undermine the tooth-composite bond. Our group recently analyzed phase partitioning of dentin adhesives using high-performance liquid chromatography (HPLC). The concentration measurements provided by HPLC offered a more thorough representation of current adhesive performance and elucidated directions to be taken for further improvement. The sample preparation and instrument analysis using HPLC are, however, time-consuming and labor-intensive. The objective of this work was to develop a methodology for rapid, reliable, and accurate quantitative analysis of near-equilibrium phase partitioning in adhesives exposed to conditions simulating the wet oral environment. Analysis by Fourier transform infrared (FT-IR) spectroscopy in combination with multivariate statistical methods, including partial least squares (PLS) regression and principal component regression (PCR), were used for multivariate calibration to quantify the compositions in separated phases. Excellent predictions were achieved when either the hydrophobic-rich phase or the hydrophilic-rich phase mixtures were analyzed. These results indicate that FT-IR spectroscopy has excellent potential as a rapid method of detection and quantification of dentin adhesives that experience phase separation under conditions that simulate the wet oral environment.

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

On Analog of Fourier Transform in Interior of the Light Cone

Directory of Open Access Journals (Sweden)

Tatyana Shtepina

2014-01-01

Full Text Available We introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that Fhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.

Physiological response of Arundo donax to cadmium stress by Fourier transform infrared spectroscopy.

Science.gov (United States)

Yu, Shunhui; Sheng, Li; Zhang, Chunyan; Deng, Hongping

2018-06-05

The present paper deals with the physiological response of the changes in chemical contents of the root, stem and leaf of Arundo donax seedlings stressed by excess cadmium using Fourier transform infrared spectroscopy technique, cadmium accumulation in plant by atomic absorption spectroscopy were tested after different concentrations cadmium stress. The results showed that low cadmium concentrations (Fourier transform infrared spectroscopy technique for the non-invasive and rapid monitoring of the plants stressed with heavy metals, Arundo donax is suitable for phytoremediation of cadmium -contaminated wetland. Copyright © 2018 Elsevier B.V. All rights reserved.

The Fourier transform as a signature for chaos in nuclear energy levels

International Nuclear Information System (INIS)

Bybee, C.R.; Mitchell, G.E.; Shriner, J.F. Jr.

1996-01-01

The Fourier transform of the autocorrelation function is an alternative test to characterize level statistics. For GOE statistics there is a suppression of the Fourier transform near the origin; this correlation hole is absent for Poisson statistics. Numerical modeling has been used to quantify the method and determine the dependence of the correlation-hole area on number, density, sampling interval, and fraction of missing or spurious levels. For large N the normalized correlation-hole area is a nearly universal constant and insensitive to missing and spurious levels. However, for the smaller sample sizes typical of nuclear data, application of the FT method yields ambiguous results. (orig.)

The Fourier transform as a signature for chaos in nuclear energy levels

Energy Technology Data Exchange (ETDEWEB)

Bybee, C.R. [North Carolina State Univ., Raleigh, NC (United States)]|[Triangle Universities Nuclear Lab., Durham, NC (United States); Mitchell, G.E. [North Carolina State Univ., Raleigh, NC (United States)]|[Triangle Universities Nuclear Lab., Durham, NC (United States); Shriner, J.F. Jr. [Tennessee Technological Univ., Cookeville (United States)

1996-08-01

The Fourier transform of the autocorrelation function is an alternative test to characterize level statistics. For GOE statistics there is a suppression of the Fourier transform near the origin; this correlation hole is absent for Poisson statistics. Numerical modeling has been used to quantify the method and determine the dependence of the correlation-hole area on number, density, sampling interval, and fraction of missing or spurious levels. For large N the normalized correlation-hole area is a nearly universal constant and insensitive to missing and spurious levels. However, for the smaller sample sizes typical of nuclear data, application of the FT method yields ambiguous results. (orig.)

PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

Science.gov (United States)

Open-path Fourier transform infrared (OP-FT1R) spectroscopy is an accepted technology for measuring gaseous air contaminants. OP-FT1R absorbance spectra acquired during changing aerosols conditions reveal related changes in very broad baseline features. Usually, this shearing of ...

Analog fourier transform channelizer and OFDM receiver

OpenAIRE

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 ...

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.

Fourier transform inequalities for phylogenetic trees.

Science.gov (United States)

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.

Progress report of a static Fourier transform spectrometer breadboard

Science.gov (United States)

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.

Fourier transform infrared spectroscopy of peptides.

Science.gov (United States)

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.

On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity

OpenAIRE

Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.

2008-01-01

It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.

APPLICATION OF STANDARDIZED QUALITY CONTROL PROCEDURES TO OPEN-PATH FOURIER TRANSFORM INFRARED DATA COLLECTED AT A CONCENTRATED SWINE PRODUCTION FACILITY

Science.gov (United States)

Open-path Fourier transform infrared (OP/FT-IR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric eases at a concentrated swine production facility. A total of 2200 OP/FT-IR spectra were acquired along nine different monitoring paths d...

OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation

DEFF Research Database (Denmark)

Palushani, Evarist; Richter, T.; Ludwig, R.

2012-01-01

We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information.......We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information....

Products of multiple Fourier series with application to the multiblade transformation

Science.gov (United States)

Kunz, D. L.

1981-01-01

A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.

Diffuse reflectance infrared Fourier-Transform spectra of selected organic compounds

Energy Technology Data Exchange (ETDEWEB)

Harmon, S.H.; Caton, J.E.

1982-05-01

Diffuse reflectance infrared spectra of a variety of different organic compounds have been determined. Profiles of the spectra along with the location and relative intensity of the principal bands have been included for each compound studied. In addition both diffuse reflectance and transmittance infrared spectra were obtained for the same samples, and the spectral results were compared. Although some minor variations are observed between a diffuse reflectance spectrum and the corresponding transmittance spectrum, the diffuse reflectance is quite useful and may be a superior technique for the study of many samples because it possesses an inherently higher signal-to-noise response, requires less sample preparation and allows a very wide range of samples (solids, liquids of low volatility, neat sample, or sample diluted in a reflecting medium) to be studied under very similar conditions.

Spectrogram analysis of selected tremor signals using short-time Fourier transform and continuous wavelet transform

Energy Technology Data Exchange (ETDEWEB)

Bartosch, T. [Erlanger-Nuernberg Univ., Erlanger (Germany). Lehrstul fuer Nachrichtentechnik I; Seidl, D. [Seismologisches Zentralobservatorium Graefenberg, Erlanegen (Greece). Bundesanstalt fuer Geiwissenschaften und Rohstoffe

1999-06-01

Among a variety of spectrogram methods short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were selected to analyse transients in non-stationary signals. Depending on the properties of the tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli (Italy).

HIGH-RESOLUTION FOURIER TRANSFORM SPECTROSCOPY OF Nb i IN THE NEAR-INFRARED

Energy Technology Data Exchange (ETDEWEB)

Er, A.; Güzelçimen, F.; Başar, Gö.; Öztürk, I. K. [Faculty of Science, Physics Department, Istanbul University, TR-34134 Vezneciler, Istanbul (Turkey); Tamanis, M.; Ferber, R. [Laser Centre, The University of Latvia, Rainis Boulevard 19, LV-1586 Riga (Latvia); Kröger, S., E-mail: gbasar@istanbul.edu.tr, E-mail: sophie.kroeger@htw-berlin.de [Hochschule für Technik und Wirtschaft Berlin, Wilhelminenhofstrasse 75A, D-12459 Berlin (Germany)

2015-11-15

In this study, a Fourier Transform spectrum of Niobium (Nb) is investigated in the near-infrared spectral range from 6000 to 12,000 cm{sup −1} (830–1660 nm). The Nb spectrum is produced using a hollow cathode discharge lamp in an argon atmosphere. Both Nb and Ar spectral lines are visible in the spectrum. A total of 110 spectral lines are assigned to the element Nb. Of these lines, 90 could be classified as transitions between known levels of atomic Nb. From these classified Nb i transitions, 27 have not been listed in literature previously. Additionally, 8 lines are classified for the first time.

Attenuated total internal reflection infrared microspectroscopic imaging using a large-radius germanium internal reflection element and a linear array detector.

Science.gov (United States)

Patterson, Brian M; Havrilla, George J

2006-11-01

The number of techniques and instruments available for Fourier transform infrared (FT-IR) microspectroscopic imaging has grown significantly over the past few years. Attenuated total internal reflectance (ATR) FT-IR microspectroscopy reduces sample preparation time and has simplified the analysis of many difficult samples. FT-IR imaging has become a powerful analytical tool using either a focal plane array or a linear array detector, especially when coupled with a chemometric analysis package. The field of view of the ATR-IR microspectroscopic imaging area can be greatly increased from 300 x 300 microm to 2500 x 2500 microm using a larger internal reflection element of 12.5 mm radius instead of the typical 1.5 mm radius. This gives an area increase of 70x before aberrant effects become too great. Parameters evaluated include the change in penetration depth as a function of beam displacement, measurements of the active area, magnification factor, and change in spatial resolution over the imaging area. Drawbacks such as large file size will also be discussed. This technique has been successfully applied to the FT-IR imaging of polydimethylsiloxane foam cross-sections, latent human fingerprints, and a model inorganic mixture, which demonstrates the usefulness of the method for pharmaceuticals.

Numerical computation of the discrete Fourier transform and its applications in the statistic processing of experimental data

International Nuclear Information System (INIS)

Marinescu, D.C.; Radulescu, T.G.

