A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Nash, Patrick L.
2008-01-01
Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium
Huang, Lianjie
2013-10-29
Methods for enhancing ultrasonic reflection imaging are taught utilizing a split-step Fourier propagator in which the reconstruction is based on recursive inward continuation of ultrasonic wavefields in the frequency-space and frequency-wave number domains. The inward continuation within each extrapolation interval consists of two steps. In the first step, a phase-shift term is applied to the data in the frequency-wave number domain for propagation in a reference medium. The second step consists of applying another phase-shift term to data in the frequency-space domain to approximately compensate for ultrasonic scattering effects of heterogeneities within the tissue being imaged (e.g., breast tissue). Results from various data input to the method indicate significant improvements are provided in both image quality and resolution.
2015-06-01
31 APPENDIX. MATLAB CODES FOR HYBRID METHOD ............................................33 LIST OF REFERENCES...plasma physics, seismic propagation and underwater acoustics [1]. Tappert was the first to introduce the PE method for underwater acoustic...MMPE model, a Matlab version of the SSF algorithm has been developed for this thesis based on the same operator approximations as the MMPE model. It
DEFF Research Database (Denmark)
Rasmussen, Christian Jørgen
2001-01-01
Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method.......Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method....
Zia, Haider
2017-06-01
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.
Multilevel hybrid split-step implicit tau-leap
Ben Hammouda, Chiheb
2016-06-17
In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been shown to be more relevant than continuous state-space and deterministic ones. In systems characterized by having simultaneously fast and slow timescales, existing discrete space-state stochastic path simulation methods, such as the stochastic simulation algorithm (SSA) and the explicit tau-leap (explicit-TL) method, can be very slow. Implicit approximations have been developed to improve numerical stability and provide efficient simulation algorithms for those systems. Here, we propose an efficient Multilevel Monte Carlo (MLMC) method in the spirit of the work by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012). This method uses split-step implicit tau-leap (SSI-TL) at levels where the explicit-TL method is not applicable due to numerical stability issues. We present numerical examples that illustrate the performance of the proposed method. © 2016 Springer Science+Business Media New York
Propagation of a general-type beam through a truncated fractional Fourier transform optical system.
Zhao, Chengliang; Cai, Yangjian
2010-03-01
Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.
Fourier Transform Ultrasound Spectroscopy for the determination of wave propagation parameters.
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.
Directory of Open Access Journals (Sweden)
Filipčič Aleš
2017-01-01
Full Text Available This study investigated tennis players’ speed before, during and after the split-step, deceleration before and acceleration after the split-step in four different stroke groups in three age categories. Seven male professional, eleven male and ten female junior tennis players were recorded with video cameras at official tournaments. Using the SAGIT system, we gathered data on 8,545 split-steps. Tennis players performed a split-step in 82.9% of cases. A tennis player’s speed, deceleration and acceleration were measured 0.2 s before and after the split-step. Differences between categories and stroke groups for each of the five variables were analyzed with a two-way ANOVA. The differences between the groups of players were generally much higher in the speed before, during and after the split-step than in the deceleration before and acceleration after the split-step. Most of these differences were observed between the various stroke groups. These results suggest that players use three types of movement while performing a split-step. In the first type, which is typical of serving and returning, the speed before, during and after the split-step is lower (0.55 to 1.2 m/s. The second type of movement is characteristic of baseline strokes where tennis players achieve higher speed than in the first type (0.7 to 1.66 m/s. The third type occurs in strokes where a tennis player is moving or already at the net (0.78 to 1.9 m/s. Movement in tennis is an area that requires constant development in terms of designing and upgrading movement patterns, increasing speed and practice in specific game situations.
Split-step eigenvector-following technique for exploring enthalpy landscapes at absolute zero.
Mauro, John C; Loucks, Roger J; Balakrishnan, Jitendra
2006-03-16
The mapping of enthalpy landscapes is complicated by the coupling of particle position and volume coordinates. To address this issue, we have developed a new split-step eigenvector-following technique for locating minima and transition points in an enthalpy landscape at absolute zero. Each iteration is split into two steps in order to independently vary system volume and relative atomic coordinates. A separate Lagrange multiplier is used for each eigendirection in order to provide maximum flexibility in determining step sizes. This technique will be useful for mapping the enthalpy landscapes of bulk systems such as supercooled liquids and glasses.
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.
1989-01-01
We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage
DEFF Research Database (Denmark)
Benzon, Hans-Henrik; Bovith, Thomas
2008-01-01
Weather radars are essential sensors for observation of precipitation in the troposphere and play a major part in weather forecasting and hydrological modelling. Clutter caused by non-standard wave propagation is a common problem in weather radar applications, and in this paper a method...... for prediction of this type of weather radar clutter is presented. The method uses a wave propagator to identify areas of potential non-standard propagation. The wave propagator uses a three dimensional refractivity field derived from the geophysical parameters: temperature, humidity, and pressure obtained from...... a high-resolution Numerical Weather Prediction (NWP) model. The wave propagator is based on the parabolic equation approximation to the electromagnetic wave equation. The parabolic equation is solved using the well-known Fourier split-step method. Finally, the radar clutter prediction technique is used...
Influence of Sea Surface Roughness on the Electromagnetic Wave Propagation in the Duct Environment
Directory of Open Access Journals (Sweden)
X. Zhao
2010-12-01
Full Text Available This paper deals with a study of the influence of sea surface roughness on the electromagnetic wave propagation in the duct environment. The problem of electromagnetic wave propagation is modeled by using the parabolic equation method. The roughness of the sea surface is computed by modifying the smooth surface Fresnel reflection coefficient to account for the reduction in the specular reflection due to the roughness resulting from sea wind speed. The propagation model is solved by the mixed Fourier split-step algorithm. Numerical experiments indicate that wind-driven roughened sea surface has an impact on the electromagnetic wave propagation in the duct environment, and the strength is intensified along with the increment of sea wind speeds and/or the operating frequencies. In a fixed duct environment, however, proper disposition of the transmitter could reduce these impacts.
Time Resolution of Collapse Events During the Propagation of Ultraviolet Light Filaments
National Research Council Canada - National Science Library
Fondren, Teresa J
2008-01-01
.... Applications for filamentation include areas such as remote sensing and directed energy. A split-step spectral propagation simulation is used to model the behavior of a high intensity ultraviolet laser pulse propagating through air...
Parabolic Equation Modeling of Propagation over Terrain Using Digital Elevation Model
Directory of Open Access Journals (Sweden)
Xiao-Wei Guan
2018-01-01
Full Text Available The parabolic equation method based on digital elevation model (DEM is applied on propagation predictions over irregular terrains. Starting from a parabolic approximation to the Helmholtz equation, a wide-angle parabolic equation is deduced under the assumption of forward propagation and the split-step Fourier transform algorithm is used to solve it. The application of DEM is extended to the Cartesian coordinate system and expected to provide a precise representation of a three-dimensional surface with high efficiency. In order to validate the accuracy, a perfectly conducting Gaussian terrain profile is simulated and the results are compared with the shift map. As a consequence, a good agreement is observed. Besides, another example is given to provide a theoretical basis and reference for DEM selection. The simulation results demonstrate that the prediction errors will be obvious only when the resolution of the DEM used is much larger than the range step in the PE method.
Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Alexander, Andrew L.
2012-01-01
The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier orientation reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA). PMID:22963853
International Nuclear Information System (INIS)
Agnesi, A.; Gabetta, G.; Flora, F.; Hermensent, T.; Reali, G.T.
1988-01-01
Numerical methods for simulation of loaded laser cavities are largely devoted to the dynamic evolution of the transverse field distribution. Results on transverse field profile evolution have been published using various numerical methods like finite-difference schemes, Gaussian mode expansion and spectral methods based on trigonometric polynomial mode expansion. The latter methods is particular advantageous because of the existence of very efficient algorithms such as Fast Fourier Transform (FFT). A similar approach is used to solve the field in unstable laser cavities with high gain active medium such as XeCl. The preliminary test presented here constitute the first attempt to optimize our numerical code for nonlinear behaviors such as self-focussing and bistability
2008-08-01
Foucault at SAIC. – 14 – The split-step wave optics propagation simulations were all run with a frame rate of 3,000 frames per second. These simulations...formulate the analysis so that such eigen values do not show up. 7). Lastly, I would like to thank Barry Foucault for making his wave optics propagation
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Stade, Eric
2005-01-01
A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of ap
Hoch, Jeffrey C.
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.
Hoch, Jeffrey C
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.
Indian Academy of Sciences (India)
(Exercise !)) The subject of Fourier series finds a wide range of applications from crystallography to spectroscopy. It is one of the most powerful theories in the history of mathematics and has stimulated the .... satisfy the wave equation and following physical ideas Bernoulli suggested solutions of the form u ex,t) = l:ak ...
Indian Academy of Sciences (India)
assuming a lot of Lebesgue theory of integration. We would like to conclude this article with the following result. ofFejer which treats the class of continuous functions as a whole. As we know, given any point to there is a function in this class whose Fourier series diverges at that point. In 1904, the Hungarian mathematician ...
Waichman, Karol; Barmashenko, Boris D.; Rosenwaks, Salman
2017-10-01
Analysis of beam propagation, kinetic and fluid dynamic processes in Cs diode pumped alkali lasers (DPALs), using wave optics model and gasdynamic code, is reported. The analysis is based on a three-dimensional, time-dependent computational fluid dynamics (3D CFD) model. The Navier-Stokes equations for momentum, heat and mass transfer are solved by a commercial Ansys FLUENT solver based on the finite volume discretization technique. The CFD code which solves the gas conservation equations includes effects of natural convection and temperature diffusion of the species in the DPAL mixture. The DPAL kinetic processes in the Cs/He/C2H6 gas mixture dealt with in this paper involve the three lowest energy levels of Cs, (1) 62S1/2, (2) 62P1/2 and (3) 62P3/2. The kinetic processes include absorption due to the 1->3 D2 transition followed by relaxation the 3 to 2 fine structure levels and stimulated emission due to the 2->1 D1 transition. Collisional quenching of levels 2 and 3 and spontaneous emission from these levels are also considered. The gas flow conservation equations are coupled to fast-Fourier-transform algorithm for transverse mode propagation to obtain a solution of the scalar paraxial propagation equation for the laser beam. The wave propagation equation is solved by the split-step beam propagation method where the gain and refractive index in the DPAL medium affect the wave amplitude and phase. Using the CFD and beam propagation models, the gas flow pattern and spatial distributions of the pump and laser intensities in the resonator were calculated for end-pumped Cs DPAL. The laser power, DPAL medium temperature and the laser beam quality were calculated as a function of pump power. The results of the theoretical model for laser power were compared to experimental results of Cs DPAL.
Asif, Rameez; Lin, Chien-Yu; Usman, Muhammad; Schmauss, Bernhard
2012-01-01
We have numerically investigated the impact of non-linear impairments on the performance of 400Gbit/s DP-RZ- QPSK transmission system over 1200km standard single mode fiber (SMF-28) having an average span loss of 16dB and with no in-line optical dispersion compensation in the transmission link. Digital backward propagation (DBP) algorithm based on split-step Fourier method (SSFM) is employed along with the coherent receiver to compensate the fiber transmission impairments i.e. chromatic dispersion (CD) and non-linear (NL) impairments. The system performance is monitored in terms of Q-value (calculated form BER) for various signal input launch powers. We further quantify the impact of inter-channel non-linear impairments such as cross-phase-modulation (XPM) and four-wave-mixing (FWM) on the performance of DBP algorithm by investigating the multiple-channel transmission, i.e. 8x400Gbit/s DP-RZ-QPSK system. The results depict efficient performance of DBP algorithm as compared to the system where only linear dispersion compensation is implemented. This shows the promising impact of digital backward propagation algorithm on the high data-rate transmission systems such as 400Gbit/s per single channel which is expected to be a possible data rate for long-haul optical communication systems after 100Gb Ethernet in near future.
Fourier phase in Fourier-domain optical coherence tomography
Uttam, Shikhar; Liu, Yang
2015-01-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
NIEMELÄ, EERO
2008-01-01
Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...
Mateo, Eduardo F; Yaman, Fatih; Li, Guifang
2010-07-05
An advanced split-step method is employed for the digital backward-propagation (DBP) method using the coupled nonlinear Schrodinger equations for the compensation of inter-channel nonlinearities. Compared to the conventional DBP, cross-phase modulation (XPM) can be efficiently compensated by including the effect of the inter-channel walk-off in the nonlinear step of the split-step method (SSM). While self-phase modulation (SPM) compensation is inefficient in WDM systems, XPM compensation is able to increase the transmission reach by a factor of 2.5 for 16-QAM-modulated signals. The advanced SSM significantly relaxes the step size requirements resulting in a factor of 4 reduction in computational load.
Indian Academy of Sciences (India)
digital methods of spectrum estimation which influenced the research in almost every field of engineering and science. In this article, we will first introduce the conti- nuous-time Fourier transform (eFT), discrete-time Fourier transform and discrete Fourier transform (DFT) and then present an example to illustrate the relation ...
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Hall, Martin P. M.; Barclay, Leslie W.
The effects of the earth atmosphere on the radio-wave propagation (RWP) and their implications for telecommunication systems are discussed in reviews based on lectures presented at the Second IEE Vacation School on Radiowave Propagation, held at the University of Surrey in September 1986. A general overview of propagation phenomena is presented, and particular attention is given to the theory of EM wave propagation; radio system parameters; surface wave propagation; RWP in the ionosphere; VLF, LF, and MF applications and predictions; HF applications and predictions; clear-air aspects of the troposphere and their effects on RWP; and the nature of precipitation, clouds, and atmospheric gases and their effects on RWP. Also considered are terrestrial and earth-space propagation path predictions, the prediction of interference levels and coordination distances for frequencies above 1 GHz, propagation effects on VHF and UHF broadcasting, and propagation effects on mobile communication services.
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
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…
Fourier Transform Spectrometer
National Aeronautics and Space Administration — The Fourier Transform Spectrometer project demonstrates the efficacy of a miniaturized spectrometer for flight applications.A spectrometer is an instrument used to...
Fourier transformation for pedestrians
Butz, Tilman
2015-01-01
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
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....
International Nuclear Information System (INIS)
Macia, R.; Correig, A.M.
1987-01-01
Seismic wave propagation is described by a second order differential equation for medium displacement. By Fourier transforming with respect to time and space, wave equation transforms into a system of first order linear differential equations for the Fourier transform of displacement and stress. This system of differential equations is solved by means of Matrix Propagator and applied to the propagation of body waves in stratified media. The matrix propagators corresponding to P-SV and SH waves in homogeneous medium are found as an intermediate step to obtain the spectral response of body waves propagating through a stratified medium with homogeneous layers. (author) 14 refs
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
Fourier Transform Mass Spectrometry.
Gross, Michael L.; Rempel, Don L.
1984-01-01
Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)
Fast Fourier orthogonalization
L. Ducas (Léo); T. Prest; S.A. Abramov; E.V. Zima; X-S. Gao
2016-01-01
htmlabstractThe classical fast Fourier transform (FFT) allows to compute in quasi-linear time the product of two polynomials, in the {\\em circular convolution ring} R[x]/(x^d−1) --- a task that naively requires quadratic time. Equivalently, it allows to accelerate matrix-vector products when the
3-D Bidirectional Propagation Algorithm Based on Fourier Series
Czech Academy of Sciences Publication Activity Database
Čtyroký, Jiří
2012-01-01
Roč. 30, č. 23 (2012), s. 3699-30708 ISSN 0733-8724 R&D Projects: GA ČR(CZ) GAP205/10/0046; GA MŠk OC09061 Institutional support: RVO:67985882 Keywords : optics * gratings Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 2.555, year: 2012
Ortega-Cerda, Joaquim; Seip, Kristian
2000-01-01
We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies which generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with de Branges' theory of Hilbert spaces of entire functions. We show that our description of sampling sequences permits us to obtain a classical inequality of H. Landau as a consequence of Pavlov's description of Riesz bases of complex ex...
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Independent task Fourier filters
Caulfield, H. John
2001-11-01
Since the early 1960s, a major part of optical computing systems has been Fourier pattern recognition, which takes advantage of high speed filter changes to enable powerful nonlinear discrimination in `real time.' Because filter has a task quite independent of the tasks of the other filters, they can be applied and evaluated in parallel or, in a simple approach I describe, in sequence very rapidly. Thus I use the name ITFF (independent task Fourier filter). These filters can also break very complex discrimination tasks into easily handled parts, so the wonderful space invariance properties of Fourier filtering need not be sacrificed to achieve high discrimination and good generalizability even for ultracomplex discrimination problems. The training procedure proceeds sequentially, as the task for a given filter is defined a posteriori by declaring it to be the discrimination of particular members of set A from all members of set B with sufficient margin. That is, we set the threshold to achieve the desired margin and note the A members discriminated by that threshold. Discriminating those A members from all members of B becomes the task of that filter. Those A members are then removed from the set A, so no other filter will be asked to perform that already accomplished task.
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
Fourier transforms principles and applications
Hansen, Eric W
2014-01-01
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.
The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy
DEFF Research Database (Denmark)
Pedersen, Anders Filsøe; Simons, Hugh; Detlefs, Carsten
2018-01-01
The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing...
Extending Single-Molecule Microscopy Using Optical Fourier Processing
2015-01-01
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862
Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
Said-Houari, Belkacem
2013-02-01
In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo\\'s laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier\\'s law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U0 ∈ Hs(ℝ) ∩ L1(ℝ). In addition, by restricting the initial data to U0 ∈ Hs(ℝ) ∩ L1,γ(ℝ) and γ ∈ [0, 1], we can derive faster decay estimates with the decay rate improvement by a factor of t-γ/2. © 2013 Copyright Taylor and Francis Group, LLC.