1977-06-01

The Integral Fourier Transform has a large range of applications in such areas as communication theory, circuit theory, physics, etc. In order to perform discrete Fourier Transform the Finite Fourier Transform is defined; it operates upon N samples of a uniformely sampled continuous function. All the properties known in the continuous case can be found in the discrete case also. The first part of the paper presents the relationship between the Finite Fourier Transform and the Integral one. The computing of a Finite Fourier Transform is a problem in itself since in order to transform a set of N data we have to perform N 2 ''operations'' if the transformation relations are used directly. An algorithm known as the Fast Fourier Transform (FFT) reduces this figure from N 2 to a more reasonable Nlog 2 N, when N is a power of two. The original Cooley and Tuckey algorithm for FFT can be further improved when higher basis are used. The price to be paid in this case is the increase in complexity of such algorithms. The recurrence relations and a comparation among such algorithms are presented. The key point in understanding the application of FFT resides in the convolution theorem which states that the convolution (an N 2 type procedure) of the primitive functions is equivalent to the ordinar multiplication of their transforms. Since filtering is actually a convolution process we present several procedures to perform digital filtering by means of FFT. The best is the one using the segmentation of records and the transformation of pairs of records. In the digital processing of signals, besides digital filtering a special attention is paid to the estimation of various statistical characteristics of a signal as: autocorrelation and correlation functions, periodiograms, density power sepctrum, etc. We give several algorithms for the consistent and unbiased estimation of such functions, by means of FFT. (author)

How to use the Fast Fourier Transform in Large Finite Fields

OpenAIRE

Petersen, Petur Birgir

2011-01-01

The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.

Stress wave calculations in composite plates using the fast Fourier transform.

Science.gov (United States)

Moon, F. C.

1973-01-01

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

Characterization of Printing Inks Using DART-Q-TOF-MS and Attenuated Total Reflectance (ATR) FTIR.

Science.gov (United States)

Williamson, Rhett; Raeva, Anna; Almirall, Jose R

2016-05-01

The rise in improved and widely accessible printing technology has resulted in an interest to develop rapid and minimally destructive chemical analytical techniques that can characterize printing inks for forensic document analysis. Chemical characterization of printing inks allows for both discrimination of inks originating from different sources and the association of inks originating from the same source. Direct analysis in real-time mass spectrometry (DART-MS) and attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) were used in tandem to analyze four different classes of printing inks: inkjets, toners, offset, and intaglio. A total of 319 samples or ~ 80 samples from each class were analyzed directly on a paper substrate using the two methods. DART-MS was found to characterize the semi-volatile polymeric vehicle components, while ATR-FTIR provided chemical information associated with the bulk components of these inks. Complimentary data results in improved discrimination when both techniques are used in succession resulting in >96% discrimination for all toners, 95% for all inkjets, >92% for all offset, and >54% for all intaglio inks. © 2016 American Academy of Forensic Sciences.

Experimental demonstrations of the properties of Fourier transforms using diffraction phenomena

International Nuclear Information System (INIS)

Bazin, M.J.; Lucie, P.H.; Oliveira, S.M.M. de.

1984-01-01

The standard mathematical properties of Fourier transforms and the experimental characteristics of diffraction phenomena are systematically brought together. An experimental realization of a particular case of the convolution theorem is displayed in details. (Author) [pt

Calibration of the Herschel SPIRE Fourier Transform Spectrometer

OpenAIRE

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...

On Fourier re-expansions

OpenAIRE

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.

Modification of kaolinite surfaces through mechanochemical activation with quartz: A diffuse reflectance infrared fourier transform and chemometrics study.

Science.gov (United States)

Carmody, Onuma; Frost, Ray L; Kristóf, János; Kokot, Serge; Kloprogge, J Theo; Makó, Eva

2006-12-01

Studies of kaolinite surfaces are of industrial importance. One useful method for studying the changes in kaolinite surface properties is to apply chemometric analyses to the kaolinite surface infrared spectra. A comparison is made between the mechanochemical activation of Kiralyhegy kaolinites with significant amounts of natural quartz and the mechanochemical activation of Zettlitz kaolinite with added quartz. Diffuse reflectance infrared Fourier transform (DRIFT) spectra were analyzed using principal component analysis (PCA) and multi-criteria decision making (MCDM) methods, the preference ranking organization method for enrichment evaluations (PROMETHEE) and geometrical analysis for interactive assistance (GAIA). The clear discrimination of the Kiralyhegy spectral objects on the two PC scores plots (400-800 and 800-2030 cm(-1)) indicated the dominance of quartz. Importantly, no ordering of any spectral objects appeared to be related to grinding time in the PC plots of these spectral regions. Thus, neither the kaolinite nor the quartz are systematically responsive to grinding time according to the spectral criteria investigated. The third spectral region (2600-3800 cm(-1), OH vibrations), showed apparent systematic ordering of the Kiralyhegy and, to a lesser extent, Zettlitz spectral objects with grinding time. This was attributed to the effect of the natural quartz on the delamination of kaolinite and the accompanying phenomena (i.e., formation of kaolinite spheres and water). The mechanochemical activation of kaolinite and quartz, through dry grinding, results in changes to the surface structure. Different grinding times were adopted to study the rate of destruction of the kaolinite and quartz structures. This relationship (i.e., grinding time) was classified using PROMETHEE and GAIA methodology.

All-optical signal processing of OTDM and OFDM signals based on time-domain optical fourier transformation

DEFF Research Database (Denmark)

Galili, Michael; Guan, Pengyu; Lillieholm, Mads

2017-01-01

In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed.......In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed....

Subwavelength Fourier-transform imaging without a lens or a beamsplitter

International Nuclear Information System (INIS)

Liu Rui-Feng; Yuan Xin-Xing; Fang Yi-Zhen; Zhang Pei; Zhou Yu; Gao Hong; Li Fu-Li

2014-01-01

The fourier-transform patterns of an object are usually observed in the far-field region or obtained in the near-field region with the help of lenses. Here we propose and experimentally demonstrate a scheme of Fourier-transform patterns in the Fresnel diffraction region with thermal light. In this scheme, neither a lens nor a beamsplitter is used, and only one single charge coupled device (CCD) is employed. It means that dividing one beam out of a light source into signal and reference beams is not as necessary as the one done by the use of a beamsplitter in usual ghost interference experiments. Moreover, the coincidence measurement of two point detectors is not necessary and data recorded on a single CCD are sufficient for reconstructing the ghost diffraction patterns. The feature of the scheme promises a great potential application in the fields of X-ray and neutron diffraction imaging processes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Development of an ultra-compact mid-infrared attenuated total reflectance spectrophotometer

Science.gov (United States)

Kim, Dong Soo; Lee, Tae-Ro; Yoon, Gilwon

2014-07-01

Mid-infrared spectroscopy has been an important tool widely used for qualitative analysis in various fields. However, portable or personal use is size and cost prohibitive for either Fourier transform infrared or attenuated total reflectance (ATR) spectrophotometers. In this study, we developed an ultra-compact ATR spectrophotometer whose frequency band was 5.5-11.0 μm. We used miniature components, such as a light source fabricated by semiconductor technology, a linear variable filter, and a pyro-electric array detector. There were no moving parts. Optimal design based on two light sources, a zippered configuration of the array detector and ATR optics could produce absorption spectra that might be used for qualitative analysis. A microprocessor synchronized the pulsed light sources and detector, and all the signals were processed digitally. The size was 13.5×8.5×3.5 cm3 and the weight was 300 grams. Due to its low cost, our spectrophotometer can replace many online monitoring devices. Another application could be for a u-healthcare system installed in the bathroom or attached to a smartphone for monitoring substances in body fluids.

Description of the electron-hydrogen collision by the Coulomb Fourier transform method

International Nuclear Information System (INIS)

Levin, S.B.

2005-01-01

A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals

Fourier transform distribution function of relaxation times; application and limitations

NARCIS (Netherlands)

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

Orthonormal mode sets for the two-dimensional fractional Fourier transformation

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2007-01-01

A family of orthonormal mode sets arises when Hermite–Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an

Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

Science.gov (United States)

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.

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings.

Science.gov (United States)

Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.

Methodological effects in Fourier transform infrared (FTIR) spectroscopy: Implications for structural analyses of biomacromolecular samples

Science.gov (United States)

Kamnev, Alexander A.; Tugarova, Anna V.; Dyatlova, Yulia A.; Tarantilis, Petros A.; Grigoryeva, Olga P.; Fainleib, Alexander M.; De Luca, Stefania

2018-03-01

A set of experimental data obtained by Fourier transform infrared (FTIR) spectroscopy (involving the use of samples ground and pressed with KBr, i.e. in a polar halide matrix) and by matrix-free transmission FTIR or diffuse reflectance infrared Fourier transform (DRIFT) spectroscopic methodologies (involving measurements of thin films or pure powdered samples, respectively) were compared for several different biomacromolecular substances. The samples under study included poly-3-hydroxybutyrate (PHB) isolated from cell biomass of the rhizobacterium Azospirillum brasilense; dry PHB-containing A. brasilense biomass; pectin (natural carboxylated heteropolysaccharide of plant origin; obtained from apple peel) as well as its chemically modified derivatives obtained by partial esterification of its galacturonide-chain hydroxyl moieties with palmitic, oleic and linoleic acids. Significant shifts of some FTIR vibrational bands related to polar functional groups of all the biomacromolecules under study, induced by the halide matrix used for preparing the samples for spectroscopic measurements, were shown and discussed. A polar halide matrix used for preparing samples for FTIR measurements was shown to be likely to affect band positions not only per se, by affecting band energies or via ion exchange (e.g., with carboxylate moieties), but also by inducing crystallisation of metastable amorphous biopolymers (e.g., PHB of microbial origin). The results obtained have important implications for correct structural analyses of polar, H-bonded and/or amphiphilic biomacromolecular systems using different methodologies of FTIR spectroscopy.