Ferrarese, Giorgio
2011-01-01
Lectures: A. Jeffrey: Lectures on nonlinear wave propagation.- Y. Choquet-Bruhat: Ondes asymptotiques.- G. Boillat: Urti.- Seminars: D. Graffi: Sulla teoria dell'ottica non-lineare.- G. Grioli: Sulla propagazione del calore nei mezzi continui.- T. Manacorda: Onde nei solidi con vincoli interni.- T. Ruggeri: "Entropy principle" and main field for a non linear covariant system.- B. Straughan: Singular surfaces in dipolar materials and possible consequences for continuum mechanics
Fourier multispectral imaging.
Jia, Jie; Ni, Chuan; Sarangan, Andrew; Hirakawa, Keigo
2015-08-24
Current multispectral imaging systems use narrowband filters to capture the spectral content of a scene, which necessitates different filters to be designed for each application. In this paper, we demonstrate the concept of Fourier multispectral imaging which uses filters with sinusoidally varying transmittance. We designed and built these filters employing a single-cavity resonance, and made spectral measurements with a multispectral LED array. The measurements show that spectral features such as transmission and absorption peaks are preserved with this technique, which makes it a versatile technique than narrowband filters for a wide range of multispectral imaging applications.
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
Fourier transforms in spectroscopy
Kauppinen, Jyrki
2000-01-01
This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi
Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform
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…
Fourier Transform Spectrometer System
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Ultrasonic Transducers for Fourier Analysis.
Greenslade, Thomas B., Jr.
1995-01-01
Describes an experiment that uses the ultrasonic transducer for demonstrating the Fourier components of waveshapes such as the square and triangular waves produced by laboratory function generators. (JRH)
Fourier-Hermite communications; where Fourier meets Hermite
Korevaar, C.W.; Kokkeler, Andre B.J.; de Boer, Pieter-Tjerk; Smit, Gerardus Johannes Maria
A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency
Braun, Daniel; Monjid, Younes; Rougé, Bernard; Kerr, Yann
2018-02-01
We investigated whether correlations between the Fourier components at slightly shifted frequencies of the fluctuations of the electric field measured with a one-dimensional antenna array on board a satellite flying over a plane allow one to measure the two-dimensional brightness temperature as a function of position in the plane. We found that the achievable spatial resolution that resulted from just two antennas is on the order of h χ , with χ = c / ( Δ r ω 0 ) , both in the direction of the flight of the satellite and in the direction perpendicular to it, where Δ r is the distance between the antennas, ω0 is the central frequency, h is the height of the satellite over the plane, and c is the speed of light. Two antennas separated by a distance of about 100 m on a satellite flying with a speed of a few km/s at a height of the order of 1000 km and a central frequency of order GHz allow, therefore, the imaging of the brightness temperature on the surface of Earth with a resolution of the order of 1 km. For a single point source, the relative radiometric resolution is on the order of √{ χ} , but, for a uniform temperature field in a half plane left or right of the satellite track, it is only on the order of 1 / χ 3 / 2 , which indicates that two antennas do not suffice for a precise reconstruction of the temperature field. Several ideas are discussed regarding how the radiometric resolution could be enhanced. In particular, having N antennas all separated by at least a distance on the order of the wave-length allows one to increase the signal-to-noise ratio by a factor of order N but requires averaging over N2 temperature profiles obtained from as many pairs of antennas.
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Fourier reconstruction with sparse inversions
Zwartjes, P.M.
2005-01-01
In seismic exploration an image of the subsurface is generated from seismic data through various data processing algorithms. When the data is not acquired on an equidistantly spaced grid, artifacts may result in the final image. Fourier reconstruction is an interpolation technique that can reduce these artifacts by generating uniformly sampled data from such non-uniformly sampled data. The method works by estimating via least-squares inversion the Fourier coefficients that describe the non-un...
Iterative wave-front reconstruction in the Fourier domain.
Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry
2017-05-15
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.
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)
Sonic boom propagation through atmospheric turbulence
Yamashita, Hiroshi; Obayashi, Shigeru; 山下, 博; 大林, 茂
2009-01-01
The effect of the homogeneous atmospheric turbulence on the sonic boom propagation has been investigated. The turbulence field is represented by a finite sum of discrete Fourier modes based on the von Karman and Pao energy spectrum. The sonic boom signature is calculated by the modified Waveform Parameter Method, considering the turbulent velocities. The results show that in 59 % of the cases, the intensity of the sonic boom had decreased, and in other 41 % of the cases had increased the soni...
International Nuclear Information System (INIS)
Picard, R.R.
1989-01-01
Topics covered in this chapter include a discussion of exact results as related to nuclear materials management and accounting in nuclear facilities; propagation of error for a single measured value; propagation of error for several measured values; error propagation for materials balances; and an application of error propagation to an example of uranium hexafluoride conversion process
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Fourier series, Fourier transform and their applications to mathematical physics
Serov, Valery
2017-01-01
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...
Synthetic Fourier transform light scattering.
Lee, Kyeoreh; Kim, Hyeon-Don; Kim, Kyoohyun; Kim, Youngchan; Hillman, Timothy R; Min, Bumki; Park, Yongkeun
2013-09-23
We present synthetic Fourier transform light scattering, a method for measuring extended angle-resolved light scattering (ARLS) from individual microscopic samples. By measuring the light fields scattered from the sample plane and numerically synthesizing them in Fourier space, the angle range of the ARLS patterns is extended up to twice the numerical aperture of the imaging system with unprecedented sensitivity and precision. Extended ARLS patterns of individual microscopic polystyrene beads, healthy human red blood cells (RBCs), and Plasmodium falciparum-parasitized RBCs are presented.
Fourier series in orthogonal polynomials
Osilenker, Boris
1999-01-01
This book presents a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness).The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical
Error propagation analysis for a sensor system
International Nuclear Information System (INIS)
Yeater, M.L.; Hockenbury, R.W.; Hawkins, J.; Wilkinson, J.
1976-01-01
As part of a program to develop reliability methods for operational use with reactor sensors and protective systems, error propagation analyses are being made for each model. An example is a sensor system computer simulation model, in which the sensor system signature is convoluted with a reactor signature to show the effect of each in revealing or obscuring information contained in the other. The error propagation analysis models the system and signature uncertainties and sensitivities, whereas the simulation models the signatures and by extensive repetitions reveals the effect of errors in various reactor input or sensor response data. In the approach for the example presented, the errors accumulated by the signature (set of ''noise'' frequencies) are successively calculated as it is propagated stepwise through a system comprised of sensor and signal processing components. Additional modeling steps include a Fourier transform calculation to produce the usual power spectral density representation of the product signature, and some form of pattern recognition algorithm
FOURIER SERIES MODELS THROUGH TRANSFORMATION
African Journals Online (AJOL)
DEPT
This study considers the application of Fourier series analysis (FSA) to seasonal time series data. The ultimate objective of the study is to construct an FSA model that can lead to reliable forecast. Specifically, the study evaluates data for the assumptions of time series analysis; applies the necessary transformation to the ...
Fourier reconstruction with sparse inversions
Zwartjes, P.M.
2005-01-01
In seismic exploration an image of the subsurface is generated from seismic data through various data processing algorithms. When the data is not acquired on an equidistantly spaced grid, artifacts may result in the final image. Fourier reconstruction is an interpolation technique that can reduce
Uncertainty Principles and Fourier Analysis
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 2. Uncertainty Principles and Fourier Analysis. Alladi Sitaram. General Article Volume 4 Issue 2 February 1999 pp 20-23. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/004/02/0020-0023 ...
Fourier Analysis of Musical Intervals
LoPresto, Michael C.
2008-01-01
Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace. A recent article in "The Physics Teacher" aptly demonstrated the use of MacScope in just such a manner as a way to teach Fourier analysis. A logical continuation of this project is to…
Nootz, Gero; Matt, Silvia; Kanaev, Andrey; Judd, Kyle P; Hou, Weilin
2017-08-01
The propagation of a laser beam through Rayleigh-Bénard (RB) turbulence is investigated experimentally and by way of numerical simulation. For the experimental part, a focused laser beam transversed a 5 m×0.5 m×0.5 m water filled tank lengthwise. The tank is heated from the bottom and cooled from the top to produce convective RB turbulence. The effect of the turbulence on the beam is recorded on the exit of the beam from the tank. From the centroid motion of the beam, the index of refraction structure constant Cn2 is determined. For the numerical efforts RB turbulence is simulated for a tank of the same geometry. The simulated temperature fields are converted to the index of refraction distributions, and Cn2 is extracted from the index of refraction structure functions, as well as from the simulated beam wander. To model the effect on beam propagation, the simulated index of refraction fields are converted to discrete index of refraction phase screens. These phase screens are then used in a split-step beam propagation method to investigate the effect of the turbulence on a laser beam. The beam wander as well as the index of refraction structure parameter Cn2 determined from the experiment and simulation are compared and found to be in good agreement.
Fourier transform digital holographic adaptive optics imaging system
Liu, Changgeng; Yu, Xiao; Kim, Myung K.
2013-01-01
A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541
Mateo, Eduardo F; Zhou, Xiang; Li, Guifang
2011-01-17
An improved split-step method (SSM) for digital backward propagation (DBP) applicable to wavelength-division multiplexed (WDM) transmission with polarization-division multiplexing (PDM) is presented. A coupled system of nonlinear partial differential equations, derived from the Manakov equations, is used for DBP. The above system enables the implementation of DBP on a channel-by-channel basis, where only the effect of phase-mismatched four-wave mixing (FWM) is neglected. A novel formulation of the SSM for PDM-WDM systems is presented where new terms are included in the nonlinear step to account for inter-polarization mixing effects. In addition, the effect of inter-channel walk-off is included. This substantially reduces the computational load compared to the conventional SSM.
Fourier analysis for rotating-element ellipsometers.
Cho, Yong Jai; Chegal, Won; Cho, Hyun Mo
2011-01-15
We introduce a Fourier analysis of the waveform of periodic light-irradiance variation to capture Fourier coefficients for multichannel rotating-element ellipsometers. In this analysis, the Fourier coefficients for a sample are obtained using a discrete Fourier transform on the exposures. The analysis gives a generic function that encompasses the discrete Fourier transform or the Hadamard transform, depending on the specific conditions. Unlike the Hadamard transform, a well-known data acquisition method that is used only for conventional multichannel rotating-element ellipsometers with line arrays with specific readout-mode timing, this Fourier analysis is applicable to various line arrays with either nonoverlap or overlap readout-mode timing. To assess the effects of the novel Fourier analysis, the Fourier coefficients for a sample were measured with a custom-built rotating-polarizer ellipsometer, using this Fourier analysis with various numbers of scans, integration times, and rotational speeds of the polarizer.
Statistical Characterization of Electromagnetic Wave Propagation in Mine Environments
Yucel, Abdulkadir C.
2013-01-01
A computational framework for statistically characterizing electromagnetic (EM) wave propagation through mine tunnels and galleries is presented. The framework combines a multi-element probabilistic collocation method with a full-wave fast Fourier transform and fast multipole method accelerated surface integral equation-based EM simulator to statistically characterize fields from wireless transmitters in complex mine environments. 1536-1225 © 2013 IEEE.
Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging
International Nuclear Information System (INIS)
Soloviev, Vadim Y.
2006-01-01
A novel adaptive mesh technique in the Fourier domain is introduced for problems in fluorescence lifetime imaging. A dynamical adaptation of the three-dimensional scheme based on the finite volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. Light propagation in the medium is modeled by the telegraph equation, while the lifetime reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the method are demonstrated by image reconstruction of two spherical fluorescent objects embedded in a tissue phantom
Fourier filtering of synchrotron white-beam topographs
Energy Technology Data Exchange (ETDEWEB)
Pilard, M. [Paris-6 Univ., 75 (France). Lab. de Mineralogie-Cristallographie; Epelboin, Y. [Paris-6 Univ., 75 (France). Lab. de Mineralogie-Cristallographie; Soyer, A. [Paris-6 Univ., 75 (France). Lab. de Mineralogie-Cristallographie
1995-06-01
Numerical image treatment has been used for the enhancement and the analysis of synchrotron white-beam topographs. Images are recorded either during the experiment by means of an X-ray-sensitive camera or after the experiment from photographic films. Filters are designed to avoid artefacts such as the Gibbs effect. Filtering has been applied to the study of the propagation of surface acoustic waves in piezoelectric materials and ferromagnetic domains in Fe-Si crystals, illustrating the interest of Fourier filtering for a deep analysis of X-ray topographs. (orig.).
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...
Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Uncertainty Principles and Fourier Analysis
Indian Academy of Sciences (India)
analysis on the part of the reader. Those who are not fa- miliar with Fourier analysis are encouraged to look up Box. 1 along with [3]. (A) Heisenberg's inequality: Let us measure concentration in terms of standard deviation i.e. for a square integrable func-. 00 tion defined on 1R and normalized so that J If(x)12d,x = 1,. -00. 00.
An introduction to Fourier series and integrals
Seeley, Robert T
2006-01-01
This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Fourier techniques in X-ray timing
van der Klis, M.
1988-01-01
Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum
Improved Fourier-transform profilometry
International Nuclear Information System (INIS)
Mao Xianfu; Chen Wenjing; Su Xianyu
2007-01-01
An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object
Fourier-transform optical microsystems
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
Fourier Transform Methods. Chapter 4
Kaplan, Simon G.; Quijada, Manuel A.
2015-01-01
This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
Infrared propagator corrections for constant deceleration
Energy Technology Data Exchange (ETDEWEB)
Janssen, T M; Miao, S P; Prokopec, T [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, Postbus 80.195, 3508 TD Utrecht (Netherlands); Woodard, R P [Department of Physics, University of Florida Gainesville, FL 32611 (United States)], E-mail: T.M.Janssen@uu.nl, E-mail: S.Miao@uu.nl, E-mail: T.Prokopec@uu.nl, E-mail: woodard@phys.ufl.edu
2008-12-21
We derive the propagator for a massless, minimally coupled scalar on a D-dimensional, spatially flat, homogeneous and isotropic background with arbitrary constant deceleration parameter. Our construction uses the operator formalism by integrating the Fourier mode sum. We give special attention to infrared corrections from the nonzero lower limit associated with working on finite spatial sections. These corrections eliminate infrared divergences that would otherwise be incorrectly treated by dimensional regularization, resulting in off-coincidence divergences for those special values of the deceleration parameter at which the infrared divergence is logarithmic. As an application we compute the expectation value of the scalar stress-energy tensor.
Non-Fourier heat conduction and phase transition in laser ablation of polytetrafluoroethylene (PTFE)
Zhang, Yu; Zhang, Daixian; Wu, Jianjun; Li, Jian; He, Zhaofu
2017-11-01
The phase transition in heat conduction of polytetrafluoroethylene-like polymers was investigated and applied in many fields of science and engineering. Considering more details including internal absorption of laser radiation, reflectivity of material and non-Fourier effect etc., the combined heat conduction and phase transition in laser ablation of polytetrafluoroethylene were modeled and investigated numerically. The thermal and mechanic issues in laser ablation were illustrated and analyzed. Especially, the phenomenon of temperature discontinuity formed in the combined phase transition and non-Fourier heat conduction was discussed. Comparisons of target temperature profiles between Fourier and non-Fourier heat conduction in melting process were implemented. It was indicated that the effect of non-Fourier plays an important role in the temperature evolvement. The effect of laser fluence was proven to be significant and the thermal wave propagation was independent on the laser intensity for the non-Fourier heat conduction. Besides, the effect of absorption coefficients on temperature evolvements was studied. For different ranges of absorption coefficients, different temperature evolvements can be achieved. The above numerical simulation provided insight into physical processes of combined non-Fourier heat conduction and phase transition in laser ablation.
Fourier Spectroscopy: A Bayesian Way
Directory of Open Access Journals (Sweden)
Stefan Schmuck
2017-01-01
Full Text Available The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.
Salomons, E.; Polinder, H.; Lohman, W.; Zhou, H.; Borst, H.
2009-01-01
A new engineering model for sound propagation in cities is presented. The model is based on numerical and experimental studies of sound propagation between street canyons. Multiple reflections in the source canyon and the receiver canyon are taken into account in an efficient way, while weak
Modelling the gluon propagator
Energy Technology Data Exchange (ETDEWEB)
Leinweber, D.B.; Parrinello, C.; Skullerud, J.I.; Williams, A.G
1999-03-01
Scaling of the Landau gauge gluon propagator calculated at {beta} = 6.0 and at {beta} = 6.2 is demonstrated. A variety of functional forms for the gluon propagator calculated on a large (32{sup 3} x 64) lattice at {beta} = 6.0 are investigated.
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.
Dual Comb Fourier Transform Spectroscopy
Hänsch, T. W.; Picqué, N.
2010-06-01
The advent of laser frequency combs a decade ago has already revolutionized optical frequency metrology and precision spectroscopy. Extensions of laser combs from the THz region to the extreme ultraviolet and soft x-ray frequencies are now under exploration. Such laser combs have become enabling tools for a growing tree of applications, from optical atomic clocks to attosecond science. Recently, the millions of precisely controlled laser comb lines that can be produced with a train of ultrashort laser pulses have been harnessed for highly multiplexed molecular spectroscopy. Fourier multi-heterodyne spectroscopy, dual comb spectroscopy, or asynchronous optical sampling spectroscopy with frequency combs are emerging as powerful new spectroscopic tools. Even the first proof-of-principle experiments have demonstrated a very exciting potential for ultra-rapid and ultra-sensitive recording of complex molecular spectra. Compared to conventional Fourier transform spectroscopy, recording times could be shortened from seconds to microseconds, with intriguing prospects for spectroscopy of short lived transient species. Longer recording times allow high resolution spectroscopy of molecules with extreme precision, since the absolute frequency of each laser comb line can be known with the accuracy of an atomic clock. The spectral structure of sharp lines of a laser comb can be very useful even in the recording of broadband spectra without sharp features, as they are e.g. encountered for molecular gases or in the liquid phase. A second frequency comb of different line spacing permits the generation of a comb of radio frequency beat notes, which effectively map the optical spectrum into the radio frequency regime, so that it can be recorded with a single fast photodetector, followed by digital signal analysis. In the time domain, a pulse train of a mode-locked femtosecond laser excites some molecular medium at regular time intervals. A second pulse train of different repetition
Applications of Fourier transforms to generalized functions
Rahman, M
2011-01-01
This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...
Tunable fractional-order Fourier transformer
International Nuclear Information System (INIS)
Malyutin, A A
2006-01-01
A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)
Fourier transform n.m.r. spectroscopy
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
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Metasurface Enabled Wide-Angle Fourier Lens.
Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo
2018-04-19
Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Fourier's law: insight from a simple derivation.
Dubi, Y; Di Ventra, M
2009-04-01
The onset of Fourier's law in a one-dimensional quantum system is addressed via a simple model of weakly coupled quantum systems in contact with thermal baths at their edges. Using analytical arguments we show that the crossover from the ballistic (invalid Fourier's law) to diffusive (valid Fourier's law) regimes is characterized by a thermal length scale, which is directly related to the profile of the local temperature. In the same vein, dephasing is shown to give rise to classical Fourier's law, similarly to the onset of Ohm's law in mesoscopic conductors.
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
Light propagation in a magneto-optical hyperbolic biaxial crystal
Kuznetsov, Evgeniy V.; Merzlikin, Alexander M.
2017-12-01
The light propagation through a magneto-optical hyperbolic biaxial crystal is investigated. Magnetization of the structure results in splitting and reconnection of an isofrequency near the self-intersection point and thus it leads to the disappearance of conical refraction in a crystal. In its turn the isofrequency splitting leads to band gap opening and makes it possible to steer the beam. These effects allow to control the light propagation by means of an external magnetostatic field. The Poynting's vector distribution in the crystal is calculated by means of a Fourier transform in order to demonstrate the aforementioned effects.
Fourier analysis and synthesis tomography.
Energy Technology Data Exchange (ETDEWEB)
Wagner, Kelvin H. (University of Colorado at Boulder, Boulder, CO); Sinclair, Michael B.; Feldkuhn, Daniel (University of Colorado at Boulder, Boulder, CO)
2010-05-01
Most far-field optical imaging systems rely on a lens and spatially-resolved detection to probe distinct locations on the object. We describe and demonstrate a novel high-speed wide-field approach to imaging that instead measures the complex spatial Fourier transform of the object by detecting its spatially-integrated response to dynamic acousto-optically synthesized structured illumination. Tomographic filtered backprojection is applied to reconstruct the object in two or three dimensions. This technique decouples depth-of-field and working-distance from resolution, in contrast to conventional imaging, and can be used to image biological and synthetic structures in fluoresced or scattered light employing coherent or broadband illumination. We discuss the electronically programmable transfer function of the optical system and its implications for imaging dynamic processes. Finally, we present for the first time two-dimensional high-resolution image reconstructions demonstrating a three-orders-of-magnitude improvement in depth-of-field over conventional lens-based microscopy.
Fourier Spectroscopy: A Simple Analysis Technique
Oelfke, William C.
1975-01-01
Presents a simple method of analysis in which the student can integrate, point by point, any interferogram to obtain its Fourier transform. The manual technique requires no special equipment and is based on relationships that most undergraduate physics students can derive from the Fourier integral equations. (Author/MLH)
Teaching Fourier optics through ray matrices
International Nuclear Information System (INIS)
Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F
2005-01-01
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics
Fourier analysis of numerical algorithms for the Maxwell equations
Liu, Yen
1993-01-01
The Fourier method is used to analyze the dispersive, dissipative, and isotropy errors of various spatial and time discretizations applied to the Maxwell equations on multi-dimensional grids. Both Cartesian grids and non-Cartesian grids based on hexagons and tetradecahedra are studied and compared. The numerical errors are quantitatively determined in terms of phase speed, wave number, propagation direction, gridspacings, and CFL number. The study shows that centered schemes are more efficient than upwind schemes. The non-Cartesian grids yield superior isotropy and higher accuracy than the Cartesian ones. For the centered schemes, the staggered grids produce less errors than the unstaggered ones. A new unstaggered scheme which has all the best properties is introduced. The study also demonstrates that a proper choice of time discretization can reduce the overall numerical errors due to the spatial discretization.
Packed domain Rayleigh-Sommerfeld wavefield propagation for large targets.
Wuttig, Andreas; Kanka, Mario; Kreuzer, Hans Jürgen; Riesenberg, Rainer
2010-12-20
For applications in the domain of digital holographic microscopy, we present a fast algorithm to propagate scalar wave fields from a small source area to an extended, parallel target area of coarser sampling pitch, using the first Rayleigh-Sommerfeld diffraction formula. Our algorithm can take full advantage of the fast Fourier transform by decomposing the convolution kernel of the propagation into several convolution kernel patches. Using partial overlapping of the patches together with a soft blending function, the Fourier spectrum of these patches can be reduced to a low number of significant components, which can be stored in a compact sparse array structure. This allows for rapid evaluation of the partial convolution results by skipping over negligible components through the Fourier domain pointwise multiplication and direct mapping of the remaining multiplication results into a Fourier domain representation of the coarsly sampled target patch. The algorithm has been verified experimentally at a numerical aperture of 0.62, not showing any significant resolution limitations.
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Error propagation analysis for a sensor system
Energy Technology Data Exchange (ETDEWEB)
Yeater, M.L.; Hockenbury, R.W.; Hawkins, J.; Wilkinson, J.
1976-01-01
As part of a program to develop reliability methods for operational use with reactor sensors and protective systems, error propagation analyses are being made for each model. An example is a sensor system computer simulation model, in which the sensor system signature is convoluted with a reactor signature to show the effect of each in revealing or obscuring information contained in the other. The error propagation analysis models the system and signature uncertainties and sensitivities, whereas the simulation models the signatures and by extensive repetitions reveals the effect of errors in various reactor input or sensor response data. In the approach for the example presented, the errors accumulated by the signature (set of ''noise'' frequencies) are successively calculated as it is propagated stepwise through a system comprised of sensor and signal processing components. Additional modeling steps include a Fourier transform calculation to produce the usual power spectral density representation of the product signature, and some form of pattern recognition algorithm.
International Nuclear Information System (INIS)
Nalegaev, S S; Petrov, N V; Bespalov, V G
2014-01-01
A numerical reconstruction of spatial distributions of optical radiation propagating through a volume of nonlinear medium at input and output planes of the medium was demonstrated using a scheme of digital holography. A nonlinear Schrodinger equation with Fourier Split-Step method was used as a tool to propagate wavefront in the volume of the medium. Time dependence of the refractive index change was not taken into account.
Urrutxua, H.; Sanjurjo-Rivo, M.; Peláez, J.
2013-12-01
In year 2000 a house-made orbital propagator was developed by the SDGUPM (former Grupo de Dinámica de Tethers) based in a set of redundant variables including Euler parameters. This propagator was called DROMO. and it was mainly used in numerical simulations of electrodynamic tethers. It was presented for the first time in the international meeting V Jornadas de Trabajo en Mecánica Celeste, held in Albarracín, Spain, in 2002 (see reference 1). The special perturbation method associated with DROMO can be consulted in the paper.2 In year 1975, Andre Deprit in reference 3 proposes a propagation scheme very similar to the one in which DROMO is based, by using the ideal frame concept of Hansen. The different approaches used in references 3 and 2 gave rise to a small controversy. In this paper we carried out a different deduction of the DROMO propagator, underlining its close relation with the Hansen ideal frame concept, and also the similarities and the differences with the theory carried out by Deprit in 3. Simultaneously we introduce some improvements in the formulation that leads to a more synthetic propagator.
Scheibler, Robin; Hurley, Paul
2012-03-01
We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.
David, P
2013-01-01
Propagation of Waves focuses on the wave propagation around the earth, which is influenced by its curvature, surface irregularities, and by passage through atmospheric layers that may be refracting, absorbing, or ionized. This book begins by outlining the behavior of waves in the various media and at their interfaces, which simplifies the basic phenomena, such as absorption, refraction, reflection, and interference. Applications to the case of the terrestrial sphere are also discussed as a natural generalization. Following the deliberation on the diffraction of the "ground? wave around the ear
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.
X-ray interferometric Fourier holography
International Nuclear Information System (INIS)
Balyan, M.K.
2016-01-01
The X-ray interferometric Fourier holography is proposed and theoretically investigated. Fourier The X-ray interferometric Young fringes and object image reconstruction are investigated. It is shown that the interference pattern of two slits formed on the exit surface of the crystal-analyzer (the third plate of the interferometer) is the X-ray interferometric Young fringes. An expression for X-ray interferometric Young fringes period is obtained. The subsequent reconstruction of the slit image as an object is performed by means of Fourier transform of the intensity distribution on the hologram. Three methods of reconstruction of the amplitude transmission complex function of the object are presented: analytical - approximate method, method of iteration and step by step method. As an example the X-ray Fourier interferometric hologram recording and the complex amplitude transmission function reconstruction for a beryllium circular wire are considered
Mountain Wave Analysis Using Fourier Methods
National Research Council Canada - National Science Library
Roadcap, John R
2007-01-01
...) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms...
Mapped Fourier Methods for stiff problems in toroidal geometry
Guillard , Herve
2014-01-01
Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the compositio...
National Research Council Canada - National Science Library
Gray, William
1994-01-01
This paper discusses the question of tropical cyclone propagation or why the average tropical cyclone moves 1-2 m/s faster and usually 10-20 deg to the left of its surrounding (or 5-7 deg radius) deep layer (850-300 mb) steering current...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 5. Flood Wave Propagation-The Saint Venant Equations. P P Mujumdar. General Article Volume 6 Issue 5 May 2001 pp 66-73. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/05/0066-0073 ...
Sciacchitano, A.; Wieneke, Bernhard
2016-01-01
This paper discusses the propagation of the instantaneous uncertainty of PIV measurements to statistical and instantaneous quantities of interest derived from the velocity field. The expression of the uncertainty of vorticity, velocity divergence, mean value and Reynolds stresses is derived. It
Czech Academy of Sciences Publication Activity Database
Schejbal, V.; Bezoušek, P.; Čermák, D.; NĚMEC, Z.; Fišer, Ondřej; Hájek, M.
2006-01-01
Roč. 15, č. 1 (2006), s. 17-24 ISSN 1210-2512 R&D Projects: GA MPO(CZ) FT-TA2/030 Institutional research plan: CEZ:AV0Z30420517 Keywords : Ultra wide band * UWB antenna s * UWB propagation * multipath effects Subject RIV: JB - Sensors, Measurment, Regulation
Atmospheric and laser propagation
Eijk, A.M.J. van; Stein, K.
2017-01-01
This paper reviews three phenomena that affect the propagation of electro-optical radiation through the atmosphere: absorption and scattering, refraction and turbulence. The net effect on imaging or laser systems is a net reduction of the effective range, or a degradation of the information
Indian Academy of Sciences (India)
I available for forecasting the propagation of the flood wave. Introduction. Among all natural disasters, floods are the most frequently occurring phenomena that affect a large section of population all over the world, every year. Throughout the last century, flood- ing has been one of the most devastating disasters both in terms.
Fourier phasing with phase-uncertain mask
International Nuclear Information System (INIS)
Fannjiang, Albert; Liao, Wenjing
2013-01-01
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)
Gauge engineering and propagators
Directory of Open Access Journals (Sweden)
Maas Axel
2017-01-01
The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.
2013-09-30
ice terminates or regenerates along the propagation direction. (2) New capabilities for elastic and poro-elastic sediments • Range-dependent...standard Euler- Bernoulli bean theory can be applied in the x-z plane. The top right panel illustrates a side view of the subunit. A shearing force F...bottom panel is a table in which the second column has representative values for these three quantities, for the most common types of clay minerals in
Rayleigh-Sommerfield Diffraction vs Fresnel-Kirchhoff, Fourier Propagation and Poisson's Spot
National Research Council Canada - National Science Library
Lucke, Robert
2004-01-01
.... But when this approximation is not valid, FK can lead to unacceptable answers. Calculating the on-axis intensity of Poisson s spot provides a critical test, a test passed by RS and failed by FK. FK fails because (a) convergence of the integral depends on how it is evaluated and (b) when the convergence problem is xed, the predicted amplitude at points near the obscuring disk is not consistent with the assumed boundary conditions.
Fourier Series-Based Bidirectional Propagation Algorithm With Adaptive Spatial Resolution
Czech Academy of Sciences Publication Activity Database
Čtyroký, Jiří; Kwiecien, P.; Richter, I.
2010-01-01
Roč. 28, č. 20 (2010), s. 2969-2976 ISSN 0733-8724 R&D Projects: GA MŠk OC09061 Institutional research plan: CEZ:AV0Z20670512 Keywords : optical waveguide theory * modelling * integrated optics Subject RIV: BH - Optics , Masers, Lasers Impact factor: 2.255, year: 2010
Efficient Boundary Conditions for Bidirectional Propagation Algorithm Based on Fourier Series
Czech Academy of Sciences Publication Activity Database
Čtyroký, Jiří
2009-01-01
Roč. 27, č. 14 (2009), s. 2575-2582 ISSN 0733-8724 Institutional research plan: CEZ:AV0Z20670512 Keywords : integrated optics * modelling * optical waveguide theory Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 2.185, year: 2009
Dynamical Models for Computer Viruses Propagation
Directory of Open Access Journals (Sweden)
José R. C. Piqueira
2008-01-01
Full Text Available Nowadays, digital computer systems and networks are the main engineering tools, being used in planning, design, operation, and control of all sizes of building, transportation, machinery, business, and life maintaining devices. Consequently, computer viruses became one of the most important sources of uncertainty, contributing to decrease the reliability of vital activities. A lot of antivirus programs have been developed, but they are limited to detecting and removing infections, based on previous knowledge of the virus code. In spite of having good adaptation capability, these programs work just as vaccines against diseases and are not able to prevent new infections based on the network state. Here, a trial on modeling computer viruses propagation dynamics relates it to other notable events occurring in the network permitting to establish preventive policies in the network management. Data from three different viruses are collected in the Internet and two different identification techniques, autoregressive and Fourier analyses, are applied showing that it is possible to forecast the dynamics of a new virus propagation by using the data collected from other viruses that formerly infected the network.
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
Practical Fourier analysis for multigrid methods
Wienands, Roman
2004-01-01
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions.This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the detai...
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
On nonlinear Fourier transform: towards the nonlinear superposition
Saksida, Pavle
2017-01-01
In the paper we consider the nonlinear Fourier transform associated to the AKNSZS systems. In particular, we discuss the construction of the nonlinear Fourier modes of this transform by means of a perturbation scheme. The linearization of the AKNS-ZS nonlinear Fourier transform is the usual, linear Fourier transform and the linearization of a nonlinear Fourier mode of frequency d is the linear Fourier mode of the same frequency. We show that the first non-trivial term in the perturbation expression of any nonlinear Fourier mode is given by the dilogarithm function.
Implementation of quantum and classical discrete fractional Fourier transforms
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-01-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089
An optical Fourier transform coprocessor with direct phase determination.
Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D
2017-10-20
The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Fourier transforms and convolutions for the experimentalist
Jennison, RC
1961-01-01
Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t
A Fourier analysis approach for capillary polarimetry.
Markov, Dmitry A; Swinney, Kelly; Norville, Kristin; Lu, David; Bornhop, Darryl J
2002-03-01
A new method of fringe interrogation based on Fourier analysis was implemented and tested for a capillary polarimetry detector. It has significant advantages over the previously employed depth of modulation (DOM) approach, including speed and alignment insensitivity. The new and old methods were compared using a set of interference fringes typically used to facilitate nanoliter volume polarimetric determinations. Polarimetric response was calculated with both methods over the range from 0 degrees to 180 degrees. The results were found to be in good agreement with Malus Law and indicate that an fast Fourier transform (fft) could be used for real-time capillary scale polarimetry in a probe volume of 40 nL.
Interferogram analysis using Fourier transform techniques
Roddier, Claude; Roddier, Francois
1987-01-01
A method of interferogram analysis is described in which Fourier transform techniques are used to map the complex fringe visibility in several types of interferograms. Algorithms are developed for estimation of both the amplitude and the phase of the fringes (yielding the modulus and the phase of the holographically recorded object Fourier transform). The algorithms were applied to the reduction of interferometric seeing measurements (i.e., the estimation of the fringe amplitude only), and the reduction of interferometric tests (i.e., estimation of the fringe phase only). The method was used to analyze scatter-plate interferograms obtained at NOAO.
Wave propagation in elastic solids
Achenbach, Jan
1984-01-01
The propagation of mechanical disturbances in solids is of interest in many branches of the physical scienses and engineering. This book aims to present an account of the theory of wave propagation in elastic solids. The material is arranged to present an exposition of the basic concepts of mechanical wave propagation within a one-dimensional setting and a discussion of formal aspects of elastodynamic theory in three dimensions, followed by chapters expounding on typical wave propagation phenomena, such as radiation, reflection, refraction, propagation in waveguides, and diffraction. The treat
Stochastic model in microwave propagation
International Nuclear Information System (INIS)
Ranfagni, A.; Mugnai, D.