Utilização de filtro de transformada de fourier para a minimização de ruídos em sinais analíticos Utilization of fourier transform filter for noise minimization in analytical signals

Directory of Open Access Journals (Sweden)

Eduardo O. Cerqueira

2000-10-01

Full Text Available Instrumental data always present some noise. The analytical data information and instrumental noise generally has different frequencies. Thus is possible to remove the noise using a digital filter based on Fourier transform and inverse Fourier transform. This procedure enhance the signal/noise ratio and consecutively increase the detection limits on instrumental analysis. The basic principle of Fourier transform filter with modifications implemented to improve its performance is presented. A numerical example, as well as a real voltammetric example are showed to demonstrate the Fourier transform filter implementation. The programs to perform the Fourier transform filter, in Matlab and Visual Basic languages, are included as appendices

Source brightness fluctuation correction of solar absorption fourier transform mid infrared spectra

Directory of Open Access Journals (Sweden)

T. Ridder

2011-06-01

Full Text Available The precision and accuracy of trace gas observations using solar absorption Fourier Transform infrared spectrometry depend on the stability of the light source. Fluctuations in the source brightness, however, cannot always be avoided. Current correction schemes, which calculate a corrected interferogram as the ratio of the raw DC interferogram and a smoothed DC interferogram, are applicable only to near infrared measurements. Spectra in the mid infrared spectral region below 2000 cm⁻¹ are generally considered uncorrectable, if they are measured with a MCT detector. Such measurements introduce an unknown offset to MCT interferograms, which prevents the established source brightness fluctuation correction. This problem can be overcome by a determination of the offset using the modulation efficiency of the instrument. With known modulation efficiency the offset can be calculated, and the source brightness correction can be performed on the basis of offset-corrected interferograms. We present a source brightness fluctuation correction method which performs the smoothing of the raw DC interferogram in the interferogram domain by an application of a running mean instead of high-pass filtering the corresponding spectrum after Fourier transformation of the raw DC interferogram. This smoothing can be performed with the onboard software of commercial instruments. The improvement of MCT spectra and subsequent ozone profile and total column retrievals is demonstrated. Application to InSb interferograms in the near infrared spectral region proves the equivalence with the established correction scheme.

Tabletop single-shot extreme ultraviolet Fourier transform holography of an extended object.

Science.gov (United States)

Malm, Erik B; Monserud, Nils C; Brown, Christopher G; Wachulak, Przemyslaw W; Xu, Huiwen; Balakrishnan, Ganesh; Chao, Weilun; Anderson, Erik; Marconi, Mario C

2013-04-22

We demonstrate single and multi-shot Fourier transform holography with the use of a tabletop extreme ultraviolet laser. The reference wave was produced by a Fresnel zone plate with a central opening that allowed the incident beam to illuminate the sample directly. The high reference wave intensity allows for larger objects to be imaged compared to mask-based lensless Fourier transform holography techniques. We obtain a spatial resolution of 169 nm from a single laser pulse and a resolution of 128 nm from an accumulation of 20 laser pulses for an object ~11x11μm(2) in size. This experiment utilized a tabletop extreme ultraviolet laser that produces a highly coherent ~1.2 ns laser pulse at 46.9 nm wavelength.

Discrete Fourier and wavelet transforms an introduction through linear algebra with applications to signal processing

CERN Document Server

Goodman, Roe W

2016-01-01

This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

Coulomb Fourier transformation: A novel approach to three-body scattering with charged particles

International Nuclear Information System (INIS)

Alt, E.O.; Levin, S.B.; Yakovlev, S.L.

2004-01-01

A unitary transformation of the three-body Hamiltonian which describes a system of two charged and one neutral particles is constructed such that the Coulomb potential which acts between the charged particles is explicitly eliminated. The transformed Hamiltonian and, in particular, the transformed short-range pair interactions are worked out in detail. Thereby it is found that, after transformation, the short-range potentials acting between the neutral and either one of the charged particles become simply Fourier transformed but, in addition, multiplied by a function that represents the Coulombic three-body correlations originating from the action of the other charged particle on the considered pair. This function which is universal as it does not depend on any property of the short-range interaction is evaluated explicitly and its singularity structure is described in detail. In contrast, the short-range potential between the charged particles remains of two-body type but occurs now in the 'Coulomb representation'. Specific applications to Yukawa and Gaussian potentials are given. Since the Coulomb-Fourier-transformed Hamiltonian does no longer contain the Coulomb potential or any other effective interaction of long range, standard methods of short-range few-body scattering theory are applicable

Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes

KAUST Repository

Lin, Sian-Jheng

2016-09-13

In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h is the number of evaluation points. Based on the proposed Fourier-like algorithm, we then develop the encoding/ decoding algorithms for (n = 2m; k) Reed-Solomon erasure codes. The proposed encoding/erasure decoding algorithm requires O(n lg(n)), in both additive and multiplicative complexities. As the complexity leading factor is small, the proposed algorithms are advantageous in practical applications. Finally, the approaches to convert the basis between the monomial basis and the new basis are proposed.

Chemometric analysis of attenuated total reflectance infrared spectra of Proteus mirabilis strains with defined structures of LPS.

Science.gov (United States)

Zarnowiec, Paulina; Mizera, Andrzej; Chrapek, Magdalena; Urbaniak, Mariusz; Kaca, Wieslaw

2016-07-01

Proteus spp. strains are some of the most important pathogens associated with complicated urinary tract infections and bacteremia affecting patients with immunodeficiency and long-term urinary catheterization. For epidemiological purposes, various molecular typing methods have been developed for this pathogen. However, these methods are labor intensive and time consuming. We evaluated a new method of differentiation between strains. A collection of Proteus spp. strains was analyzed by attenuated total reflectance Fourier transform infrared (ATR FT-IR) spectroscopy in the mid-infrared region. ATR FT-IR spectroscopy used in conjunction with a diamond ATR accessory directly produced the biochemical profile of the surface chemistry of bacteria. We conclude that a combination of ATR FT-IR spectroscopy and mathematical modeling provides a fast and reliable alternative for discrimination between Proteus isolates, contributing to epidemiological research. © The Author(s) 2016.

The smoothing and fast Fourier transformation of experimental X-ray and neutron data from amorphous materials

International Nuclear Information System (INIS)

Dixon, M.; Wright, A.C.; Hutchinson, P.

1977-01-01

The application of fast Fourier transformation techniques to the analysis of experimental X-ray and neutron diffraction patterns from amorphous materials is discussed and compared with conventional techniques using Filon's quadrature. The fast Fourier transform package described also includes cubic spline smoothing and has been extensively tested, using model data to which statistical errors have been added by means of a pseudo-random number generator with Gaussian shaper. Neither cubic spline nor hand smoothing has much effect on the resulting transform since the noise removed is of too high a frequency. (Auth.)

Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

Science.gov (United States)

Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

2010-01-01

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

Monitoring wine aging with Fourier transform infrared spectroscopy (FT-IR

Directory of Open Access Journals (Sweden)

Basalekou Marianthi

2015-01-01

Full Text Available Oak wood has commonly been used in wine aging but recently other wood types such as Acacia and Chestnut, have attracted the interest of the researchers due to their possible positive contribution to wine quality. However, only the use of oak and chestnut woods is approved by the International Enological Codex of the International Organisation of Vine and Wine. In this study Fourier Transform (FT-mid-infrared spectroscopy combined with Discriminant Analysis was used to differentiate wines aged in barrels made from French oak, American oak, Acacia and Chestnut and in tanks with oak chips, over a period of 12 months. Two red (Mandilaria, Kotsifali and two white (Vilana, Dafni native Greek grape varieties where used to produce four wines. The Fourier Transform Infrared (FT-IR spectra of the samples were recorded on a Zinc Selenide (ZnSe window after incubation at 40 °C for 30 min. A complete differentiation of the samples according to both the type of wood used and the contact time was achieved based on their FT-IR spectra.

Application of fast Fourier transform in thermo-magnetic convection analysis

International Nuclear Information System (INIS)

Pyrda, L

2014-01-01

Application of Fast Fourier Transform in thermo-magnetic convection is reported. Cubical enclosure filled with paramagnetic fluid heated from below and placed in the strong magnetic field gradients was investigated. The main aim of study was connected with identification of flow types, especially transition to turbulence. For this purpose the Fast Fourier Transform (FFT) analysis was applied. It was followed by the heat transfer characteristic for various values of magnetic induction gradient. The analysis was done at two Rayleigh numbers 7.89·10 5 and 1.86·10 6 with thermo-magnetic Rayleigh numbers up to 1.8·10 8 and 4.5·10 8 respectively. The presented results clearly indicate flow types and also demonstrate augmented heat transfer in dependence on magnetic induction gradient. Detailed analysis of flow transition to turbulent state was compared with transition line for natural convection reported in literature. The transition to turbulence in the case of thermo-magnetic convection of paramagnetic fluid was in very good agreement with transition in the case of natural convection.

Teaching stable two-mirror resonators through the fractional Fourier transform

International Nuclear Information System (INIS)

Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

2010-01-01

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects.

3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography

Science.gov (United States)

Michael C. Martin; Charlotte Dabat-Blondeau; Miriam Unger; Julia Sedlmair; Dilworth Y. Parkinson; Hans A. Bechtel; Barbara Illman; Jonathan M. Castro; Marco Keiluweit; David Buschke; Brenda Ogle; Michael J. Nasse; Carol J. Hirschmugl

2013-01-01

We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical...