2011-01-01
Further experimental results of delay time in microwave propagation are reported in the presence of a lossy medium (wood). The measurements show that the presence of a lossy medium makes the propagation slightly superluminal. The results are interpreted on the basis of a stochastic (or path integral) model, showing how this model is able to describe each kind of physical system in which multi-path trajectories are present. -- Highlights: ► We present new experimental results on electromagnetic “anomalous” propagation. ► We apply a path integral theoretical model to wave propagation. ► Stochastic processes and multi-path trajectories in propagation are considered.
CMB in a box: Causal structure and the Fourier-Bessel expansion
International Nuclear Information System (INIS)
Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.
2010-01-01
This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.
Beam propagation in Cu +-Na + ion exchange channel waveguides
Energy Technology Data Exchange (ETDEWEB)
Villegas Vicencio, L. J.; Khomenko, A. V.; Salazar, D.; Marquez, H. [Centro de Investigacion Cientifica y de Educacion Superior de Ensenada, Baja California (Mexico); Porte, H. [Universite de Franche-Comte, UFR des Sciences et Techniques, Besancon, Cedex (France)
2001-06-01
We employ the fast Fourier transform beam propagation method to simulate the propagation of light in graded index channel waveguides, these have been obtained by solid state diffusion of copper ions in soda-lime glass substrates. Longitudinal propagation has been simulated, the input light beam has a gaussian profile. Two cases have been analyzed, in the first, the Gaussian beam is collinear center to center with respect to waveguide; in the second, a small lateral offset and angular tilt have been introduced. Modal beating and bending effects have been founded. We have proven the validity of our numerical results in detailed comparison with experimental data. [Spanish] Se ha empleado el metodo de propagacion de haces por la transformada rapida de Fourier para simular la propagacion de la luz en guias de onda de indice de gradiente. Estas han sido fabricadas por difusion de iones de cobre en estado solido en substratos de vidrios sodicos-calcicos. Se han simulado dos casos, el primero, el perfil de luz de entrada, que es gaussiano, es colineal centro a centro respecto al centro de la guia de ondas: el segundo, se ha dado un pequeno corrimiento lateral y una inclinacion angular. Como consecuencia de los casos anteriores se ha observado efectos de batimiento modal. Los resultados de la simulacion se han validado con resultados experimentales.
Temporal scaling in information propagation
Huang, Junming; Li, Chao; Wang, Wen-Qiang; Shen, Hua-Wei; Li, Guojie; Cheng, Xue-Qi
2014-06-01
For the study of information propagation, one fundamental problem is uncovering universal laws governing the dynamics of information propagation. This problem, from the microscopic perspective, is formulated as estimating the propagation probability that a piece of information propagates from one individual to another. Such a propagation probability generally depends on two major classes of factors: the intrinsic attractiveness of information and the interactions between individuals. Despite the fact that the temporal effect of attractiveness is widely studied, temporal laws underlying individual interactions remain unclear, causing inaccurate prediction of information propagation on evolving social networks. In this report, we empirically study the dynamics of information propagation, using the dataset from a population-scale social media website. We discover a temporal scaling in information propagation: the probability a message propagates between two individuals decays with the length of time latency since their latest interaction, obeying a power-law rule. Leveraging the scaling law, we further propose a temporal model to estimate future propagation probabilities between individuals, reducing the error rate of information propagation prediction from 6.7% to 2.6% and improving viral marketing with 9.7% incremental customers.
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.
Wave propagation scattering theory
Birman, M Sh
1993-01-01
The papers in this collection were written primarily by members of the St. Petersburg seminar in mathematical physics. The seminar, now run by O. A. Ladyzhenskaya, was initiated in 1947 by V. I. Smirnov, to whose memory this volume is dedicated. The papers in the collection are devoted mainly to wave propagation processes, scattering theory, integrability of nonlinear equations, and related problems of spectral theory of differential and integral operators. The book is of interest to mathematicians working in mathematical physics and differential equations, as well as to physicists studying va
Rockower, Edward B.
1985-01-01
A number of laser propagation codes have been assessed as to their suitability for modeling Army High Energy Laser (HEL) weapons used in an anti- sensor mode. We identify a number of areas in which systems analysis HEL codes are deficient. Most notably, available HEL scaling law codes model the laser aperture as circular, possibly with a fixed (e.g. 10%) obscuration. However, most HELs have rectangular apertures with up to 30% obscuration. We present a beam-quality/aperture shape scaling rela...
Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
Fourier Series The Mathematics of Periodic Phenomena
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 10. Fourier Series The Mathematics of Periodic Phenomena. S Thangavelu ... Author Affiliations. S Thangavelu1. Department of Mathematics and Statistics, University of New Mexico, Humanities Building 419, Albuquerque, NM 87131-1141, USA ...
An Uncertainty Principle for Quaternion Fourier Transform
BAHRI, Mawardi; HITZER, Eckhard S. M; HAYASHI, Akihisa; ASHINO, Ryuichi
2008-01-01
We review the quaternionic Fourier transform(QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT.This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty.
Fourier series models through transformation | Omekara | Global ...
African Journals Online (AJOL)
This study considers the application of Fourier series analysis (FSA) to seasonal time series data. The ultimate objective of the study is to construct an FSA model that can lead to reliable forecast. Specifically, the study evaluates data for the assumptions of time series analysis; applies the necessary transformation to the ...
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
Discrete Fourier analysis of multigrid algorithms
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2011-01-01
The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
A Fourier analysis of extremal events
DEFF Research Database (Denmark)
Zhao, Yuwei
is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...
The periodogram at the Fourier frequencies
Kokoszka, P; Mikosch, T
In the time series literature one can often find the claim that the periodogram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,
Spatially incoherent single channel digital Fourier holography.
Kelner, Roy; Rosen, Joseph
2012-09-01
We present a new method for recording digital Fourier holograms under incoherent illumination. A single exposure recorded by a digital camera is sufficient to record a real-valued hologram that encodes the complete three-dimensional properties of an object.
Fast Fourier Transform Spectral Analysis Program
Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.
1969-01-01
Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.
Fourier Multiplier Theorems Involving Type and Cotype
Rozendaal, J.; Veraar, M.C.
2017-01-01
In this paper we develop the theory of Fourier multiplier operators (Formula presented.), for Banach spaces X and Y, (Formula presented.) and (Formula presented.) an operator-valued symbol. The case (Formula presented.) has been studied extensively since the 1980s, but far less is known for
Fourier Analysis Of Vibrations Of Round Structures
Davis, Gary A.
1990-01-01
Fourier-series representation developed for analysis of vibrations in complicated, round structures like turbopump impellers. Method eliminates guesswork involved in characterization of shapes of vibrational modes. Easy way to characterize complicated modes, leading to determination of responsiveness of given mode to various forcing functions. Used in conjunction with finite-element numerical simulation of vibrational modes of structure.
Fourier Analysis and the Rhythm of Conversation.
Dabbs, James M., Jr.
Fourier analysis, a common technique in engineering, breaks down a complex wave form into its simple sine wave components. Communication researchers have recently suggested that this technique may provide an index of the rhythm of conversation, since vocalizing and pausing produce a complex wave form pattern of alternation between two speakers. To…
Fourier phase demodulation of interferometric fiber sensor
Fu, Xin; Lu, Ping; Liu, Deming; Zhang, Jiangshan
2017-10-01
A novel demodulation method for interferometric fiber sensor is proposed in this paper. The physical parameters to be measured by the sensor is obtained by calculating the phase variation of the interference components. The phase variation is computed with the assist of the fast Fourier analysis. For fiber interferometers, most of the energy is contained in the few spatial frequencies corresponding to the components that produce the interference. Therefore, the information of the interference fringe can be presented by the Fourier results at those intrinsic frequencies. Based on this assumption, we proposed a novel method to interrogate the fiber interferometer by calculating the Fourier phase at the spatial frequency. Theoretical derivation proves that the Fourier phase variation is equal to the phase change of the interferometer. Simulation results demonstrate the ability of noise resistance of the proposed method since the information of all wavelength sampling points are adopted for the demodulation process. A Sagnac interferometer based on a section of polarization-maintaining photonic crystal fiber is utilized to verify the feasibility of the phase demodulation technique by lateral pressure sensing. Experimental results of -0.069rad/kPa is acquired.
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Schlichtkrull, H.
1994-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Carmona, J.; Delorme, P.
1997-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.
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.
An analysis of rumor propagation based on propagation force
Zhao, Zhen-jun; Liu, Yong-mei; Wang, Ke-xi
2016-02-01
A propagation force is introduced into the analysis of rumor propagation to address uncertainty in the process. The propagation force is portrayed as a fuzzy variable, and a category of new parameters with fuzzy variables is defined. The classic susceptible, infected, recovered (SIR) model is modified using these parameters, a fuzzy reproductive number is introduced into the modified model, and the rationality of the fuzzy reproductive number is illuminated through calculation and comparison. Rumor control strategies are also discussed.
Zhou, Feng-xi
2016-02-01
The method of the reverberation-ray matrix has been developed and successfully applied to analyse the wave propagation in a multibranched framed structure or in a layered medium. However, the method is confined to the case of mechanical loads applied at the medium until now. This paper aims to extend the formulation of the reverberation-ray matrix to cases of thermal propagation and diffusion. The thermal response in functionally graded materials (FGM) with the non-Fourier heat conduction model is analysed. In the present work, it is assumed that the material properties of an FG plate vary only in the thickness direction by following the power law function. The effect of non-Fourier and material inhomogeneity in the plate subjected to a periodic thermal disturbance is investigated. The present approach is validated by comparing it with the solutions obtained by other methods.
Thermal parameter identification for non-Fourier heat transfer from molecular dynamics
Singh, Amit; Tadmor, Ellad B.
2015-10-01
Fourier's law leads to a diffusive model of heat transfer in which a thermal signal propagates infinitely fast and the only material parameter is the thermal conductivity. In micro- and nano-scale systems, non-Fourier effects involving coupled diffusion and wavelike propagation of heat can become important. An extension of Fourier's law to account for such effects leads to a Jeffreys-type model for heat transfer with two relaxation times. We propose a new Thermal Parameter Identification (TPI) method for obtaining the Jeffreys-type thermal parameters from molecular dynamics simulations. The TPI method makes use of a nonlinear regression-based approach for obtaining the coefficients in analytical expressions for cosine and sine-weighted averages of temperature and heat flux over the length of the system. The method is applied to argon nanobeams over a range of temperature and system sizes. The results for thermal conductivity are found to be in good agreement with standard Green-Kubo and direct method calculations. The TPI method is more efficient for systems with high diffusivity and has the advantage, that unlike the direct method, it is free from the influence of thermostats. In addition, the method provides the thermal relaxation times for argon. Using the determined parameters, the Jeffreys-type model is able to reproduce the molecular dynamics results for a short-duration heat pulse where wavelike propagation of heat is observed thereby confirming the existence of second sound in argon. An implementation of the TPI method in MATLAB is available as part of the online supplementary material.
(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
C. T. Samlan; Dinesh N. Naik; Nirmal K. Viswanathan
2016-01-01
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally va...
Spatial variation of AIA coronal Fourier power spectra
Ireland, J.; Mcateer, R. T. J.
2015-12-01
We describe a study of the spatial distribution of the properties of the Fourier power spectrum of time-series of AIA 171Å and 193Å data. The area studied includes examples of physically different components of the corona, such as coronal moss, a sunspot, quiet Sun and fan loop footpoints. We show that a large fraction of the power spectra are well modeled by a power spectrum that behaves like a power law f-n (n>0)at lower frequencies f, dropping to a constant value at higher frequencies. We also show that there are areas where the power spectra are better described by the above power spectrum model, plus a narrow band oscillatory feature, centered in the 3-5 minute oscillation range. These narrow-band spectral features are thought to be due to the propagation of oscillations from lower down in solar atmosphere to hotter. This allows us to produce maps of large areas of the corona showing where the propagation from one waveband to another does and does not occur. This is an important step in understanding wave propagation in different layers in the corona. We also show the 171Å and 193Å power spectrum power law indices are correlated, with 171Å power law indices in the range n = 1.8 to 2.8, and 193Å power law indices n = 2 to 3.5 approximately. Maps of the power law index show that different ranges of values of the power law indices occur in spatially contiguous parts of the corona, indicating that local spatial structure may play a role in defining the power law index value. Taken with our previous result from Ireland et al. (2015) that physically different parts of the corona have different mean values of the power law index, this new result strongly suggests that the same mechanism producing the observed power law power spectrum is operating everywhere across the corona. We discuss the nanoflare hypothesis as a possible explanation of these observations.
Propagation into an unstable state
International Nuclear Information System (INIS)
Dee, G.
1985-01-01
We describe propagating front solutions of the equations of motion of pattern-forming systems. We make a number of conjectures concerning the properties of such fronts in connection with pattern selection in these systems. We describe a calculation which can be used to calculate the velocity and state selected by certain types of propagating fronts. We investigate the propagating front solutions of the amplitude equation which provides a valid dynamical description of many pattern-forming systems near onset
Broadband unidirectional ultrasound propagation
Sinha, Dipen N.; Pantea, Cristian
2017-12-12
A passive, linear arrangement of a sonic crystal-based apparatus and method including a 1D sonic crystal, a nonlinear medium, and an acoustic low-pass filter, for permitting unidirectional broadband ultrasound propagation as a collimated beam for underwater, air or other fluid communication, are described. The signal to be transmitted is first used to modulate a high-frequency ultrasonic carrier wave which is directed into the sonic crystal side of the apparatus. The apparatus processes the modulated signal, whereby the original low-frequency signal exits the apparatus as a collimated beam on the side of the apparatus opposite the sonic crystal. The sonic crystal provides a bandpass acoustic filter through which the modulated high-frequency ultrasonic signal passes, and the nonlinear medium demodulates the modulated signal and recovers the low-frequency sound beam. The low-pass filter removes remaining high-frequency components, and contributes to the unidirectional property of the apparatus.
Precursors in Front Propagation
International Nuclear Information System (INIS)
Kessler, D.A
1998-01-01
We investigate the dynamical construction of the leading edge of propagating fronts. Whereas the steady-state front is typically an exponential, far ahead of the front, the front falls off much faster, in a fashion determined by the Green's function of tile problem. We show that there is a universal transition Tom the steady-state exponential front to a Gaussian falloff. The transition region is of width t 1/2 , and moves out ahead of the front at a constant velocity greater than the steady-state front speed. This Gaussian front then is in general modified even further ahead of the front to match onto the expected Green's function behavior. We demonstrate this in the case of the Ginzburg-Landau and Korteweg-De Vries equations. We also discuss the relevance of this mechanism for velocity selection in the Fisher equation
Curvilinear crack layer propagation
Chudnovsky, Alexander; Chaoui, Kamel; Moet, Abdelsamie
1987-01-01
An account is given of an experiment designed to allow observation of the effect of damage orientation on the direction of crack growth in the case of crack layer propagation, using polystyrene as the model material. The direction of crack advance under a given loading condition is noted to be determined by a competition between the tendency of the crack to maintain its current direction and the tendency to follow the orientation of the crazes at its tip. The orientation of the crazes is, on the other hand, determined by the stress field due to the interaction of the crack, the crazes, and the hole. The changes in craze rotation relative to the crack define the active zone rotation.
Atomistics of crack propagation
International Nuclear Information System (INIS)
Sieradzki, K.; Dienes, G.J.; Paskin, A.; Massoumzadeh, B.
1988-01-01
The molecular dynamic technique is used to investigate static and dynamic aspects of crack extension. The material chosen for this study was the 2D triangular solid with atoms interacting via the Johnson potential. The 2D Johnson solid was chosen for this study since a sharp crack in this material remains stable against dislocation emission up to the critical Griffith load. This behavior allows for a meaningful comparison between the simulation results and continuum energy theorems for crack extension by appropriately defining an effective modulus which accounts for sample size effects and the non-linear elastic behavior of the Johnson solid. Simulation results are presented for the stress fields of moving cracks and these dynamic results are discussed in terms of the dynamic crack propagation theories, of Mott, Eshelby, and Freund
Resonant-state expansion of light propagation in nonuniform waveguides
Lobanov, S. V.; Zoriniants, G.; Langbein, W.; Muljarov, E. A.
2017-05-01
A rigorous approach for precise and efficient calculation of light propagation along nonuniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a nonuniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of nonuniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.
Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics
Wu, Yinghua; Herman, Michael F.; Batista, Victor S.
2005-03-01
A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuit/split-operator Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MP/SOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.
Fourier analysis: from cloaking to imaging
International Nuclear Information System (INIS)
Wu, Kedi; Ping Wang, Guo; Cheng, Qiluan
2016-01-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers. (review)
Fourier analysis: from cloaking to imaging
Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping
2016-04-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.
Fourier Transform Fabry-Perot Interferometer
Snell, Hilary E.; Hays, Paul B.
1992-01-01
We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.
The PROSAIC Laplace and Fourier Transform
International Nuclear Information System (INIS)
Smith, G.A.
1994-01-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting
Fourier transform of momentum distribution in vanadium
International Nuclear Information System (INIS)
Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.
1985-01-01
Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)
Correcting sample drift using Fourier harmonics.
Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L
2018-04-21
During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.
Complete way to fractionalize Fourier transform
Yeung, Daniel S.; Ran, Qiwen; Tsang, Eric C. C.; Teo, Kok Lay
2004-01-01
We propose a complete way to fractionalize Fourier transform. This fractionalization can perfectly extend the fractional Fourier transform (FRFT) defined in [C.C. Shih, Opt. Commun. 118 (1995) 495] to the original one in [V. Namias, J. Inst. Math. Appl. 25 (1980) 241]. The new FRFT proposed in this paper can have any integer M(⩾3)-periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform, and it will be reduced to the FRFT in [Namias, loc. cit.; Shih, loc. cit.; S. Liu, J. Jiang, Y. Zhang, J. Zhang, J. Phys. A: Math. Gen. 30 (1997) 973] at the three limits with M=+∞, M=4, M=4 k ( k is a natural number), respectively.