Speeding-up exchange-mediated saturation transfer experiments by Fourier transform

Energy Technology Data Exchange (ETDEWEB)

Carneiro, Marta G.; Reddy, Jithender G.; Griesinger, Christian; Lee, Donghan, E-mail: dole@nmr.mpibpc.mpg.de [Max-Planck Institute for Biophysical chemistry, Department of NMR-based Structural Biology (Germany)

2015-11-15

Protein motions over various time scales are crucial for protein function. NMR relaxation dispersion experiments play a key role in explaining these motions. However, the study of slow conformational changes with lowly populated states remained elusive. The recently developed exchange-mediated saturation transfer experiments allow the detection and characterization of such motions, but require extensive measurement time. Here we show that, by making use of Fourier transform, the total acquisition time required to measure an exchange-mediated saturation transfer profile can be reduced by twofold in case that one applies linear prediction. In addition, we demonstrate that the analytical solution for R{sub 1}ρ experiments can be used for fitting the exchange-mediated saturation transfer profile. Furthermore, we show that simultaneous analysis of exchange-mediated saturation transfer profiles with two different radio-frequency field strengths is required for accurate and precise characterization of the exchange process and the exchanging states.

Speeding-up exchange-mediated saturation transfer experiments by Fourier transform

International Nuclear Information System (INIS)

Carneiro, Marta G.; Reddy, Jithender G.; Griesinger, Christian; Lee, Donghan

2015-01-01

Protein motions over various time scales are crucial for protein function. NMR relaxation dispersion experiments play a key role in explaining these motions. However, the study of slow conformational changes with lowly populated states remained elusive. The recently developed exchange-mediated saturation transfer experiments allow the detection and characterization of such motions, but require extensive measurement time. Here we show that, by making use of Fourier transform, the total acquisition time required to measure an exchange-mediated saturation transfer profile can be reduced by twofold in case that one applies linear prediction. In addition, we demonstrate that the analytical solution for R 1 ρ experiments can be used for fitting the exchange-mediated saturation transfer profile. Furthermore, we show that simultaneous analysis of exchange-mediated saturation transfer profiles with two different radio-frequency field strengths is required for accurate and precise characterization of the exchange process and the exchanging states

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/

Fourier transform based scalable image quality measure.

Science.gov (United States)

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.

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.

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.

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

A high-resolution Fourier Transform Spectrometer for planetary spectroscopy

Science.gov (United States)

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.

Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer

Energy Technology Data Exchange (ETDEWEB)

Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.

1993-10-01

We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.

Renal geology (quantitative renal stone analysis) by 'Fourier transform infrared spectroscopy'.

Science.gov (United States)

Singh, Iqbal

2008-01-01

To prospectively determine the precise stone composition (quantitative analysis) by using infrared spectroscopy in patients with urinary stone disease presenting to our clinic. To determine an ideal method for stone analysis suitable for use in a clinical setting. After routine and a detailed metabolic workup of all patients of urolithiasis, stone samples of 50 patients of urolithiasis satisfying the entry criteria were subjected to the Fourier transform infrared spectroscopic analysis after adequate sample homogenization at a single testing center. Calcium oxalate monohydrate and dihydrate stone mixture was most commonly encountered in 35 (71%) followed by calcium phosphate, carbonate apatite, magnesium ammonium hexahydrate and xanthine stones. Fourier transform infrared spectroscopy allows an accurate, reliable quantitative method of stone analysis. It also helps in maintaining a computerized large reference library. Knowledge of precise stone composition may allow the institution of appropriate prophylactic therapy despite the absence of any detectable metabolic abnormalities. This may prevent and or delay stone recurrence.

Nycterohemeral eating and ruminating patterns in heifers fed grass or corn silage: analysis by finite Fourier transform.

Science.gov (United States)

Deswysen, A G; Dutilleul, P; Godfrin, J P; Ellis, W C

1993-10-01

Average daily and within-day nycterohemeral patterns of eating and ruminating behavior were determined in six Holstein-Friesian heifers (average BW = 427 kg) given ad libitum access to either corn or grass silage in a two-period crossover design. Rhythm components (number of cycles/24 h) were characterized by finite Fourier transform of the 24-h mastication activities as measured during 4 d by continuous jaw movement recordings. Average daily voluntary intake of corn silage was 8.2% greater (P = .05) than that for grass silage and was associated (P finite Fourier transform was reparameterized to express the amplitude (as periodograms) and phase of each rhythm component. Rhythm Components 1, 3, and 4 contributed primarily to explaining the total dispersion of the 24-h series of time spent eating and ruminating, for both silage types and individual heifers. Relative importance of Rhythm Component 1 of time spent eating, indicative of a main circadian pattern, was related positively to pedigree value for milk production (P = .01) and negatively to milk protein concentration (P = .09).(ABSTRACT TRUNCATED AT 250 WORDS)

QUANTITATIVE FOURIER TRANSFORM INFRARED SPECTROSCOPIC INVESTIGATION OF HUMIC SUBSTANCE FUNCTIONAL GROUP COMPOSITION

Science.gov (United States)

Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...

Improved method of generating bit reversed numbers for calculating fast fourier transform

Digital Repository Service at National Institute of Oceanography (India)

Suresh, T.

Fast Fourier Transform (FFT) is an important tool required for signal processing in defence applications. This paper reports an improved method for generating bit reversed numbers needed in calculating FFT using radix-2. The refined algorithm takes...

Spectrogram analysis of selected tremor signals using short-time Fourier transform and continuous wavelet transform

Directory of Open Access Journals (Sweden)

D. Seidl

1999-06-01

Full Text Available Among a variety of spectrogram methods Short-Time Fourier Transform (STFT and Continuous Wavelet Transform (CWT were selected to analyse transients in non-stationary tremor signals. Depending on the properties of the tremor signal a more suitable representation of the signal is gained by CWT. Three selected broadband tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli.

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

Application of Fourier transform infrared spectroscopy with chemometrics on postmortem interval estimation based on pericardial fluids.

Science.gov (United States)

Zhang, Ji; Li, Bing; Wang, Qi; Wei, Xin; Feng, Weibo; Chen, Yijiu; Huang, Ping; Wang, Zhenyuan

2017-12-21

Postmortem interval (PMI) evaluation remains a challenge in the forensic community due to the lack of efficient methods. Studies have focused on chemical analysis of biofluids for PMI estimation; however, no reports using spectroscopic methods in pericardial fluid (PF) are available. In this study, Fourier transform infrared (FTIR) spectroscopy with attenuated total reflectance (ATR) accessory was applied to collect comprehensive biochemical information from rabbit PF at different PMIs. The PMI-dependent spectral signature was determined by two-dimensional (2D) correlation analysis. The partial least square (PLS) and nu-support vector machine (nu-SVM) models were then established based on the acquired spectral dataset. Spectral variables associated with amide I, amide II, COO - , C-H bending, and C-O or C-OH vibrations arising from proteins, polypeptides, amino acids and carbohydrates, respectively, were susceptible to PMI in 2D correlation analysis. Moreover, the nu-SVM model appeared to achieve a more satisfactory prediction than the PLS model in calibration; the reliability of both models was determined in an external validation set. The study shows the possibility of application of ATR-FTIR methods in postmortem interval estimation using PF samples.

The discrete Fourier transform theory, algorithms and applications

CERN Document Server

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

Application of reflectance micro-Fourier Transform infrared analysis to the study of coal macerals: An example from the Late Jurassic to Early Cretaceous coals of the Mist Mountain Formation, British Columbia, Canada

Science.gov (United States)

Mastalerz, Maria; Bustin, R.M.

1996-01-01

The applicability of the reflectance micro-Fourier Transform infra-red spectroscopy (FTIR) technique for analyzing the distribution of functional groups in coal macerals is discussed. High quality of spectra, comparable to those obtained using other FTIR techniques (KBr pellet and transmission micro-FTIR), indicate this technique can be applied to characterizing functional groups under most conditions. The ease of sample preparation, the potential to analyze large intact samples, and ability to characterize organic matter in areas as small as 20 ??m are the main advantages of reflectance micro-FTIR. The quantitative aspects of reflectance micro-FTIR require further study. The examples from the coal seams of the Mist Mountain Formation, British Columbia show that at high volatile bituminous rank, reflectance micro-FTIR provides valuable information on the character of aliphatic chains of vitrinite and liptinite macerals. Because the character of aliphatic chains influences bond disassociation energies, such information is useful from a hydrocarbon generation viewpoint. In medium volatile bituminous coal liptinite macerals are usually not detectable but this technique can be used to study the degree of oxidation and reactivity of vitrinite and semifusinite.

Investigations of the functional states of dendritic cells under different conditioned microenvironments by Fourier transformed infrared spectroscopy.

Science.gov (United States)

Dong, Rong; Long, Jinhua; Xu, Xiaoli; Zhang, Chunlin; Wen, Zongyao; Li, Long; Yao, Weijuan; Zeng, Zhu

2014-01-10

Dendritic cells are potent and specialized antigen presenting cells, which play a crucial role in initiating and amplifying both the innate and adaptive immune responses. The dendritic cell-based vaccination against cancer has been clinically achieved promising successes. But there are still many challenges in its clinical application, especially for how to identify the functional states. The CD14+ monocytes were isolated from human peripheral blood after plastic adherence and purified to approximately 98% with cocktail immunomagnetic beads. The immature dendritic cells and mature dendritic cells were induced by traditional protocols. The resulting dendritic cells were cocultured with normal cells and cancer cells. The functional state of dendritic cells including immature dendritic cells (imDCs) and mature dendritic cells (mDCs) under different conditioned microenvironments were investigated by Fourier transformed infrared spectroscopy (FTIR) and molecular biological methods. The results of Fourier transformed infrared spectroscopy showed that the gene transcription activity and energy states of dendritic cells were specifically suppressed by tumor cells (P Fourier transformed infrared spectroscopy at given wave numbers were closely correlated with the expression levels of NF-κB (R2:0.69 and R2:0.81, respectively). Our results confirmed that the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were positively correlated with the expression levels of NF-κB, suggesting that Fourier transformed infrared spectroscopy technology could be clinically applied to identify the functional states of dendritic cell when performing dendritic cell-based vaccination. It's significant for the simplification and standardization of dendritic cell-based vaccination clinical preparation protocols.

Simple example of track finding by Fourier transform and possibilities for vector or optical processors

International Nuclear Information System (INIS)

Underwood, D.

1986-01-01

Simple examples of finding tracks by Fourier transform with filter or correlation function are presented. Possibilities for using this method in more complicated real situations and the processing times which might be achieved are discussed. The method imitates the simplest examples in the literature on optical pattern recognition and optical processing. The possible benefits of the method are in speed of processing in the optical Fourier transform wherein an entire picture is processed simultaneously. The speed of a computer vector processor may be competitive with present electro-optical devices. 2 refs., 6 figs

All-optical WDM Regeneration of DPSK Signals using Optical Fourier Transformation and Phase Sensitive Amplification

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian

2015-01-01

We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time.......We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time....

Fourier Transform Infrared Imaging analysis of dental pulp inflammatory diseases.

Science.gov (United States)

Giorgini, E; Sabbatini, S; Conti, C; Rubini, C; Rocchetti, R; Fioroni, M; Memè, L; Orilisi, G

2017-05-01

Fourier Transform Infrared microspectroscopy let characterize the macromolecular composition and distribution of tissues and cells, by studying the interaction between infrared radiation and matter. Therefore, we hypothesize to exploit this analytical tool in the analysis of inflamed pulps, to detect the different biochemical features related to various degrees of inflammation. IR maps of 13 irreversible and 12 hyperplastic pulpitis, together with 10 normal pulps, were acquired, compared with histological findings and submitted to multivariate (HCA, PCA, SIMCA) and statistical (one-way ANOVA) analysis. The fit of convoluted bands let calculate meaningful band area ratios (means ± s.d., P < 0.05). The infrared imaging analysis pin-pointed higher amounts of water and lower quantities of type I collagen in all inflamed pulps. Specific vibrational markers were defined for irreversible pulpitis (Lipids/Total Biomass, PhII/Total Biomass, CH 2 /CH 3 , and Ty/AII) and hyperplastic ones (OH/Total Biomass, Collagen/Total Biomass, and CH 3 Collagen/Total Biomass). The study confirmed that FTIR microspectroscopy let discriminate tissues' biological features. The infrared imaging analysis evidenced, in inflamed pulps, alterations in tissues' structure and composition. Changes in lipid metabolism, increasing amounts of tyrosine, and the occurrence of phosphorylative processes were highlighted in irreversible pulpitis, while high amounts of water and low quantities of type I collagen were detected in hyperplastic samples. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Fourier X-ray line shape analysis of lattice defects from a single reflection

International Nuclear Information System (INIS)

Misra, N.K.; Bhanumurthy, K.

1981-01-01

A method of single reflection Fourier analysis has been described considering the fact that the rms strain (averaged over a distance) is not independent of averaging distance. Following the procedure of N.K. Misra and T.B. Ghosh (1976) and considering the initial slopes of dAsub(L)/dL against L curves, (Asub(L) is the Lsub(th) order Fourier coefficient) the effective size of the coherently diffracting domains and the rms strain in them are determined. The results of this analysis for pure Ti and Ag-3.55% Ga, Ag-15% In and Cu-12.46% Ge alloys compare fairly well with those obtained from different multiple reflections techniques. (author)

Attenuated total reflectance-FT-IR spectroscopy for gunshot residue analysis: potential for ammunition determination.

Science.gov (United States)

Bueno, Justin; Sikirzhytski, Vitali; Lednev, Igor K

2013-08-06

The ability to link a suspect to a particular shooting incident is a principal task for many forensic investigators. Here, we attempt to achieve this goal by analysis of gunshot residue (GSR) through the use of attenuated total reflectance (ATR) Fourier transform infrared spectroscopy (FT-IR) combined with statistical analysis. The firearm discharge process is analogous to a complex chemical process. Therefore, the products of this process (GSR) will vary based upon numerous factors, including the specific combination of the firearm and ammunition which was discharged. Differentiation of FT-IR data, collected from GSR particles originating from three different firearm-ammunition combinations (0.38 in., 0.40 in., and 9 mm calibers), was achieved using projection to latent structures discriminant analysis (PLS-DA). The technique was cross (leave-one-out), both internally and externally, validated. External validation was achieved via assignment (caliber identification) of unknown FT-IR spectra from unknown GSR particles. The results demonstrate great potential for ATR-FT-IR spectroscopic analysis of GSR for forensic purposes.

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Directory of Open Access Journals (Sweden)

Salman Ahmad

2014-06-01

Full Text Available Magneto-Hydrodynamic (MHD flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

Simplification of gamma-ray spectral data by using Fourier transform

International Nuclear Information System (INIS)

Tominaga, Shoji; Nagata, Shojiro; Nayatani, Yoshinobu; Ueda, Isamu; Sasaki, Satoshi.

1977-01-01

A method is proposed to represent γ-ray response spectra by Fourier series for the purpose of compressing spectral data. The usefulness of the method was confirmed by applying it to a spectral library of a NaI detector. In the method, a response spectrum as a wave is described by superposition of sine (cosine) waves with low frequencies, whose coefficient parameters can be obtained by a Fast Fourier Transform program. The relation between the number of parameters and the fitting error is discussed, and as the result, it is shown that the number of parameters can be reduced to about a half. The merits and features are presented in practical application of the method to the analysis of γ-ray spectra. (auth.)

Compositional features of cotton plant biomass fractions characterized by attenuated total reflection Fourier transform infrared spectroscopy

Science.gov (United States)

Cotton is one of the most important and widely grown crops in the world. In addition to natural textile fiber production as a primary purpose, it yields a high grade vegetable oil for human consumption and also carbohydrate fiber and protein byproducts for animal feed. In this work, attenuated total...

Detection of Gastric Cancer with Fourier Transform Infrared Spectroscopy and Support Vector Machine Classification

Directory of Open Access Journals (Sweden)

Qingbo Li

2013-01-01

Full Text Available Early diagnosis and early medical treatments are the keys to save the patients' lives and improve the living quality. Fourier transform infrared (FT-IR spectroscopy can distinguish malignant from normal tissues at the molecular level. In this paper, programs were made with pattern recognition method to classify unknown samples. Spectral data were pretreated by using smoothing and standard normal variate (SNV methods. Leave-one-out cross validation was used to evaluate the discrimination result of support vector machine (SVM method. A total of 54 gastric tissue samples were employed in this study, including 24 cases of normal tissue samples and 30 cases of cancerous tissue samples. The discrimination results of SVM method showed the sensitivity with 100%, specificity with 83.3%, and total discrimination accuracy with 92.2%.

An OTDM-To-WDM Converter Using Optical Fourier Transformation

OpenAIRE

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...

Fast Fourier transformation results from gamma-ray burst profiles

Science.gov (United States)

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.

Experimental demonstration of an OFDM receiver based on a silicon-nanophot onic discrete Fourier transform filter

DEFF Research Database (Denmark)

Da Ros, Francesco; Nolle, Markus; Meuer, C.

2014-01-01

We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit.......We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit....

Aliasless fresnel transform image reconstruction in phase scrambling fourier transform technique by data interpolation

International Nuclear Information System (INIS)

Yamada, Yoshifumi; Liu, Na; Ito, Satoshi

2006-01-01

The signal in the Fresnel transform technique corresponds to a blurred one of the spin density image. Because the amplitudes of adjacent sampled signals have a high interrelation, the signal amplitude at a point between sampled points can be estimated with a high degree of accuracy even if the sampling is so coarse as to generate aliasing in the reconstructed images. In this report, we describe a new aliasless image reconstruction technique in the phase scrambling Fourier transform (PSFT) imaging technique in which the PSFT signals are converted to Fresnel transform signals by multiplying them by a quadratic phase term and are then interpolated using polynomial expressions to generate fully encoded signals. Numerical simulation using MR images showed that almost completely aliasless images are reconstructed by this technique. Experiments using ultra-low-field PSFT MRI were conducted, and aliasless images were reconstructed from coarsely sampled PSFT signals. (author)

An algorithm for the basis of the finite Fourier transform

Science.gov (United States)

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.

A fast Fourier transform program for the deconvolution of IN10 data

International Nuclear Information System (INIS)

Howells, W.S.

1981-04-01

A deconvolution program based on the Fast Fourier Transform technique is described and some examples are presented to help users run the programs and interpret the results. Instructions are given for running the program on the RAL IBM 360/195 computer. (author)

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

Adaptive synchrosqueezing based on a quilted short-time Fourier transform

Science.gov (United States)

Berrian, Alexander; Saito, Naoki

2017-08-01

In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST, based on the short-time Fourier transform (STFT), enables the sharpening of instantaneous frequency (IF) information derived from the STFT, as well as the separation of amplitude-phase components corresponding to distinct IF curves. However, this SST is limited by the time-frequency resolution of the underlying window function, and may not resolve signals exhibiting diverse time-frequency behaviors with sufficient accuracy. In this work, we develop a framework for an SST based on a "quilted" short-time Fourier transform (SST-QSTFT), which allows adaptation to signal behavior in separate time-frequency regions through the use of multiple windows. This motivates us to introduce a discrete reassignment frequency formula based on a finite difference of the phase spectrum, ensuring computational accuracy for a wider variety of windows. We develop a theoretical framework for the SST-QSTFT in both the continuous and the discrete settings, and describe an algorithm for the automatic selection of optimal windows depending on the region of interest. Using synthetic data, we demonstrate the superior numerical performance of SST-QSTFT relative to other SST methods in a noisy context. Finally, we apply SST-QSTFT to audio recordings of animal calls to demonstrate the potential of our method for the analysis of real bioacoustic signals.