Laser Field Imaging Through Fourier Transform Heterodyne
Energy Technology Data Exchange (ETDEWEB)
Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.
1999-04-05
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.
A Fourier analysis of extreme events
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
Fourier Transform 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....
Study of Fourier descriptors statistical features
Darwish, Ahmed M.; Mohamed, Emad-Eldin H.
1993-12-01
In this paper we present a new approach to reduce the computations involved in recognition applications. Fourier descriptors are treated as a occurrence of a complex random variable. Statistical function measures are then used to characterize the behavior of the complex variable. A study of pattern regeneration based on these statistical features was carried out. Some of these statistical measures were found to comprehend most of the object global features. Thus, they could be used for classification and recognition purposes.
Fourier analysis of the SOR iteration
Leveque, R. J.; Trefethen, L. N.
1986-01-01
The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. It is shown that for the standard model problem of Poisson's equation on a rectangle, the optimal omega and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives insight into the relation between convergence rates of several variants.
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-01-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Sets of Fourier coefficients using numerical quadrature
International Nuclear Information System (INIS)
Lyness, J. N.
2001-01-01
One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r)=(line i ntegral)(sub 0)(sup 1) f(x)e(sup -2(pi)irx)dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x)= h(sub p-1)(x)+ g(sub p)(x), where h(sub -1)(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g(sub p)(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h(sub p-1)(x) and numerical quadrature to approximately those of g(sub p)(x)
Simple Numerical Schemes for the Korteweg-deVries Equation
International Nuclear Information System (INIS)
McKinstrie, C. J.; Kozlov, M.V.
2000-01-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves
Energy Technology Data Exchange (ETDEWEB)
Luquet, David; Marchiano, Régis; Coulouvrat, François, E-mail: francois.coulouvrat@upmc.fr [Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005, Paris (France)
2015-10-28
Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D
Luquet, David; Marchiano, Régis; Coulouvrat, François
2015-10-01
Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D
International Nuclear Information System (INIS)
Luquet, David; Marchiano, Régis; Coulouvrat, François
2015-01-01
Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D
The derivative-free Fourier shell identity for photoacoustics.
Baddour, Natalie
2016-01-01
In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.
Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
Zhang, Zhihua
2014-01-01
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842
Fourier spectral simulations for wake fields in conducting cavities
International Nuclear Information System (INIS)
Min, M.; Chin, Y.-H.; Fischer, P.F.; Chae, Y.-Chul; Kim, K.-J.
2007-01-01
We investigate Fourier spectral time-domain simulations applied to wake field calculations in two-dimensional cylindrical structures. The scheme involves second-order explicit leap-frogging in time and Fourier spectral approximation in space, which is obtained from simply replacing the spatial differentiation operator of the YEE scheme by the Fourier differentiation operator on nonstaggered grids. This is a first step toward investigating high-order computational techniques with the Fourier spectral method, which is relatively simple to implement.
A Note on Fourier and the Greenhouse Effect
Postma, Joseph E.
2015-01-01
Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...
Propagation of Ion Acoustic Perturbations
DEFF Research Database (Denmark)
Pécseli, Hans
1975-01-01
Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered.......Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered....
Some Applications of Fourier's Great Discovery for Beginners
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…
Propagation Engineering in Wireless Communications
Ghasemi, Abdollah; Ghasemi, Farshid
2012-01-01
Wireless communications has seen explosive growth in recent decades, in a realm that is both broad and rapidly expanding to include satellite services, navigational aids, remote sensing, telemetering, audio and video broadcasting, high-speed data communications, mobile radio systems and much more. Propagation Engineering in Wireless Communications deals with the basic principles of radiowaves propagation for frequency bands used in radio-communications, offering descriptions of new achievements and newly developed propagation models. The book bridges the gap between theoretical calculations and approaches, and applied procedures needed for advanced radio links design. The primary objective of this two-volume set is to demonstrate the fundamentals, and to introduce propagation phenomena and mechanisms that engineers are likely to encounter in the design and evaluation of radio links of a given type and operating frequency. Volume one covers basic principles, along with tropospheric and ionospheric propagation,...
Dressing the nucleon propagator
International Nuclear Information System (INIS)
Fishman, S.; Gersten, A.
1976-01-01
The nucleon propagator in the ''nested bubbles'' approximation is analyzed. The approximation is built from the minimal set of diagrams which is needed to maintain the unitarity condition under two-pion production threshold in the two-nucleon Bethe--Salpeter equation. Recursive formulas for subsets of ''nested bubbles'' diagrams calculated in the framework of the pseudoscalar interaction are obtained by the use of dispersion relations. We prove that the sum of all the ''nested bubbles'' diverges. Moreover, the successive iterations are plagued with ghost poles. We prove that the first approximation--which is the so-called chain approximation--has ghost poles for any nonvanishing coupling constant. In an earlier paper we have shown that ghost poles lead to ghost cuts. These cuts are present in the ''nested bubbles.'' Ghost elimination procedures are discussed. Modifications of the ''nested bubbles'' approximation are introduced in order to obtain convergence and in order to eliminate the ghost poles and ghost cuts. In a similar way as in the Lee model, cutoff functions are introduced in order to eliminate the ghost poles. The necessary and sufficient conditions for the absence of ghost poles are formulated and analyzed. The spectral functions of the modified ''nested bubbles'' are analyzed and computed. Finally, we present a theorem, similar in its form to Levinson's theorem in scattering theory, which enables one to compute in a simple way the number of ghost poles
Transionospheric propagation predictions
Klobucher, J. A.; Basu, S.; Basu, S.; Bernhardt, P. A.; Davies, K.; Donatelli, D. E.; Fremouw, E. J.; Goodman, J. M.; Hartmann, G. K.; Leitinger, R.
1979-01-01
The current status and future prospects of the capability to make transionospheric propagation predictions are addressed, highlighting the effects of the ionized media, which dominate for frequencies below 1 to 3 GHz, depending upon the state of the ionosphere and the elevation angle through the Earth-space path. The primary concerns are the predictions of time delay of signal modulation (group path delay) and of radio wave scintillation. Progress in these areas is strongly tied to knowledge of variable structures in the ionosphere ranging from the large scale (thousands of kilometers in horizontal extent) to the fine scale (kilometer size). Ionospheric variability and the relative importance of various mechanisms responsible for the time histories observed in total electron content (TEC), proportional to signal group delay, and in irregularity formation are discussed in terms of capability to make both short and long term predictions. The data base upon which predictions are made is examined for its adequacy, and the prospects for prediction improvements by more theoretical studies as well as by increasing the available statistical data base are examined.
Alternating multivariate trigonometric functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2008-01-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel
Validation of Fourier analysis of videokeratographic data.
Sideroudi, Haris; Labiris, Georgios; Ditzel, Fienke; Tsaragli, Efi; Georgatzoglou, Kimonas; Siganos, Haralampos; Kozobolis, Vassilios
2017-06-15
The aim was to assess the repeatability of Fourier transfom analysis of videokeratographic data using Pentacam in normal (CG), keratoconic (KC) and post-CXL (CXL) corneas. This was a prospective, clinic-based, observational study. One randomly selected eye from all study participants was included in the analysis: 62 normal eyes (CG group), 33 keratoconus eyes (KC group), while 34 eyes, which had already received CXL treatment, formed the CXL group. Fourier analysis of keratometric data were obtained using Pentacam, by two different operators within each of two sessions. Precision, repeatability and Intraclass Correlation Coefficient (ICC), were calculated for evaluating intrassesion and intersession repeatability for the following parameters: Spherical Component (SphRmin, SphEcc), Maximum Decentration (Max Dec), Regular Astigmatism, and Irregularitiy (Irr). Bland-Altman analysis was used for assessing interobserver repeatability. All parameters were presented to be repeatable, reliable and reproductible in all groups. Best intrasession and intersession repeatability and reliability were detected for parameters SphRmin, SphEcc and Max Dec parameters for both operators using ICC (intrasession: ICC > 98%, intersession: ICC > 94.7%) and within subject standard deviation. Best precision and lowest range of agreement was found for the SphRmin parameter (CG: 0.05, KC: 0.16, and CXL: 0.2) in all groups, while the lowest repeatability, reliability and reproducibility was detected for the Irr parameter. The Pentacam system provides accurate measurements of Fourier tranform keratometric data. A single Pentacam scan will be sufficient for most clinical applications.
Bruzzo, Ugo; Maciocia, Antony
2017-12-01
This special issue celebrates the 34 years since the discovery of the Fourier-Mukai Transform by Shigeru Mukai. It mostly contains papers presented at the conference held in the Mathematics Research Centre of the University of Warwick, 15th to 19th June 2015 as part of a year long Warwick symposium on Derived categories and applications. The conference was also the annual conference of the Vector Bundles on Algebraic Curves series led by Peter Newstead. The symposium was principally supported by the Engineering and Physical Sciences Research Council of the UK and there was further funding from the London Mathematical Society and the Foundation Compositio.
Fourier transform infrared spectroscopy of peptides.
Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell
2014-01-01
Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data.
Doppler-free Fourier transform spectroscopy.
Meek, Samuel A; Hipke, Arthur; Guelachvili, Guy; Hänsch, Theodor W; Picqué, Nathalie
2018-01-01
Sub-Doppler broadband multi-heterodyne spectroscopy is proposed and experimentally demonstrated. Using two laser frequency combs of slightly different repetition frequencies, we have recorded Doppler-free two-photon dual-comb spectra of atomic rubidium resonances of a width of 6 MHz, while simultaneously interrogating a spectral span of 10 THz. The atomic transitions are uniquely identified via the intensity modulation of the observed fluorescence radiation. To the best of our knowledge, these results represent the first demonstration of Doppler-free Fourier transform spectroscopy and extend the range of applications of broadband spectroscopy towards precision nonlinear spectroscopy.
Generalized Fourier transforms Fk,a
DEFF Research Database (Denmark)
Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent
2009-01-01
We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....
Fourier transforms in the complex domain
Wiener, N
1934-01-01
With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of MÃ¼nz and SzÃ¡sz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,
Analysis method for Fourier transform spectroscopy
Park, J. H.
1983-01-01
A fast Fourier transform technique is given for the simulation of those distortion effects in the instrument line shape of the interferometric spectrum that are due to errors in the measured interferogram. The technique is applied to analyses of atmospheric absorption spectra and laboratory spectra. It is shown that the nonlinear least squares method can retrieve the correct information from the distorted spectrum. Analyses of HF absorption spectra obtained in a laboratory and solar CO absorption spectra gathered by a balloon-borne interferometer indicate that the retrieved amount of absorbing gas is less than the correct value in most cases, if the interferogram distortion effects are not included in the analysis.
Analog fourier transform channelizer and OFDM receiver
2007-01-01
An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...
Energy Technology Data Exchange (ETDEWEB)
NA
2002-03-04
The purpose of this Analysis and Model Report (AMR) supporting the Site Recommendation/License Application (SR/LA) for the Yucca Mountain Project is the development of elementary analyses of the interactions of a hypothetical dike with a repository drift (i.e., tunnel) and with the drift contents at the potential Yucca Mountain repository. This effort is intended to support the analysis of disruptive events for Total System Performance Assessment (TSPA). This AMR supports the Process Model Report (PMR) on disruptive events (CRWMS M&O 2000a). This purpose is documented in the development plan (DP) ''Coordinate Modeling of Dike Propagation Near Drifts Consequences for TSPA-SR/LA'' (CRWMS M&O 2000b). Evaluation of that Development Plan and the work to be conducted to prepare Interim Change Notice (ICN) 1 of this report, which now includes the design option of ''Open'' drifts, indicated that no revision to that DP was needed. These analyses are intended to provide reasonable bounds for a number of expected effects: (1) Temperature changes to the waste package from exposure to magma; (2) The gas flow available to degrade waste containers during the intrusion; (3) Movement of the waste package as it is displaced by the gas, pyroclasts and magma from the intruding dike (the number of packages damaged); (4) Movement of the backfill (Backfill is treated here as a design option); (5) The nature of the mechanics of the dike/drift interaction. These analyses serve two objectives: to provide preliminary analyses needed to support evaluation of the consequences of an intrusive event and to provide a basis for addressing some of the concerns of the Nuclear Regulatory Commission (NRC) expressed in the Igneous Activity Issue Resolution Status Report.
International Nuclear Information System (INIS)
2002-01-01
The purpose of this Analysis and Model Report (AMR) supporting the Site Recommendation/License Application (SR/LA) for the Yucca Mountain Project is the development of elementary analyses of the interactions of a hypothetical dike with a repository drift (i.e., tunnel) and with the drift contents at the potential Yucca Mountain repository. This effort is intended to support the analysis of disruptive events for Total System Performance Assessment (TSPA). This AMR supports the Process Model Report (PMR) on disruptive events (CRWMS M and O 2000a). This purpose is documented in the development plan (DP) ''Coordinate Modeling of Dike Propagation Near Drifts Consequences for TSPA-SR/LA'' (CRWMS M and O 2000b). Evaluation of that Development Plan and the work to be conducted to prepare Interim Change Notice (ICN) 1 of this report, which now includes the design option of ''Open'' drifts, indicated that no revision to that DP was needed. These analyses are intended to provide reasonable bounds for a number of expected effects: (1) Temperature changes to the waste package from exposure to magma; (2) The gas flow available to degrade waste containers during the intrusion; (3) Movement of the waste package as it is displaced by the gas, pyroclasts and magma from the intruding dike (the number of packages damaged); (4) Movement of the backfill (Backfill is treated here as a design option); (5) The nature of the mechanics of the dike/drift interaction. These analyses serve two objectives: to provide preliminary analyses needed to support evaluation of the consequences of an intrusive event and to provide a basis for addressing some of the concerns of the Nuclear Regulatory Commission (NRC) expressed in the Igneous Activity Issue Resolution Status Report
Laser beam propagation generation and propagation of customized light
Forbes, Andrew
2014-01-01
""The text is easy to read and is accompanied by beautiful illustrations. It is an excellent book for anyone working in laser beam propagation and an asset for any library.""-Optics & Photonics News, July 2014
CSIR Research Space (South Africa)
Litvin, IA
2007-01-01
Full Text Available The authors investigate the phase conjugating element of a two element Fourier transform beam shaping scheme and the impact this element has on the resulting propagation. It is shown that there are stricter limitations placed on the system when...
The Fourier transform of tubular densities
Prior, C B
2012-05-18
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.
Digital Fourier microscopy for soft matter dynamics
International Nuclear Information System (INIS)
Giavazzi, Fabio; Cerbino, Roberto
2014-01-01
Soft matter is studied with a large portfolio of methods. Light scattering and video microscopy are the most employed at optical wavelengths. Light scattering provides ensemble-averaged information on soft matter in the reciprocal space. The wave-vectors probed correspond to length scales ranging from a few nanometers to fractions of millimetre. Microscopy probes the sample directly in the real space, by offering a unique access to the local properties. However, optical resolution issues limit the access to length scales smaller than approximately 200 nm. We describe recent work that bridges the gap between scattering and microscopy. Several apparently unrelated techniques are found to share a simple basic idea: the correlation properties of the sample can be characterized in the reciprocal space via spatial Fourier analysis of images collected in the real space. We describe the main features of such digital Fourier microscopy (DFM), by providing examples of several possible experimental implementations of it, some of which not yet realized in practice. We also provide an overview of experimental results obtained with DFM for the study of the dynamics of soft materials. Finally, we outline possible future developments of DFM that would ease its adoption as a standard laboratory method. (topical review)
Algorithm for the propagation of electromagnetic fields through etalons and crystals.
Zhang, Site; Hellmann, Christian; Wyrowski, Frank
2017-05-20
We investigate the propagation of general electromagnetic fields through optical layer structures made of either isotropic or anisotropic media, by using the spectrum-of-plane-waves analysis together with the S-matrix method. We also develop an algorithm based on the fast Fourier transform technique, with a numerically efficient sampling rule. By using this algorithm in combination with other system modeling techniques, we present a few simulation examples, such as field propagation through an isotropic Fabry-Perot etalon, as well as uniaxial crystal slabs with arbitrary orientation and optic axis direction.
Propagation engineering in wireless communications
Ghasemi, Abdollah; Ghasemi, Farshid
2016-01-01
This book covers the basic principles for understanding radio wave propagation for common frequency bands used in radio-communications. This includes achievements and developments in propagation models for wireless communication. This book is intended to bridge the gap between the theoretical calculations and approaches to the applied procedures needed for radio links design in a proper manner. The authors emphasize propagation engineering by giving fundamental information and explain the use of basic principles together with technical achievements. This new edition includes additional information on radio wave propagation in guided media and technical issues for fiber optics cable networks with several examples and problems. This book also includes a solution manual - with 90 solved examples distributed throughout the chapters - and 158 problems including practical values and assumptions.
Wave propagation in electromagnetic media
Davis, Julian L
1990-01-01
This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessi...
Modeling Seismic Wave Propagation Using Time-Dependent Cauchy-Navier Splines
Kammann, P.
2005-12-01
Our intention is the modeling of seismic wave propagation from displacement measurements by seismographs at the Earth's surface. The elastic behaviour of the Earth is usually described by the Cauchy-Navier equation. A system of fundamental solutions for the Fourier transformed Cauchy-Navier equation are the Hansen vectors L, M and N. We apply an inverse Fourier transform to obtain an orthonormal function system depending on time and space. By means of this system we construct certain splines, which are then used for interpolating the given data. Compared to polynomial interpolation, splines have the advantage that they minimize some curvature measure and are, therefore, smoother. First, we test this method on a synthetic wave function. Afterwards, we apply it to realistic earthquake data. (P. Kammann, Modelling Seismic Wave Propagation Using Time-Dependent Cauchy-Navier Splines, Diploma Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, 2005)
Propagation of dynamic measurement uncertainty
Hessling, J. P.