Fourier transform and mean quadratic variation of Bernoulli convolution on homogeneous Cantor set

Energy Technology Data Exchange (ETDEWEB)

Yu Zuguo E-mail: yuzg@hotmail.comz.yu

2004-07-01

For the Bernoulli convolution on homogeneous Cantor set, under some condition, it is proved that the mean quadratic variation and the average of Fourier transform of this measure are bounded above and below.

Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses

Science.gov (United States)

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

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.

Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms

International Nuclear Information System (INIS)

Prakash, A; Lebensohn, R A

2009-01-01

In this work, we compare finite element and fast Fourier transform approaches for the prediction of the micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases—rolling of aluminum and wire drawing of tungsten—are used to evaluate the predictions of the two models. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison with the fast Fourier transform simulations. Figure 9 was corrected in this article on the 25 August 2009. The corrected electronic version is identical to the print version

Advances in hyperspectral remote sensing I: The visible Fourier transform hyperspectral imager

Directory of Open Access Journals (Sweden)

J. Bruce Rafert

2015-05-01

Full Text Available We discuss early hyperspectral research and development activities during the 1990s that led to the deployment of aircraft and satellite payloads whose heritage was based on the use of visible, spatially modulated, imaging Fourier transform spectrometers, beginning with early experiments at the Florida Institute of Technology, through successful launch and deployment of the Visible Fourier Transform Hyperspectral Imager on MightySat II.1 on 19 July 2000. In addition to a brief chronological overview, we also discuss several of the most interesting optical engineering challenges that were addressed over this timeframe, present some as-yet un-exploited features of field-widened (slit-less SMIFTS instruments, and present some images from ground-based, aircraft-based and satellite-based instruments that helped provide the impetus for the proliferation and development of entire new families of instruments and countless new applications for hyperspectral imaging.

Measurement of rumen dry matter and neutral detergent fiber degradability of feeds by Fourier-transform infrared spectroscopy

DEFF Research Database (Denmark)

Belanche, A.; Weisbjerg, Martin Riis; Allison, G.G.

2014-01-01

This study explored the potential of partial least squares (PLS) and Fourier-transform infrared spectroscopy (FTIR) to predict rumen dry matter (DM) and neutral detergent fiber (NDF) degradation parameters of a wide range of feeds for ruminants, as an alternative to the in situ method. In total...... components, such as cellulose, pectin, lignin, cutin, and suberin, but also with nonstructural carbohydrates and certain active compounds. In conclusion, FTIR spectroscopy could be considered a low-cost alternative to in situ measurements in feed evaluation....

Robust alignment of chromatograms by statistically analyzing the shifts matrix generated by moving window fast Fourier transform cross-correlation.

Science.gov (United States)

Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

2015-03-01

Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

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.

Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

Science.gov (United States)

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-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform

Science.gov (United States)

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

Time lens based optical fourier transformation for advanced processing of spectrally-efficient OFDM and N-WDM signals

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Morioka, Toshio

2016-01-01

We review recent progress in the use of time lens based optical Fourier transformation for advanced optical signal processing, with focus on all-optical generation, detection and format conversion of spectrally-efficient OFDM and N-WDM signals.......We review recent progress in the use of time lens based optical Fourier transformation for advanced optical signal processing, with focus on all-optical generation, detection and format conversion of spectrally-efficient OFDM and N-WDM signals....

Fourier Transform Surface Plasmon Resonance of Nanodisks Embedded in Magnetic Nanorods.

Science.gov (United States)

Jung, Insub; Ih, Seongkeun; Yoo, Haneul; Hong, Seunghun; Park, Sungho

2018-03-14

In this study, we demonstrate the synthesis and application of magnetic plasmonic gyro-nanodisks (GNDs) for Fourier transform surface plasmon resonance based biodetection. Plasmonically active and magnetically responsive gyro-nanodisks were synthesized using electrochemical methods with anodized aluminum templates. Due to the unique properties of GNDs (magnetic responsiveness and surface plasmon bands), periodic extinction signals were generated under an external rotating magnetic field, which is, in turn, converted into frequency domains using Fourier transformation. After the binding of a target on GNDs, an increase in the shear force causes a shift in the frequency domain, which allows us to investigate biodetection for HA1 (the influenza virus). Most importantly, by modulating the number and the location of plasmonic nanodisks (a method for controlling the hydrodynamic forces by rationally designing the nanomaterial architecture), we achieved enhanced biodetection sensitivity. We expect that our results will contribute to improved sensing module performance, as well as a better understanding of dynamic nanoparticle systems, by harnessing the perturbed periodic fluctuation of surface plasmon bands under the modulated magnetic field.

Specification of the Fast Fourier Transform algorithm as a term rewriting system

NARCIS (Netherlands)

Rodenburg, P.H.; Hoekzema, D.J.

1987-01-01

We specify an algorithm for multiplying polynomials with complex coefficients incorporating, the Fast Fourier Transform algorithm of Cooley and Tukey [CT]. The specification formalism we use is a variant of the formalism ASF described in. [BHK]. The difference with ASF is essentially a matter of

Superexponentially damped Vlasov plasma oscillations in the Fourier transformed velocity space

International Nuclear Information System (INIS)

Sedlacek, Z.; Nocera, L.

2002-01-01

The Landau (exponentially) damped solutions of the Vlasov-Poisson equation Fourier transformed with respect to velocity are genuine eigenmodes corresponding to complex eigenvalues. In addition there exist solutions decaying faster than exponentially which exhibit no oscillatory behaviour. A new characterization is given of the initial conditions that give rise to these solutions together with a numerical demonstration

Fourier-transform ghost imaging with pure far-field correlated thermal light

International Nuclear Information System (INIS)

Liu Honglin; Shen Xia; Han Shensheng; Zhu Daming

2007-01-01

Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed

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.

Total energy calculations for structural phase transformations

International Nuclear Information System (INIS)

Ye, Y.Y.; Chan, C.T.; Ho, K.M.; Harmon, B.N.

1990-01-01

The structural integrity and physical properties of crystalline solids are frequently limited or enhanced by the occurrence of phase transformations. Martensitic transformations involve the collective displacement of atoms from one ordered state to another. Modern methods to determine the microscopic electronic changes as the atoms move are now accurate enough to evaluate the very small energy differences involved. Extensive first principles calculations for the prototypical martensitic transformation from body-centered cubic (bcc) to closepacked 9R structure in sodium metal are described. The minimum energy coordinate or configuration path between the bcc and 9R structures is determined as well as paths to other competing close-packed structures. The energy barriers and important anharmonic interactions are identified and general conclusions drawn. The calculational methods used to solve the Schrodinger equation include pseudopotentials, fast Fourier transforms, efficient matrix diagnonalization, and supercells with many atoms

Fourier transform infrared emission spectra of atomic rubidium: g- and h-states

Czech Academy of Sciences Publication Activity Database

Civiš, Svatopluk; Ferus, Martin; Kubelík, Petr; Chernov, Vladislav E.; Zanozina, Ekaterina M.

2012-01-01

Roč. 45, č. 17 (2012), s. 175002 ISSN 0953-4075 R&D Projects: GA AV ČR IAAX00100903 Institutional support: RVO:61388955 Keywords : Fourier transform infrared emission spectra * atomic rubidium * physical chemistry Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.031, year: 2012

Qualitative analysis of thin films of crude oil deposits on the metallic substrate by Fourier transform infrared (FTIR) microscopy

DEFF Research Database (Denmark)

Batina, N.; Reyna-Cordova, A.; Trinidad-Reyes, Y.

2005-01-01

Thin films of crude oil samples were prepared for atomic force microscopy (AFM) analysis on the gold substrate. Sample preparation involved evaporation during a long (24 h) but mild thermal exposure (80 °C). Fourier transform infrared (FTIR) microscopy (reflectance spectroscopy) was employed...... of oxidation state was compared to surface morphology data by AFM previously reported. The reported results emphasize the advantage of complementary techniques (AFM/FTIR microscopy) in the analysis of petroleum thin films that should be considered during analysis and interpretation of this type of data....... to determinate the quality of the thin film surface, before the morphology characterization. The surface reflectance spectra were compared to direct transmittance FTIR of liquid oil samples. The two FTIR techniques showed different spectral characteristics related to oxygenated functionalities. This clearly...

Principles of Fourier analysis

CERN Document Server

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 ...

Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses

Directory of Open Access Journals (Sweden)

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.

Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

Science.gov (United States)

Barnett, Patrick D; Strange, K Alicia; Angel, S Michael

2017-06-01

This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

Flat-top pulse generation by the optical Fourier transform technique for ultrahigh speed signal processing

DEFF Research Database (Denmark)

Palushani, Evarist; Oxenløwe, Leif Katsuo; Galili, Michael

2009-01-01

This paper reports on the generation of 1.6-ps fullwidth at half-maximum flat-top pulses by the optical Fourier transform technique, and the utilization of these pulses in a 320-Gb/s demultiplexing experiment. It is demonstrated how a narrow pulse having a 15-nm wide third-order super-Gaussian sp......This paper reports on the generation of 1.6-ps fullwidth at half-maximum flat-top pulses by the optical Fourier transform technique, and the utilization of these pulses in a 320-Gb/s demultiplexing experiment. It is demonstrated how a narrow pulse having a 15-nm wide third-order super...