2011-10-01
The time-dependent measurement uncertainty has been evaluated in a number of recent publications, starting from a known uncertain dynamic model. This could be defined as the 'downward' propagation of uncertainty from the model to the targeted measurement. The propagation of uncertainty 'upward' from the calibration experiment to a dynamic model traditionally belongs to system identification. The use of different representations (time, frequency, etc) is ubiquitous in dynamic measurement analyses. An expression of uncertainty in dynamic measurements is formulated for the first time in this paper independent of representation, joining upward as well as downward propagation. For applications in metrology, the high quality of the characterization may be prohibitive for any reasonably large and robust model to pass the whiteness test. This test is therefore relaxed by not directly requiring small systematic model errors in comparison to the randomness of the characterization. Instead, the systematic error of the dynamic model is propagated to the uncertainty of the measurand, analogously but differently to how stochastic contributions are propagated. The pass criterion of the model is thereby transferred from the identification to acceptance of the total accumulated uncertainty of the measurand. This increases the relevance of the test of the model as it relates to its final use rather than the quality of the calibration. The propagation of uncertainty hence includes the propagation of systematic model errors. For illustration, the 'upward' propagation of uncertainty is applied to determine if an appliance box is damaged in an earthquake experiment. In this case, relaxation of the whiteness test was required to reach a conclusive result.
Propagation of dynamic measurement uncertainty
International Nuclear Information System (INIS)
Hessling, J P
2011-01-01
The time-dependent measurement uncertainty has been evaluated in a number of recent publications, starting from a known uncertain dynamic model. This could be defined as the 'downward' propagation of uncertainty from the model to the targeted measurement. The propagation of uncertainty 'upward' from the calibration experiment to a dynamic model traditionally belongs to system identification. The use of different representations (time, frequency, etc) is ubiquitous in dynamic measurement analyses. An expression of uncertainty in dynamic measurements is formulated for the first time in this paper independent of representation, joining upward as well as downward propagation. For applications in metrology, the high quality of the characterization may be prohibitive for any reasonably large and robust model to pass the whiteness test. This test is therefore relaxed by not directly requiring small systematic model errors in comparison to the randomness of the characterization. Instead, the systematic error of the dynamic model is propagated to the uncertainty of the measurand, analogously but differently to how stochastic contributions are propagated. The pass criterion of the model is thereby transferred from the identification to acceptance of the total accumulated uncertainty of the measurand. This increases the relevance of the test of the model as it relates to its final use rather than the quality of the calibration. The propagation of uncertainty hence includes the propagation of systematic model errors. For illustration, the 'upward' propagation of uncertainty is applied to determine if an appliance box is damaged in an earthquake experiment. In this case, relaxation of the whiteness test was required to reach a conclusive result
Pravda-Starov, Karel
2017-01-01
We study evolution equations associated to time-dependent dissipative non-selfadjoint quadratic operators. We prove that the solution operators to these non-autonomous evolution equations are given by Fourier integral operators whose kernels are Gaussian tempered distributions associated to non-negative complex symplectic linear transformations, and we derive a generalized Mehler formula for their Weyl symbols. Some applications to the study of the propagation of Gabor singularities (characte...
Davis, Jeffrey A.; Cottrell, Don M.; Berg, Cassidy A.; Freeman, Christopher Li; Carmona, Adriana; Debenham, William; Moreno, Ignacio
2015-09-01
In this paper the fast Fresnel diffraction algorithm is reviewed and applied to some novel applications. The algorithm (also named the convolution or angular spectrum method) is a very powerful numerical technique that has been employed in the calculation of diffraction patterns. It utilizes two Fourier transform operations, thus becoming computationally much faster than the conventional approach. We analyze the practical implementation with spatial light modulators (SLM). First, the ray matrix approach is applied to derive and reexamine this computational technique. This approach easily allows us to find explicit expressions for the maximum and minimum distances over which the algorithm is accurate. Then, we describe the practical implementation of this algorithm to encode Fresnel propagated masks onto a SLM. We discuss the limitations caused by the Nyquist limit. Finally, we apply the technique to create an experimental virtual optical beam propagator system. This system uses one SLM and allows the experimental study of the beam propagation without physically moving any element. This laboratory propagator system can be extremely useful to build compact optical architectures or to emulate beam propagation without misalignments caused by moving elements in the experimental system. As examples, we design holograms capable of producing different patterns at different distances, and we can change the effective plane of observation by changing the encoded propagation. The technique can find applications in many different contexts, including the analysis of propagation dynamics of nondiffracting beams, and Airy beams.
Measurement and Analysis of Multiple Output Transient Propagation in BJT Analog Circuits
Roche, Nicolas J.-H.; Khachatrian, A.; Warner, J. H.; Buchner, S. P.; McMorrow, D.; Clymer, D. A.
2016-08-01
The propagation of Analog Single Event Transients (ASETs) to multiple outputs of Bipolar Junction Transistor (BJTs) Integrated Circuits (ICs) is reported for the first time. The results demonstrate that ASETs can appear at several outputs of a BJT amplifier or comparator as a result of a single ion or single laser pulse strike at a single physical location on the chip of a large-scale integrated BJT analog circuit. This is independent of interconnect cross-talk or charge-sharing effects. Laser experiments, together with SPICE simulations and analysis of the ASET's propagation in the s-domain are used to explain how multiple-output transients (MOTs) are generated and propagate in the device. This study demonstrates that both the charge collection associated with an ASET and the ASET's shape, commonly used to characterize the propagation of SETs in devices and systems, are unable to explain quantitatively how MOTs propagate through an integrated analog circuit. The analysis methodology adopted here involves combining the Fourier transform of the propagating signal and the current-source transfer function in the s-domain. This approach reveals the mechanisms involved in the transient signal propagation from its point of generation to one or more outputs without the signal following a continuous interconnect path.
Numerical simulation of extremely chirped pulse formation with an optical fiber
Energy Technology Data Exchange (ETDEWEB)
Itoh, Tamitake; Nishimura, Akihiko; Tei, Kazuyoku; Matoba, Tohru; Takuma, Hiroshi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Yamashita, Mikio; Morita, Ryuji
1998-03-01
A nonlinear propagation code which used a symmetric split-step Fourier method as an algorithm was improved to simulate a propagation behavior of extremely chirped pulse in a long fiber. The performances of pulse propagation in noble gases cored hollow fibers and a pulse stretcher using a nonlinear and normal silicate fibers have been simulated by the code. The calculation results in the case of the hollow fiber are consistent with their experimental results. We estimated that this pulse stretcher could give a extremely chirped pulse whose spectral width was 84.2 nm and temporal duration was 1.5 ns. (author)
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
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
Ion cyclotron resonance spectrometer with fourier transformation
International Nuclear Information System (INIS)
Pikver, R.; Suurmaa, Eh.; Syugis, A.; Tammik, A.; Lippmaa, Eh.
1983-01-01
The ion cyclotron resonance spectrometer with Fourier transformation intended for investigating mass specta and chemical reaction kinetics in the gaseous phase is described. The mass-spectrum of CO and N 2 positive ions is shown. The spectrometer consists of an electromagnet with power supply, a vacuum system, a cell with electronic equipment and a minicomputer. In the vacuum system (5x10 -9 Torr) there is a cubic measuring cell heated up to 400 deg C. The spectrometer mass resolution is of the 10 5 order. The spectrometer is able to operate as a high-resolution analytical mass-spectrometer of positive and negative ions. The experience of the spectrometer operation confirms its effectiveness for investigating ion-molecular reactions, in particular, proton transfer reactions
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
Modeling the vehicle-to-vehicle propagation channel: A review
Matolak, David W.
2014-09-01
In this paper we provide a review of the vehicle-to-vehicle (V2V) wireless propagation channel. This "car-to-car" application will be used to improve roadway efficiency, provide unique traveler services, and can also enable safety applications that can save lives. We briefly review some currently envisioned applications and the initial V2V radio technology, then address the V2V propagation channel. Propagation basics germane to the V2V setting are described, followed by a discussion of channel dispersion and time variation. The channel impulse response and its Fourier transform, the channel transfer function, are described in detail, and their common statistical characterizations are also reviewed. The most common models for the V2V channel—the tapped delay line and geometry-based stochastic channel models—are covered in some detail. We highlight key differences between the V2V channel and the well-known cellular radio channel. These differences are the more rapid time variation and the higher probability of obstruction of the direct line of sight component; modeling of these effects has required some novel approaches. The V2V channel's nonstationary statistical behavior is addressed, as is the use of multiple-antenna systems. The remaining areas for future work are also described.
On a General Class of Trigonometric Functions and Fourier Series
Pavao, H. Germano; Capelas de Oliveira, E.
2008-01-01
We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Group symmetries and information propagation
International Nuclear Information System (INIS)
Draayer, J.P.
1980-01-01
Spectroscopy concerns itself with the ways in which the Hamiltonian and other interesting operators defined in few-particle spaces are determined or determine properties of many-particle systems. But the action of the central limit theorem (CLT) filters the transmission of information between source and observed so whether propagating forward from a few-particle defining space, as is usual in theoretical studies, or projecting backward to it from measured things, each is only sensitive to averaged properties of the other. Our concern is with the propagation of spectroscopic information in the presence of good symmetries when filtering action of the CLT is effective. Specifically, we propose to address the question, What propagates and how. We begin with some examples, using both scalar and isospin geometries to illustrate simple propagation. Examples of matrix propagation are studied; contact with standard tensor algebra is established and an algorithm put forward for the expansion of any operator in terms of another set, complete or not; shell-model results for 20 Ne using a realistic interaction and two trace-equivalent forms are presented; and some further challenges are mentioned
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.
Signal propagation along the axon.
Rama, Sylvain; Zbili, Mickaël; Debanne, Dominique
2018-03-08
Axons link distant brain regions and are usually considered as simple transmission cables in which reliable propagation occurs once an action potential has been generated. Safe propagation of action potentials relies on specific ion channel expression at strategic points of the axon such as nodes of Ranvier or axonal branch points. However, while action potentials are generally considered as the quantum of neuronal information, their signaling is not entirely digital. In fact, both their shape and their conduction speed have been shown to be modulated by activity, leading to regulations of synaptic latency and synaptic strength. We report here newly identified mechanisms of (1) safe spike propagation along the axon, (2) compartmentalization of action potential shape in the axon, (3) analog modulation of spike-evoked synaptic transmission and (4) alteration in conduction time after persistent regulation of axon morphology in central neurons. We discuss the contribution of these regulations in information processing. Copyright © 2018 Elsevier Ltd. All rights reserved.
Wave equations for pulse propagation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.
1987-06-24
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.
SIS Epidemic Propagation on Hypergraphs.
Bodó, Ágnes; Katona, Gyula Y; Simon, Péter L
2016-04-01
Mathematical modelling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix. Based on these, moment closure approximation and mean-field models are introduced and compared to individual-based stochastic simulations. The simulation algorithm, developed for networks, is extended to hypergraphs. The effects of hypergraph structure and the model parameters are investigated via individual-based simulation results.
Vegetative propagation of Bambusa vulgaris
Directory of Open Access Journals (Sweden)
Rafael Malfitano Braga
2017-06-01
Full Text Available Bamboo is an important source of raw material of multiple uses. The development of simple techniques for its propagation is a practical way to enable its implementation in ownership of low technology. The present work had the objective of evaluating artisanal propagation methods for Bambusa vulgaris. Two types of propagules were tested, with buds budded or not, and three relative positions to the removal of vegetative material on the culm. The best propagule was with only one node, extracted from the lower thirds of the stem, presenting 72% of rooting. This result demonstrates its potential for seedling production of this species under low tech.
Wave propagation in electromagnetic media
International Nuclear Information System (INIS)
Davis, J.L.
1990-01-01
This book is concerned with wave propagation in reacting media, specifically in electromagnetic materials. An account is presented of the mathematical methods of wave phenomena in electromagnetic materials. The author presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations and their application to electromagnetic wave propagation under a variety of conditions. The author gives a discussion of magnetohydrodynamics and plasma physics. Chapters are included on quantum mechanics and the theory of relativity. The mathematical foundation of electromagnetic waves vis a vis partial differential equations is discussed
Nonequilibrium theory of flame propagation
International Nuclear Information System (INIS)
Merzhanov, A.G.
1995-01-01
The nonequilibrium theory of flame propagation is considered as applied to the following three processes of wave propagation: the combustion waves of the second kind, the combustion waves with broad reaction zones, and the combustion waves with chemical stages. Kinetic and combustion wave parameters are presented for different in composition mixtures of boron and transition metals, such as Zr, Hf, Ti, Nb, Ta, Mo, as well as for the Ta-N, Zr-C-H, Nb-B-O systems to illustrate specific features of the above-mentioned processes [ru
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)
Fast algorithm of adaptive Fourier series
Gao, You; Ku, Min; Qian, Tao
2018-05-01
Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was originated for the goal of positive frequency representations of signals. It achieved the goal and at the same time offered fast decompositions of signals. There then arose several types of AFDs. AFD merged with the greedy algorithm idea, and in particular, motivated the so-called pre-orthogonal greedy algorithm (Pre-OGA) that was proven to be the most efficient greedy algorithm. The cost of the advantages of the AFD type decompositions is, however, the high computational complexity due to the involvement of maximal selections of the dictionary parameters. The present paper offers one formulation of the 1-D AFD algorithm by building the FFT algorithm into it. Accordingly, the algorithm complexity is reduced, from the original $\\mathcal{O}(M N^2)$ to $\\mathcal{O}(M N\\log_2 N)$, where $N$ denotes the number of the discretization points on the unit circle and $M$ denotes the number of points in $[0,1)$. This greatly enhances the applicability of AFD. Experiments are carried out to show the high efficiency of the proposed algorithm.
Fourier transform spectroscopy for future planetary missions
Brasunas, John C.; Hewagama, Tilak; Kolasinski, John R.; Kostiuk, Theodor
2015-11-01
Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system.Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, NASA Goddard was funded via the Planetary Instrument Definition and Development Progrem (PIDDP) to develop CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. Following the initial validation of CIRS-lite operation in the laboratory, we have been acquiring atmospheric data in the 8-12 micron window at the 1.2 m telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) in Greenbelt, MD. Targets so far have included Earth's atmosphere (in emission, and in absorption against the moon), and Venus.We will present the roadmap for making CIRS-lite a viable candidate for future planetary missions.
Exploring Fourier Series and Gibbs Phenomenon Using Mathematica
Ghosh, Jonaki B.
2011-01-01
This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of…
The Fourier Transform for Certain HyperKähler Fourfolds
Shen, M.; Vial, C.
2016-01-01
Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle
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
Lacunary Fourier Series and a Qualitative Uncertainty Principle for ...
Indian Academy of Sciences (India)
We define lacunary Fourier series on a compact connected semisimple Lie group . If f ∈ L 1 ( G ) has lacunary Fourier series and vanishes on a non empty open subset of , then we prove that vanishes identically. This result can be viewed as a qualitative uncertainty principle.
Bilaterally symmetric Fourier approximations of the skull outlines of ...
Indian Academy of Sciences (India)
Present work illustrates a scheme of quantitative description of the shape of the skull outlines of temnospondyl amphibians using bilaterally symmetric closed Fourier curves. Some special points have been identified on the Fourier fits of the skull outlines, which are the local maxima, or minima of the distances from the ...
Infrared Fourier spectres of pectin obtained from pumpkin
International Nuclear Information System (INIS)
Usmanova, S.R.; Dzhonmurodov, A.S.; Nazirova, Kh.I.; Mukhidinov, Z.K.
2015-01-01
Present article is devoted to infrared Fourier spectres of pectin obtained from pumpkin. The analysis of pectin obtained from pumpkin was conducted by means of infrared spectrophotometer with Fourier transformation. The infrared spectroscopic study of pectin polysaccharide fraction of pectin matter, as well as pectin helium and micro helium obtained by means of fast extraction was conducted.
Fourier transforms of Dini-Lipschitz functions on Vilenkin groups
Directory of Open Access Journals (Sweden)
M. S. Younis
1992-01-01
Full Text Available In [4] we proved some theorems on the Fourier Transforms of functions satisfying conditions related to the Dini-Lipschitz conditions on the n-dimensional Euclidean space Rn and the torus group Tn. In this paper we extend those theorems for functions with Fourier series on Vilenkin groups.
Fourierdimredn: Fourier dimensionality reduction model for interferometric imaging
Kartik, S. Vijay; Carrillo, Rafael; Thiran, Jean-Philippe; Wiaux, Yves
2016-10-01
Fourierdimredn (Fourier dimensionality reduction) implements Fourier-based dimensionality reduction of interferometric data. Written in Matlab, it derives the theoretically optimal dimensionality reduction operator from a singular value decomposition perspective of the measurement operator. Fourierdimredn ensures a fast implementation of the full measurement operator and also preserves the i.i.d. Gaussian properties of the original measurement noise.
Geometric interpretations of the Discrete Fourier Transform (DFT)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
The morphing of geographical features by Fourier transformation.
Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang
2018-01-01
This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.
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)
Double Fourier analysis for Emotion Identification in Voiced Speech
International Nuclear Information System (INIS)
Sierra-Sosa, D.; Bastidas, M.; Ortiz P, D.; Quintero, O.L.
2016-01-01
We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented. (paper)
Mathematical principles of signal processing Fourier and wavelet analysis
Brémaud, Pierre
2002-01-01
Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...
Applied Fourier analysis from signal processing to medical imaging
Olson, Tim
2017-01-01
The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medical i maging, and heat and wave equations. Fo...