Time Lens based Optical Fourier Transformation for All-Optical Signal Processing of Spectrally-Efficient Data

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Lillieholm, Mads

2017-01-01

We review recent progress in the use of time lens based optical Fourier transformation for advanced all-optical signal processing. A novel time lens based complete optical Fourier transformation (OFT) technique is introduced. This complete OFT is based on two quadratic phase-modulation stages using...... four-wave mixing (FWM), separated by a dispersive medium, which enables time-to-frequency and frequency-to-time conversions simultaneously, thus performing an exchange between the temporal and spectral profiles of the input signal. Using the proposed complete OFT, several advanced all-optical signal......, such as orthogonal frequency division multiplexing (OFDM), Nyquist wavelength-division multiplexing (Nyquist-WDM) and Nyquist optical time division multiplexing (Nyquist-OTDM) signals....

Engineering Model Panchromatic Fourier Transform Spectrometer (PanFTS) Instrument for the GEO-CAPE Mission

Data.gov (United States)

National Aeronautics and Space Administration — The Panchromatic Fourier Transform Spectrometer (PanFTS) is an imaging spectrometer that can measure pollutants, greenhouse gases, and aerosols as called for in the...

Symmetries of the second-difference matrix and the finite Fourier transform

International Nuclear Information System (INIS)

Aguilar, A.; Wolf, K.B.

1979-01-01

The finite Fourier transformation is well known to diagonalize the second-difference matrix and has been thus applied extensively to describe finite crystal lattices and electric networks. In setting out to find all transformations having this property, we obtain a multiparameter class of them. While permutations and unitary scaling of the eigenvectors constitute the trivial freedom of choice common to all diagonalization processes, the second-difference matrix has a larger symmetry group among whose elements we find the dihedral manifest symmetry transformations of the lattice. The latter are nevertheless sufficient for the unique specification of eigenvectors in various symmetry-adapted bases for the constrained lattice. The free symmetry parameters are shown to lead to a complete set of conserved quantities for the physical lattice motion. (author)

Copy-move forgery detection utilizing Fourier-Mellin transform log-polar features

Science.gov (United States)

Dixit, Rahul; Naskar, Ruchira

2018-03-01

In this work, we address the problem of region duplication or copy-move forgery detection in digital images, along with detection of geometric transforms (rotation and rescale) and postprocessing-based attacks (noise, blur, and brightness adjustment). Detection of region duplication, following conventional techniques, becomes more challenging when an intelligent adversary brings about such additional transforms on the duplicated regions. In this work, we utilize Fourier-Mellin transform with log-polar mapping and a color-based segmentation technique using K-means clustering, which help us to achieve invariance to all the above forms of attacks in copy-move forgery detection of digital images. Our experimental results prove the efficiency of the proposed method and its superiority to the current state of the art.

10th International Conference on Progress in Fourier Transform Spectroscopy

CERN Document Server

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.

On the raising and lowering difference operators for eigenvectors of the finite Fourier transform

International Nuclear Information System (INIS)

Atakishiyeva, M K; Atakishiyev, N M

2015-01-01

We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)

Discrimination of organic coffee via Fourier transform infrared-photoacoustic spectroscopy.

Science.gov (United States)

Gordillo-Delgado, Fernando; Marín, Ernesto; Cortés-Hernández, Diego Mauricio; Mejía-Morales, Claudia; García-Salcedo, Angela Janet

2012-08-30

Procedures for the evaluation of the origin and quality of ground and roasted coffee are constantly needed for the associated industry due to complexity of the related market. Conventional Fourier transform infrared (FTIR) spectroscopy can be used for detecting changes in functional groups of compounds, such as coffee. However, dispersion, reflection and non-homogeneity of the sample matrix can cause problems resulting in low spectral quality. On the other hand, sample preparation frequently takes place in a destructive way. To overcome these difficulties, in this work a photoacoustic cell has been adapted as a detector in a FTIR spectrophotometer to perform a study of roasted and ground coffee from three varieties of Coffea arabica grown by organic and conventional methods. Comparison between spectra of coffee recorded by FTIR-photoacoustic spectrometry (PAS) and by FTIR spectrophotometry showed a better resolution of the former method, which, aided by principal components analysis, allowed the identification of some absorption bands that allow the discrimination between organic and conventional coffee. The results obtained provide information about the spectral behavior of coffee powder which can be useful for establishing discrimination criteria. It has been demonstrated that FTIR-PAS can be a useful experimental tool for the characterization of coffee. Copyright © 2012 Society of Chemical Industry.

VUV Fourier-Transform absorption study of the np pi (1)Pi(-)(u) nu,N

NARCIS (Netherlands)

Glass-Maujean, M.; Jungen, C.; Dickenson, G.D.; Ubachs, W.M.G.; de Oliveira, N.; Joyeux, D.

2015-01-01

Abstract The DESIRS beamline of the SOLEIL synchrotron facility, equipped with a vacuum ultraviolet Fourier-Transform spectrometer has been used to measure Q(N″)(N-N″=0) absorption transitions of the D

Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)

Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

Science.gov (United States)

Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.

2017-05-01

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.

Science.gov (United States)

Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei

2015-09-01

A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress.

Algorithm, applications and evaluation for protein comparison by Ramanujan Fourier transform.

Science.gov (United States)

Zhao, Jian; Wang, Jiasong; Hua, Wei; Ouyang, Pingkai

2015-12-01

The amino acid sequence of a protein determines its chemical properties, chain conformation and biological functions. Protein sequence comparison is of great importance to identify similarities of protein structures and infer their functions. Many properties of a protein correspond to the low-frequency signals within the sequence. Low frequency modes in protein sequences are linked to the secondary structures, membrane protein types, and sub-cellular localizations of the proteins. In this paper, we present Ramanujan Fourier transform (RFT) with a fast algorithm to analyze the low-frequency signals of protein sequences. The RFT method is applied to similarity analysis of protein sequences with the Resonant Recognition Model (RRM). The results show that the proposed fast RFT method on protein comparison is more efficient than commonly used discrete Fourier transform (DFT). RFT can detect common frequencies as significant feature for specific protein families, and the RFT spectrum heat-map of protein sequences demonstrates the information conservation in the sequence comparison. The proposed method offers a new tool for pattern recognition, feature extraction and structural analysis on protein sequences. Copyright © 2015 Elsevier Ltd. All rights reserved.

Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.

Science.gov (United States)

Volkov, V V; Han, M G; Zhu, Y

2013-11-01

We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. Published by Elsevier B.V.

Fourier transform infrared imaging and microscopy studies of Pinus radiata pulps regarding the simultaneous saccharification and fermentation process

Energy Technology Data Exchange (ETDEWEB)

Castillo, Rosario del P., E-mail: rosariocastillo@udec.cl [Faculty of Pharmacy, University of Concepcion, Concepcion (Chile); Biotechnology Center, University of Concepcion, Concepcion (Chile); Araya, Juan [Faculty of Pharmacy, University of Concepcion, Concepcion (Chile); Biotechnology Center, University of Concepcion, Concepcion (Chile); Troncoso, Eduardo [Consorcio Bioenercel S.A, University of Concepcion, Concepcion (Chile); Vinet, Silenne; Freer, Juanita [Biotechnology Center, University of Concepcion, Concepcion (Chile); Faculty of Chemical Sciences, University of Concepcion, Concepcion (Chile)

2015-03-25

The distribution and chemical patterns of lignocellulosic components at microscopic scale and their effect on the simultaneous saccharification and fermentation process (SSF) in the production of bioethanol from Pinus radiata pulps were analyzed by the application of diverse microscopical techniques, including scanning electronic microscopy (SEM), confocal laser scanning microscopy (CLSM) and attenuated total reflectance (ATR) – Fourier transform infrared microspectroscopy. This last technique was accompanied with multivariate methods, including principal component analysis (PCA) and multivariate curve resolution with alternating least squares (MCR-ALS) to evaluate the distribution patterns and to generate pure spectra of the lignocellulosic components of fibers. The results indicate that the information obtained by the techniques is complementary (ultrastructure, confocality and chemical characterization) and that the distribution of components affects the SSF yield, identifying lignin coalescence droplets as a characteristic factor to increase the SSF yield. Therefore, multivariate analysis of the infrared spectra enabled the in situ identification of the cellulose, lignin and lignin-carbohydrates arrangements. These techniques could be used to investigate the lignocellulosic components distribution and consequently their recalcitrance in many applications where minimal sample manipulation and microscale chemical information is required.

Fourier transform infrared imaging and microscopy studies of Pinus radiata pulps regarding the simultaneous saccharification and fermentation process

International Nuclear Information System (INIS)

Castillo, Rosario del P.; Araya, Juan; Troncoso, Eduardo; Vinet, Silenne; Freer, Juanita

2015-01-01

The distribution and chemical patterns of lignocellulosic components at microscopic scale and their effect on the simultaneous saccharification and fermentation process (SSF) in the production of bioethanol from Pinus radiata pulps were analyzed by the application of diverse microscopical techniques, including scanning electronic microscopy (SEM), confocal laser scanning microscopy (CLSM) and attenuated total reflectance (ATR) – Fourier transform infrared microspectroscopy. This last technique was accompanied with multivariate methods, including principal component analysis (PCA) and multivariate curve resolution with alternating least squares (MCR-ALS) to evaluate the distribution patterns and to generate pure spectra of the lignocellulosic components of fibers. The results indicate that the information obtained by the techniques is complementary (ultrastructure, confocality and chemical characterization) and that the distribution of components affects the SSF yield, identifying lignin coalescence droplets as a characteristic factor to increase the SSF yield. Therefore, multivariate analysis of the infrared spectra enabled the in situ identification of the cellulose, lignin and lignin-carbohydrates arrangements. These techniques could be used to investigate the lignocellulosic components distribution and consequently their recalcitrance in many applications where minimal sample manipulation and microscale chemical information is required

Prediction of purine derivatives, creatinine and total nitrogen concentrations in urine by FT-Near-lnfrared Reflectance spectroscopy (FT-NIR)

International Nuclear Information System (INIS)

Susmel, P.; Piani, B.; Toso, B.; Stefanon, B.