Self-Averaging Expectation Propagation
DEFF Research Database (Denmark)
Cakmak, Burak; Opper, Manfred; Fleury, Bernard Henri
We investigate the problem of approximate inference using Expectation Propagation (EP) for large systems under some statistical assumptions. Our approach tries to overcome the numerical bottleneck of EP caused by the inversion of large matrices. Assuming that the measurement matrices are realizat...... on a signal recovery problem of compressed sensing and compare with standard EP....
Wave propagation in mechanical metamaterials
Zhou, Y.
2017-01-01
In mechanical metamaterials, large deformations can occur in systems which are topological from the point of view of linear waves. The interplay between such nonlinearities and topology affects wave propagation. Beyond perfectly periodic systems, defects provide a way to modify and control
Radio Propagation into Modern Buildings
DEFF Research Database (Denmark)
Rodriguez Larrad, Ignacio; Nguyen, Huan Cong; Jørgensen, Niels T.K.
2014-01-01
constructions. These materials are used in favor of achieving a proper level of thermal isolation, but it has been noticed that they can impact heavily on radio signal propagation. This paper presents a measurement-based analysis of the outdoor-to-indoor attenuation experienced in several modern constructions...... presented along the paper are useful for future radio network planning considerations....
Invisibility cloaking without superluminal propagation
Energy Technology Data Exchange (ETDEWEB)
Perczel, Janos; Leonhardt, Ulf [School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS (United Kingdom); Tyc, Tomas, E-mail: jp394@st-andrews.ac.uk, E-mail: tomtyc@physics.muni.cz, E-mail: ulf@st-andrews.ac.uk [Faculty of Science, Kotlarska 2 and Faculty of Informatics, Botanicka 68a, Masaryk University, 61137 Brno (Czech Republic)
2011-08-15
Conventional cloaking based on Euclidean transformation optics requires that the speed of light should tend to infinity on the inner surface of the cloak. Non-Euclidean cloaking still needs media with superluminal propagation. Here we show by giving an example that this is no longer necessary.
UWB radar multipath propagation effects
Czech Academy of Sciences Publication Activity Database
Čermák, D.; Schejbal, V.; NĚMEC, Z.; Bezoušek, P.; Fišer, Ondřej
2005-01-01
Roč. 11, - (2005), --- ISSN 1211-6610 R&D Projects: GA MPO FT-TA2/030 Institutional research plan: CEZ:AV0Z30420517 Keywords : UWB radar * multipath propagation Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering
Propagating Class and Method Combination
DEFF Research Database (Denmark)
Ernst, Erik
1999-01-01
number of implicit combinations. For example, it is possible to specify separate aspects of a family of classes, and then combine several aspects into a full-fledged class family. The combination expressions would explicitly combine whole-family aspects, and by propagation implicitly combine the aspects...
Galactic propagation of cosmic rays
International Nuclear Information System (INIS)
Cesarsky, C.J.
1982-09-01
After introducing various phenomenological models of cosmic ray propagation in the galaxy, we examine how some of them fare when compared to the data. We show that a model based on resonant diffusion of cosmic rays off an interstellar spectrum of hydromagnetic waves can account for the presently available evidence on cosmic rays and the interstellar medium
1989-02-07
This report summarizes studies of enroute propfan noise propagation involving noise data obtained by DOT/TSC at ground stations during fly-over tests on October 30-31, 1987. These data have been analsyzed by DOT/TSC for comparison with in flight data...
Assessment of the hybrid propagation model, Volume 1: Analysis of noise propagation effects
2012-08-31
This is the first of two volumes of a report on the Hybrid Propagation Model (HPM), an advanced prediction model for aviation noise propagation. This volume presents the noise level predictions for eleven different sets of propagation conditions, run...
Regularized spherical polar fourier diffusion MRI with optimal dictionary learning.
Cheng, Jian; Jiang, Tianzi; Deriche, Rachid; Shen, Dinggang; Yap, Pew-Thian
2013-01-01
Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods proposed for reconstruction of diffusion-weighted signal and the Ensemble Average Propagator (EAP) utilize two kinds of Dictionary Learning (DL) methods: 1) Discrete Representation DL (DR-DL), and 2) Continuous Representation DL (CR-DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding errors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI) for effective compressed-sensing reconstruction of the q-space diffusion-weighted signal and the EAP. In DL-SPFI, a dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. Compared with the start-of-the-art CR-DL and DR-DL methods proposed by Merlet et al. and Bilgic et al., respectively, our work offers the following advantages. First, the learned dictionary is proved to be optimal for Gaussian diffusion signals. Second, to our knowledge, this is the first work to learn a voxel-adaptive dictionary. The importance of the adaptive dictionary in EAP reconstruction will be demonstrated theoretically and empirically. Third, optimization in DL-SPFI is only performed in a small subspace resided by the SPF coefficients, as opposed to the q-space approach utilized by Merlet et al. We experimentally evaluated DL-SPFI with respect to L1-norm regularized SPFI (L1-SPFI), which uses the original SPF basis, and the DR-DL method proposed by Bilgic et al. The experiment results on synthetic and real data indicate that the learned dictionary produces
Lagubeau, Guillaume; Cobelli, Pablo; Bobinski, Tomasz; Maurel, Agnes; Pagneux, Vincent; Petitjeans, Philippe
2015-11-01
Fringe projection profilometry is an instrument of choice for the instantaneous measurement of the full height map of a free-surface. It is useful to capture interfacial phenomena such as droplet impact and propagation of water waves. We present the Empirical Mode Decomposition Profilometry (EMDP) for the analysis of fringe projection profilometry images. It is based on an iterative filter, using empirical mode decomposition, that is free of spatial filtering and adapted for surfaces characterized by a broadband spectrum of deformation. Examples of such surfaces can be found in nonlinear wave interaction regimes such as wave turbulence in gravity-capillary water waves. We show both numerically and experimentally that using EMDP improves strongly the profilometry small scale capabilities compared to traditionally used Fourier Transform Profilometry. Moreover, the height reconstruction distortion is much lower: the reconstructed height field is now both spectrally and statistically accurate.
Discrete Fourier transformation processor based on complex radix (−1 + j number system
Directory of Open Access Journals (Sweden)
Anidaphi Shadap
2017-02-01
Full Text Available Complex radix (−1 + j allows the arithmetic operations of complex numbers to be done without treating the divide and conquer rules, which offers the significant speed improvement of complex numbers computation circuitry. Design and hardware implementation of complex radix (−1 + j converter has been introduced in this paper. Extensive simulation results have been incorporated and an application of this converter towards the implementation of discrete Fourier transformation (DFT processor has been presented. The functionality of the DFT processor have been verified in Xilinx ISE design suite version 14.7 and performance parameters like propagation delay and dynamic switching power consumption have been calculated by Virtuoso platform in Cadence. The proposed DFT processor has been implemented through conversion, multiplication and addition. The performance parameter matrix in terms of delay and power consumption offered a significant improvement over other traditional implementation of DFT processor.
Hiding objects and creating illusions above a carpet filter using a Fourier optics approach.
Wu, Kedi; Wang, Guo Ping
2010-09-13
Invisibility carpet cloaks are usually used to hide an object beneath carpet. In this paper we propose and demonstrate a carpet filter to hide objects and create illusions above the filter by using a Fourier optics method. Instead of using transformation optics, we get electromagnetic parameters of the filter by optical transfer functions, which play the role of modulating the propagation of the scattering angular spectrum directly from an object above the filter. By further adding a functional layer onto the filter, we can even camouflage the object so that it appears to be a different object. The analytical results are confirmed by numerical simulations. Our method is completely different from the current coordinate transfer method and may provide another point of view to more clearly understand the mechanism of invisibility cloaks.
Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations
Alzahrani, Mohammed A.; Gauthier, Robert C.
2015-02-01
For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.
International Nuclear Information System (INIS)
Viswanathan, V.K.
1979-01-01
The optical design and analysis of the LASL carbon dioxide laser fusion systems required the use of techniques that are quite different from the currently used method in conventional optical design problems. The necessity for this is explored and the method that has been successfully used at Los Alamos to understand these systems is discussed with examples. This method involves characterization of the various optical components in their mounts by a Zernike polynomial set and using fast Fourier transform techniques to propagate the beam, taking diffraction and other nonlinear effects that occur in these types of systems into account. The various programs used for analysis are briefly discussed
Cryogenic Scan Mechanism for Fourier Transform Spectrometer
Brasunas, John C.; Francis, John L.
2011-01-01
A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear
A transformada de Fourier em basic The Fourier transform (FFT in basic
Directory of Open Access Journals (Sweden)
Mauricio Gomes Constantino
2000-06-01
Full Text Available In this paper we describe three computer programs in Basic language about the Fourier transform (FFT which are available in the Internet site http://artemis.ffclrp.usp.br/SoftwareE.htm (in English or http://artemis.ffclrp.usp.br/softwareP.htm (in Portuguese since October 1998. Those are addresses to the Web Page of our Laboratory of Organic Synthesis. The programs can be downloaded and used by anyone who is interested on the subject. The texts, menus and captions in the programs are written in English.
Theory and experiment of Fourier-Bessel field calculation and tuning of a pulsed wave annular array
DEFF Research Database (Denmark)
Fox, Paul D.; Jiqi, Cheng; Jian-yu, Lu
2003-01-01
A one-dimensional (1D) Fourier-Bessel series method for computing and tuning (beamforming) the linear lossless field of flat pulsed wave annular arrays is developed and supported with both numerical simulation and experimental verification. The technique represents a new method for modeling...... and tuning the propagated field by linking the quantized surface pressure profile to a known set of limited diffraction Bessel beams propagating into the medium. This enables derivation of an analytic expression for the field at any point in space and time in terms of the transducer surface pressure profile....... Tuning of the field then also follows by formulating a least-squares design for the transducer surface pressure with respect to a given desired field in space and time. Simulated and experimental results for both field computation and tuning are presented in the context of a 10-ring annular array...
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-09-01
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-01-01
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena. PMID:27625210
Measurements of Near Sea Surface Infrared Propagation
National Research Council Canada - National Science Library
Frost, Shaun
1999-01-01
.... Measurements have been made of the atmospheric infrared transmission near the sea surface. Spectral transmission profiles were measured for a number of ranges using a fourier transform spectrometer...
Corrected Fourier series and its application to function approximation
Directory of Open Access Journals (Sweden)
Qing-Hua Zhang
2005-01-01
Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.
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 mode analysis of source iteration in spatially periodic media
International Nuclear Information System (INIS)
Zika, M.R.; Larsen, E.W.
1998-01-01
The standard Fourier mode analysis is an indispensable tool when designing acceleration techniques for transport iterations; however, it requires the assumption of a homogeneous infinite medium. For problems of practical interest, material heterogeneities may significantly impact iterative performance. Recent work has applied a Fourier analysis to the discretized two-dimensional transport operator with heterogeneous material properties. The results of these analyses may be difficult to interpret because the heterogeneity effects are inherently coupled to the discretization effects. Here, the authors describe a Fourier analysis of source iteration (SI) that allows the calculation of the eigenvalue spectrum for the one-dimensional continuous transport operator with spatially periodic heterogeneous media
Atmospheric propagation of THz radiation.
Energy Technology Data Exchange (ETDEWEB)
Wanke, Michael Clement; Mangan, Michael A.; Foltynowicz, Robert J.
2005-11-01
In this investigation, we conduct a literature study of the best experimental and theoretical data available for thin and thick atmospheres on THz radiation propagation from 0.1 to 10 THz. We determined that for thick atmospheres no data exists beyond 450 GHz. For thin atmospheres data exists from 0.35 to 1.2 THz. We were successful in using FASE code with the HITRAN database to simulate the THz transmission spectrum for Mauna Kea from 0.1 to 2 THz. Lastly, we successfully measured the THz transmission spectra of laboratory atmospheres at relative humidities of 18 and 27%. In general, we found that an increase in the water content of the atmosphere led to a decrease in the THz transmission. We identified two potential windows in an Albuquerque atmosphere for THz propagation which were the regions from 1.2 to 1.4 THz and 1.4 to 1.6 THz.
Scaling Analysis of Affinity Propagation
Furtlehner , Cyril; Sebag , Michèle; Xiangliang , Zhang
2010-01-01
14 pages, 11 figures; International audience; We analyze and exploit some scaling properties of the {\\em Affinity Propagation} (AP) clustering algorithm proposed by Frey and Dueck (2007). Following a divide and conquer strategy we setup an exact renormalization-based approach to address the question of clustering consistency, in particular, how many cluster are present in a given data set. We first observe that the divide and conquer strategy, used on a large data set hierarchically reduces t...
Propagator for finite range potentials
International Nuclear Information System (INIS)
Cacciari, Ilaria; Moretti, Paolo
2006-01-01
The Schroedinger equation in integral form is applied to the one-dimensional scattering problem in the case of a general finite range, nonsingular potential. A simple expression for the Laplace transform of the transmission propagator is obtained in terms of the associated Fredholm determinant, by means of matrix methods; the particular form of the kernel and the peculiar aspects of the transmission problem play an important role. The application to an array of delta potentials is shown
Interprocedural Analysis with Lazy Propagation
DEFF Research Database (Denmark)
Jensen, Simon Holm; Møller, Anders; Thiemann, Peter
2010-01-01
We propose lazy propagation as a technique for flow- and context-sensitive interprocedural analysis of programs with objects and first-class functions where transfer functions may not be distributive. The technique is described formally as a systematic modification of a variant of the monotone...... framework and its theoretical properties are shown. It is implemented in a type analysis tool for JavaScript where it results in a significant improvement in performance....
Development of Fourier domain optical coherence tomography
Wang, Rui
Fourier domain optical coherence tomography (FD-OCT) is a high-speed, high-resolution, and noninvasive imaging technique that can obtain cross-sectional images of light scattering medium, such as biomedical tissues. In this thesis, I report three novel methods in FD-OCT technique including common-path endoscopic FD-OCT, streak-mode FD-OCT, and Doppler streak-mode FD-OCT. Finally, I apply the streak mode FD-OCT to ultrahigh-speed, noninvasive, live imaging of embryonic chick hearts. An extension of conventional FD-OCT technique is endoscopic FD-OCT, which can access internal organs by utilizing a miniaturized catheter design. However, its image signal suffers from the bending of the endoscopic catheter. To address this problem, a common-path endoscopic FD-OCT system was developed to avoid the polarization mismatch. Consequently, the OCT images were immune to the catheter bending. In addition, a Microelectromechanical system (MEMS) motor was integrated into the miniaturized probe to achieve circumferential scanning within lumen samples. In conventional FD-OCT, the imaging speed is limited by the slow line-scan rate of the camera. We developed the streak-mode FD-OCT technique, in which an area-scan camera is used instead of a line-scan camera to record the FD-OCT spectrum. Using this technique, high temporal resolution of 1000--2000 cross-sectional images of the sample were obtained in one second. Doppler FD-OCT is a functional extension of FD-OCT technique, which can measure the flow velocity within biomedical tissues. However, conventional techniques are not available to measure high speed flow due to slow imaging speed, phase wrapping, and fringe wash out issues. Based on the streak mode FD-OCT, a novel Doppler technique was developed that addressed these problems. It has been well established that cardiac dynamics play an important role in the early development of an embryonic heart. However, the mechanism by which cardiac dynamics affect the development of a
Fourier transform spectroscopy of semiconductor materials
International Nuclear Information System (INIS)
Jonak-Auer, I.
1996-11-01
In order to determine the type of charge carriers, i.e. electrons or holes, participating in optical transitions, cyclotron resonance experiments using circularly polarized radiation were performed on strained-layer [111]-oriented InGaAs/(Al)GaAs multiple quantum wells and on a [100]-oriented InAs/GaSb double-heterostructure. Because of the rather complicated band-structures of these samples it is a priori unknown which carriers take part in transitions. The measurements yield the surprising result, that for the InGaAs/GaAs multiple quantum well the experimentally observed cyclotron resonance appears in the electron-active polarization in the frequency-regime of the Far Infrared (FIR), but in the hole-active polarization in the range of millimeter waves, whereas for the InGaAs/AlGaAs sample the resonance is caused by holes also in the FIR. Since by theoretical considerations the possibility of electrons causing the FIR cyclotron resonance could be excluded, the measurements are interpreted as being caused by holes due to broken selection rules. In the InAs/GaSb sample hole cyclotron resonance could for the first time be measured on a double-heterostructure. As for the application oriented measurements, they comprised a study of the hydrogen content of amorphous silicon nitride layers, and were performed in collaboration with Austria Mikro Systeme International AG. Fourier spectroscopy is a fast and non-destructive means for determining impurity concentrations. Radiation in the Mid Infrared regime stimulates N-H and Si-H stretching vibrations which lead to absorption peaks and can directly be attributed to the hydrogen concentration via calibration factors taken from the literature. In comparison with recommended procedures in the literature, a much higher accuracy in determining the areas of the absorption peaks could be gained in the course of this thesis by a proper polynomial fit of the background spectrum outside the absorption lines. The hydrogen content of
Propagating separable equalities in an MDD store
DEFF Research Database (Denmark)
Hadzic, Tarik; Hooker, John N.; Tiedemann, Peter
2008-01-01
We present a propagator that achieves MDD consistency for a separable equality over an MDD (multivalued decision diagram) store in pseudo-polynomial time. We integrate the propagator into a constraint solver based on an MDD store introduced in [1]. Our experiments show that the new propagator pro...... provides substantial computational advantage over propagation of two inequality constraints, and that the advantage increases when the maximum width of the MDD store increases....