2004-01-01

The objective of this study was to provide an alternative method for the determination of purine derivatives (PD, which include allantoin, uric acid, hypoxanthine and xanthine), creatinine and total nitrogen (N) concentrations in urine. About 180 urine samples from cattle, buffaloes and rabbit were collected and analyzed for PD by HPLC, creatinine by spectrophotometry and N by Kjeldahl method. The urine samples were then analyzed by Fourier Transformed Near Infrared Reflectance Spectroscopy (FT-NIR) to find conformity between this technique and the HPLC and colorimetric methods. FT-NIR can predict allantoin, uric acid, hypoxanthine, xanthine, creatinine, total N and sum of N in both allantoin and uric acid with a satisfactory level of accuracy: the determination coefficient (r 2 ) of validation ranged from 0.888% for uric acid to 0.982% for total N. The coefficients of determination for allantoin, creatinine and sum of N in both allantoin and uric acid were 0.92, 0.894 and 0.90%, respectively. Hypoxanthine and xanthine in urine samples were not detectable by NIRS, probably because of their low concentrations, and therefore they were not considered for instrumental calibration. (author)

Fourier transform infrared microspectroscopy for the analysis of the biochemical composition of C. elegans worms.

Science.gov (United States)

Sheng, Ming; Gorzsás, András; Tuck, Simon

2016-01-01

Changes in intermediary metabolism have profound effects on many aspects of C. elegans biology including growth, development and behavior. However, many traditional biochemical techniques for analyzing chemical composition require relatively large amounts of starting material precluding the analysis of mutants that cannot be grown in large amounts as homozygotes. Here we describe a technique for detecting changes in the chemical compositions of C. elegans worms by Fourier transform infrared microspectroscopy. We demonstrate that the technique can be used to detect changes in the relative levels of carbohydrates, proteins and lipids in one and the same worm. We suggest that Fourier transform infrared microspectroscopy represents a useful addition to the arsenal of techniques for metabolic studies of C. elegans worms.

A novel method for computation of the discrete Fourier transform over characteristic two finite field of even extension degree

OpenAIRE

Fedorenko, Sergei V.

2011-01-01

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.

Attenuated Total Reflection Mid-Infrared (ATR-MIR) Spectroscopy and Chemometrics for the Identification and Classification of Commercial Tannins.

Science.gov (United States)

Ricci, Arianna; Parpinello, Giuseppina P; Olejar, Kenneth J; Kilmartin, Paul A; Versari, Andrea

2015-11-01

Attenuated total reflection Fourier transform infrared (FT-IR) spectroscopy was used to characterize 40 commercial tannins, including condensed and hydrolyzable chemical classes, provided as powder extracts from suppliers. Spectral data were processed to detect typical molecular vibrations of tannins bearing different chemical groups and of varying botanical origin (univariate qualitative analysis). The mid-infrared region between 4000 and 520 cm(-1) was analyzed, with a particular emphasis on the vibrational modes in the fingerprint region (1800-520 cm(-1)), which provide detailed information about skeletal structures and specific substituents. The region 1800-1500 cm(-1) contained signals due to hydrolyzable structures, while bands due to condensed tannins appeared at 1300-900 cm(-1) and exhibited specific hydroxylation patterns useful to elucidate the structure of the flavonoid monomeric units. The spectra were investigated further using principal component analysis for discriminative purposes, to enhance the ability of infrared spectroscopy in the classification and quality control of commercial dried extracts and to enhance their industrial exploitation.

Study of influence with fourier transform on long cable in measurement of fall time of DPF neutron profile

International Nuclear Information System (INIS)

Guo Hongsheng; Li Rurong; Tang Dengpan; Yang Gaozhao; Hu Qingyuan; Si Fenni; Zhang Jianhua; Peng Taiping

2011-01-01

The influence of the Fourier Transform on long cable in the measurement of fall time of DPF neutron profile is discussed by mathematical methods. The application of anti-convolution function with the Fourier Transform on long cable is analysed. The time interval between the peak time and the time that the height falls 3 orders of magnitude after peak is measured with gated-detector array system which consists of PMT (photomultiplier tube) and organic scintillation crystal. (authors)

Vibrational analysis of Fourier transform spectrum of the B u )–X g ...

Indian Academy of Sciences (India)

improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and r-centroid values. Keywords. Fourier transform spectroscopy; electronic spectrum of selenium dimer; vibrational analysis; Franck–Condon factor; r-centroid values.

Applications of Fourier transform infrared spectroscopy to quality control of the epoxy matrix

Science.gov (United States)

Antoon, M. K.; Starkey, K. M.; Koenig, J. L.

1979-01-01

The object of the paper is to demonstrate the utility of Fourier transform infrared (FT-IR) difference spectra for investigating the composition of a neat epoxy resin, hardener, and catalysts. The composition and degree of cross-linking of the cured matrix is also considered.

On the measurement of Wigner distribution moments in the fractional Fourier transform domain

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2002-01-01

It is shown how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of fractional Fourier transform systems (generally anamorphic ones). The minimum number of (anamorphic) fractional power spectra that are needed

Progress in static fourier transform infrared spectroscopy: assessment of sifti preliminary performances

Science.gov (United States)

Hébert, Philippe; Pierangelo, Clémence; Rosak, Alain; Cansot, Elodie; Bernard, Frédéric; Camy-Peyret, Claude

2017-11-01

The concept of static Fourier transform interferometry at thermal infrared wavelengths is well suited in the case of narrow spectral bands that are looked at for targeted molecular species as CO and O3 for pollution and air quality monitoring, or H20 and CO2 for weather forecast, down to the troposphere. It permits a high spectral resolution and a very good radiometric performance, with the advantage of a static interferometer, including no moving part. Along with other molecules sounded in the UV-VIS domain, as for instance in the TRAQ mission, SIFTI will provide scientists with a complete set for pollution measurements and air quality survey. Our paper presents the principles of static Fourier transform spectrometry, the work led on the instrument performance model and our study of the SIFTI instrument. We describe the instrument, its main dimensions and characteristics, and its architecture and major subsystems. We eventually make a preliminary survey of the SIFTI performance budget items. As a conclusion, we introduce the future CNES phase A study of this instrument that is started in 2006

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

Generation of Fourier-transform-limited heralded single photons

International Nuclear Information System (INIS)

U'Ren, Alfred B.; Jeronimo-Moreno, Yasser; Garcia-Gracia, Hipolito

2007-01-01

In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets

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

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.

Geographical traceability of Marsdenia tenacissima by Fourier transform infrared spectroscopy and chemometrics

Science.gov (United States)

Li, Chao; Yang, Sheng-Chao; Guo, Qiao-Sheng; Zheng, Kai-Yan; Wang, Ping-Li; Meng, Zhen-Gui

2016-01-01

A combination of Fourier transform infrared spectroscopy with chemometrics tools provided an approach for studying Marsdenia tenacissima according to its geographical origin. A total of 128 M. tenacissima samples from four provinces in China were analyzed with FTIR spectroscopy. Six pattern recognition methods were used to construct the discrimination models: support vector machine-genetic algorithms, support vector machine-particle swarm optimization, K-nearest neighbors, radial basis function neural network, random forest and support vector machine-grid search. Experimental results showed that K-nearest neighbors was superior to other mathematical algorithms after data were preprocessed with wavelet de-noising, with a discrimination rate of 100% in both the training and prediction sets. This study demonstrated that FTIR spectroscopy coupled with K-nearest neighbors could be successfully applied to determine the geographical origins of M. tenacissima samples, thereby providing reliable authentication in a rapid, cheap and noninvasive way.

A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum estimation.

Science.gov (United States)

Holland, Alexander; Aboy, Mateo

2009-07-01

We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb-Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations.

Benefits of 2.94 μm infrared matrix-assisted laser desorption/ionization for analysis of labile molecules by Fourier transform mass spectrometry

DEFF Research Database (Denmark)

Budnik, Bogdan A.; Jensen, Kenneth Bendix; Jørgensen, Thomas J. D.

2000-01-01

A 2.94 microm Er:YAG laser was used together with a commercial Fourier transform mass spectrometer to study labile biomolecules. The combination has shown superior performance over conventional 337 nm ultraviolet matrix-assisted laser desorption/ionization (UV-MALDI) Fourier transform mass...

On the Elliptic Nonabelian Fourier Transform for Unipotent Representations of p-Adic Groups

NARCIS (Netherlands)

Ciubotaru, D.; Opdam, E.; Cogdell, J.; Kim, J.-L.; Zhu, C.-B.

2017-01-01

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these

The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.

Science.gov (United States)

Suslick, Kenneth S.; And Others

1987-01-01

Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)

Color image cryptosystem using Fresnel diffraction and phase modulation in an expanded fractional Fourier transform domain

Science.gov (United States)

Chen, Hang; Liu, Zhengjun; Chen, Qi; Blondel, Walter; Varis, Pierre

2018-05-01

In this letter, what we believe is a new technique for optical color image encryption by using Fresnel diffraction and a phase modulation in an extended fractional Fourier transform domain is proposed. Different from the RGB component separation based method, the color image is converted into one component by improved Chirikov mapping. The encryption system is addressed with Fresnel diffraction and phase modulation. A pair of lenses is placed into the fractional Fourier transform system for the modulation of beam propagation. The structure parameters of the optical system and parameters in Chirikov mapping serve as extra keys. Some numerical simulations are given to test the validity of the proposed cryptosystem.

Multi-band Image Registration Method Based on Fourier Transform