Monitoring Moisture Damage Propagation in GFRP Composites Using Carbon Nanoparticles
Directory of Open Access Journals (Sweden)
Ahmed Al-Sabagh
2017-03-01
Full Text Available Glass fiber reinforced polymer (GFRP composites are widely used in infrastructure applications including water structures due to their relatively high durability, high strength to weight ratio, and non-corrosiveness. Here we demonstrate the potential use of carbon nanoparticles dispersed during GFRP composite fabrication to reduce water absorption of GFRP and to enable monitoring of moisture damage propagation in GFRP composites. GFRP coupons incorporating 2.0 wt % carbon nanofibers (CNFs and 2.0 wt % multi-wall carbon nanotubes (MWCNTs were fabricated in order to study the effect of moisture damage on mechanical properties of GFRP. Water absorption tests were carried out by immersing the GFRP coupons in a seawater bath at two temperatures for a time period of three months. Effects of water immersion on the mechanical properties and glass transition temperature of GFRP were investigated. Furthermore, moisture damage in GFRP was monitored by measuring the electrical conductivity of the GFRP coupons. It was shown that carbon nanoparticles can provide a means of self-sensing that enables the monitoring of moisture damage in GFRP. Despite the success of the proposed technique, it might not be able to efficiently describe moisture damage propagation in GFRP beyond a specific threshold because of the relatively high electrical conductivity of seawater. Microstructural investigations using Fourier Transform Infrared (FTIR explained the significance of seawater immersion time and temperature on the different levels of moisture damage in GFRP.
Propagating pulsed Bessel beams in periodic media
International Nuclear Information System (INIS)
Longhi, S; Janner, D; Laporta, P
2004-01-01
An analytical study of vectorial pulsed Bessel beam propagation in one-dimensional photonic bandgaps, based on a Wannier-function approach, is presented, and the conditions for dispersion-free and diffraction-free propagation are derived. The analysis is applied, as a particular case, to Bessel beam propagation in periodic layered structures
Fast Heat Pulse Propagation by Turbulence Spreading
DEFF Research Database (Denmark)
Naulin, Volker; Juul Rasmussen, Jens; Mantica, Paola
2009-01-01
The propagation of a cold pulse initiated by edge cooling in JET is compared to propagation of the heat wave originating from a modulation of the heating source roughly at mid radius. It is found that the propagation of the cold pulse is by far faster than what could be predicted on the basis of ...
Greene, Samuel M; Batista, Victor S
2017-09-12
We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.
Box, M. A.; Deepak, A.
1981-01-01
The propagation of photons in a medium with strongly anisotropic scattering is a problem with a considerable history. Like the propagation of electrons in metal foils, it may be solved in the small-angle scattering approximation by the use of Fourier-transform techniques. In certain limiting cases, one may even obtain analytic expressions. This paper presents some of these results in a model-independent form and also illustrates them by the use of four different phase-function models. Sample calculations are provided for comparison purposes
CSIR Research Space (South Africa)
Fedotov, I
2006-07-01
Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...
On Sums of Numerical Series and Fourier Series
Pavao, H. Germano; de Oliveira, E. Capelas
2008-01-01
We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)
Embedding relations connected with strong approximation of Fourier ...
Indian Academy of Sciences (India)
. © Indian Academy of Sciences. Embedding relations connected with strong approximation of Fourier series. BOGDAN SZAL. Faculty of Mathematics, Computer Science and Econometrics,. University of Zielona Góra, 65-516 Zielona Góra, ul.
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)
Almost everywhere convergence over cubes of multiple trigonometric Fourier series
International Nuclear Information System (INIS)
Antonov, N Yu
2004-01-01
Under certain conditions on a function φ:[0,+∞)→[0,+∞) we prove a theorem asserting that the convergence almost everywhere of trigonometric Fourier series for all functions of class φ(L) [-π,π) implies the convergence over cubes of the multiple Fourier series and all its conjugates for an arbitrary function f element of φ(L)(log + L) d-1 ) [-π,π) d , d element of N. It follows from this and an earlier result of the author on the convergence almost everywhere of Fourier series of functions of one variable and class L(log + L)(log + log + log + L)) [-π,π) that if f element of L(log + L) d (log + log + log + L)) [-π,π) d , d element of N, then the Fourier series of f and all its conjugates converge over cubes almost everywhere
On the 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...
On the Equisummability of Hermite and Fourier Expansions
Indian Academy of Sciences (India)
We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.
Electro-Optic Imaging Fourier Transform Spectral Polarimeter, Phase I
National Aeronautics and Space Administration — Boulder Nonlinear Systems, Inc. (BNS) proposes to develop an Electro-Optic Imaging Fourier Transform Spectral Polarimeter (E-O IFTSP). The polarimetric system is...
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...
Space-charge calculations with the fast Fourier transform
International Nuclear Information System (INIS)
Vaughan, J.R.
1978-01-01
A method is described for calculating linear accelerator beam trajectories in traveling wave tubes. A grid is placed over the region of interest in which there is space charge. A matrix of the Fourier potential coefficients is obtained, and a straight Fourier synthesis is used to add these with the appropriate trigonometric multipliers to obtain the potential matrix. The pulses on a particle for the next trajectory step are found by interpolating and differencing the potentials on that matrix
A New Nonlinear Unit Root Test with Fourier Function
Güriş, Burak
2017-01-01
Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an Exponential Smooth Threshold Autore...
A discrete Fourier transform for virtual memory machines
Galant, David C.
1992-01-01
An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.
On the Mathematics of Music: From Chords to Fourier Analysis
Lenssen, Nathan; Needell, Deanna
2013-01-01
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from recorded music. We begin with a light introduction to the theory of music and motivate the use of Fourier analysis in audio processing. We introduce the discrete and continuous Fourier transforms and investigate their use in extracting important information...
Simple optical setup implementation for digital Fourier transform holography
International Nuclear Information System (INIS)
De Oliveira, G N; Rodrigues, D M C; Dos Santos, P A M
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.
Li, Shu-Nan; Cao, Bing-Yang
2017-09-01
The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.
Self-Fourier functions and coherent laser combination
International Nuclear Information System (INIS)
Corcoran, C J; Pasch, K A
2004-01-01
The Gaussian and Comb functions are generally quoted as being the two basic functions that are their own Fourier transforms. In 1991, Caola presented a recipe for generating functions that are their own Fourier transforms by symmetrizing any transformable function and then adding its own Fourier transform to it. In this letter, we present a new method for generating a set of functions that are exactly their own Fourier transforms, and which have direct application to laser cavity design for a wide variety of applications. The generated set includes the Gaussian and Comb functions as special cases and forms a continuous bridge of functions between them. The new generating method uses the Gaussian and Comb functions as bases and does not rely on the Fourier operator itself. This self-Fourier function promises to be particularly useful in high-power laser design through coherent laser beam combination. Although these results are presented in a single dimension as with a linear array, the results are equally valid in two dimensions. (letter to the editor)
Light propagation in linear optical media
Gillen, Glen D; Guha, Shekhar
2013-01-01
Light Propagation in Linear Optical Media describes light propagation in linear media by expanding on diffraction theories beyond what is available in classic optics books. In one volume, this book combines the treatment of light propagation through various media, interfaces, and apertures using scalar and vector diffraction theories. After covering the fundamentals of light and physical optics, the authors discuss light traveling within an anisotropic crystal and present mathematical models for light propagation across planar boundaries between different media. They describe the propagation o
Characteristics of Electromagnetic Pulse Propagation in Metal
Namkung, M.; Wincheski, B.; Nath, S.; Fulton, J. P.
2004-01-01
It is well known that the solution of the diffusion equation for an electromagnetic field with a time harmonic term, e(sup iwt), is in the form of a traveling wave whose amplitude attenuates over distance into a conducting medium. As the attenuation is an increasing function of frequency, the high frequency components attenuate more rapidly than those of low ones upon entering a well conducting object. At the same time, the phase velocity of an individual component is also an increasing function of frequency causing a broadening of the pulse traveling inside a conductor. In the results of our previous study of numerical simulations, the problem of using a gaussian input pulse was immediately clear. First, having the dominant frequency components distributed around zero, the movement of the peak was not well defined. Second, with the amplitude of fourier components varying slowly over a wide range, the dispersion-induced blurring of the peak position was seen to be severe. For the present study, we have used a gaussian modulated single frequency sinusoidal wave, i. e., the carrier, as an input pulse in an effort to improve the issues related to the unclear movement of peak and dispersion as described above. This was based on the following two anticipated advantages: First, the packet moves in a conductor at the group velocity calculated at the carrier frequency, which means it is well controllable. Second, the amplitude of frequency components other than that of the carrier can be almost negligible, such that the effect of dispersion can be significantly reduced. A series of experiments of transmitting electromagnetic pulses through aluminum plates of various thickness was performed to test the validity of the above points. The results of numerical simulation based on wave propagation are discussed with respect to the experimental results. Finally, a simple simulation was performed based on diffusion of a continuous sine wave input and the results are compared with
Propagation phenomena in real world networks
Fay, Damien; Gabryś, Bogdan
2015-01-01
“Propagation, which looks at spreading in complex networks, can be seen from many viewpoints; it is undesirable, or desirable, controllable, the mechanisms generating that propagation can be the topic of interest, but in the end all depends on the setting. This book covers leading research on a wide spectrum of propagation phenomenon and the techniques currently used in its modelling, prediction, analysis and control. Fourteen papers range over topics including epidemic models, models for trust inference, coverage strategies for networks, vehicle flow propagation, bio-inspired routing algorithms, P2P botnet attacks and defences, fault propagation in gene-cellular networks, malware propagation for mobile networks, information propagation in crisis situations, financial contagion in interbank networks, and finally how to maximize the spread of influence in social networks. The compendium will be of interest to researchers, those working in social networking, communications and finance and is aimed at providin...
Radio wave propagation and parabolic equation modeling
Apaydin, Gokhan
2018-01-01
A thorough understanding of electromagnetic wave propagation is fundamental to the development of sophisticated communication and detection technologies. The powerful numerical methods described in this book represent a major step forward in our ability to accurately model electromagnetic wave propagation in order to establish and maintain reliable communication links, to detect targets in radar systems, and to maintain robust mobile phone and broadcasting networks. The first new book on guided wave propagation modeling and simulation to appear in nearly two decades, Radio Wave Propagation and Parabolic Equation Modeling addresses the fundamentals of electromagnetic wave propagation generally, with a specific focus on radio wave propagation through various media. The authors explore an array of new applications, and detail various v rtual electromagnetic tools for solving several frequent electromagnetic propagation problems. All of the methods described are presented within the context of real-world scenari...
Wave Propagation in Bimodular Geomaterials
Kuznetsova, Maria; Pasternak, Elena; Dyskin, Arcady; Pelinovsky, Efim
2016-04-01
Observations and laboratory experiments show that fragmented or layered geomaterials have the mechanical response dependent on the sign of the load. The most adequate model accounting for this effect is the theory of bimodular (bilinear) elasticity - a hyperelastic model with different elastic moduli for tension and compression. For most of geo- and structural materials (cohesionless soils, rocks, concrete, etc.) the difference between elastic moduli is such that their modulus in compression is considerably higher than that in tension. This feature has a profound effect on oscillations [1]; however, its effect on wave propagation has not been comprehensively investigated. It is believed that incorporation of bilinear elastic constitutive equations within theory of wave dynamics will bring a deeper insight to the study of mechanical behaviour of many geomaterials. The aim of this paper is to construct a mathematical model and develop analytical methods and numerical algorithms for analysing wave propagation in bimodular materials. Geophysical and exploration applications and applications in structural engineering are envisaged. The FEM modelling of wave propagation in a 1D semi-infinite bimodular material has been performed with the use of Marlow potential [2]. In the case of the initial load expressed by a harmonic pulse loading strong dependence on the pulse sign is observed: when tension is applied before compression, the phenomenon of disappearance of negative (compressive) strains takes place. References 1. Dyskin, A., Pasternak, E., & Pelinovsky, E. (2012). Periodic motions and resonances of impact oscillators. Journal of Sound and Vibration, 331(12), 2856-2873. 2. Marlow, R. S. (2008). A Second-Invariant Extension of the Marlow Model: Representing Tension and Compression Data Exactly. In ABAQUS Users' Conference.
Steady propagation of delamination events
Bird, Peter; Baumgardner, John
1981-06-01
Delamination of the lithospheric thermal boundary from overlying continental crust propagates laterally from the line of initiation, accelerating as the sinking slab of detached lithosphere grows longer. This propagation has been numerically modeled with steady state equations in a moving reference frame by matching an interior finite element solution to flexible boundary conditions which represent the mechanical and thermal response of the surroundings. The form of the solution depends on the shear coupling of intruding asthenosphere to the top of the sinking slab across a thin layer of crustal material. Without coupling, the tip of the intrusion cools and stiffens to form a wedge dividing the crust (cold mode). With coupling, the intrusion is forced to convect and remains ductile (hot mode). The cold mode can propagate at all velocities; the hot mode has a lower limiting velocity of 1-2 cm/year but offers less resistance at higher speeds. Resistance to delamination includes a constant term from the buoyant crustal downwarp, plus a velocity-proportional term representing viscous deformation. However, the proportionality constant of the latter term is only weakly dependent on crust and lithosphere viscosities. Matching this resistance to loading lines of 100- to 800-km slabs sinking in a mantle of 1022 P, velocities of 0.3-8.0 cm/year are obtained. Changes in viscosity affect this rate, but cold mode delamination is unstoppable except at continental margins or by failure in the sinking slab. The surface expression of delamination is a leading `outer rise' followed by a submarine trough with a large negative free-air anomaly, which finally evolves into a 1-km plateau. If crustal viscosity and velocity are both low, however, there is a montonic crustal uplift with no trough. Thus the present lack of linear supracontinental oceans does not preclude delamination at up to 4 cm/year driven by slabs up to 400 km in length.
Fast imaging of streamer propagation
International Nuclear Information System (INIS)
Veldhuizen, E.M. van; Baede, A.H.F.M.; Hayashi, D.; Rutgers, W.R.
2001-01-01
Recently measurement methods are becoming available to study the corona discharge in more detail. One of the most promising methods is laser-induced fluorescence to determine radical density. Recent improvements in CCD cameras makes it now possible to improve measurements of the discharge structure to a resolution of 1 ns in time and 10 μm in space. This paper shows the first results of the spontaneous emission of a point-to-plane corona discharge in air using such a camera. It clearly indicates that the 2-D approach for streamer propagation under these conditions is insufficient
Multispecimen fatigue crack propagation testing
International Nuclear Information System (INIS)
Ermi, A.M.; Bauer, R.E.; Chin, B.A.; Straalsund, J.L.
1981-01-01
Chains of miniature center-cracked-tension specimens were tested on a conventional testing machine and on a prototypic in-reactor fatigue machine as part of the fusion reactor materials alloy development program. Annealed and 20 percent cold-worked 316 stainless steel specimens were cycled under various conditions of temperature, frequency, stress ratio and chain length. Crack growth rates determined from multispecimen visual measurements and from an electrical potential technique were consistent with those obtained by conventional test methods. Results demonstrate that multispecimen chain testing is a valid method of obtaining fatigue crack propagation information for alloy development. 8 refs
Wave propagation and group velocity
Brillouin, Léon
1960-01-01
Wave Propagation and Group Velocity contains papers on group velocity which were published during the First World War and are missing in many libraries. It introduces three different definitions of velocities: the group velocity of Lord Rayleigh, the signal velocity of Sommerfeld, and the velocity of energy transfer, which yields the rate of energy flow through a continuous wave and is strongly related to the characteristic impedance. These three velocities are identical for nonabsorbing media, but they differ considerably in an absorption band. Some examples are discussed in the last chapter
Quantum propagation across cosmological singularities
Gielen, Steffen; Turok, Neil
2017-05-01
The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.
International Nuclear Information System (INIS)
Okada, Toshio; Murakami, Hiroyuki; Niu, Keishiro.
1983-01-01
A method of rotating ion layer is proposed as a possible driver for inertial confinement fusion for the purpose of obtaining more stable ion beam against various micro- and macroinstabilities. The analysis was carried out within the frameworks of Vlasov and fluid models. A rotating ion layer propagating in the Z-direction is considered. The beam is described by a distribution function which satisfies the Vlasov equation. The equilibrium and microstability were studied. The filamentation instability is suppressed by a magnetic field due to the rotation of ion beam. To study the properties of the equilibrium state from the macroscopic standpoint, the equation of continuity of ion beam, the equation of motion and the Maxwell equations are considered. It is shown that the macroinstability is stabilized by the magnetic field in the Z-direction. It was found that the most dangerous instability for the problem of the propagation of ion beam was able to be atabilized by using a rotating ion layer. (Kato, T.)
Simplified propagation of standard uncertainties
International Nuclear Information System (INIS)
Shull, A.H.
1997-01-01
An essential part of any measurement control program is adequate knowledge of the uncertainties of the measurement system standards. Only with an estimate of the standards'' uncertainties can one determine if the standard is adequate for its intended use or can one calculate the total uncertainty of the measurement process. Purchased standards usually have estimates of uncertainty on their certificates. However, when standards are prepared and characterized by a laboratory, variance propagation is required to estimate the uncertainty of the standard. Traditional variance propagation typically involves tedious use of partial derivatives, unfriendly software and the availability of statistical expertise. As a result, the uncertainty of prepared standards is often not determined or determined incorrectly. For situations meeting stated assumptions, easier shortcut methods of estimation are now available which eliminate the need for partial derivatives and require only a spreadsheet or calculator. A system of simplifying the calculations by dividing into subgroups of absolute and relative uncertainties is utilized. These methods also incorporate the International Standards Organization (ISO) concepts for combining systematic and random uncertainties as published in their Guide to the Expression of Measurement Uncertainty. Details of the simplified methods and examples of their use are included in the paper
Fast Fourier single-pixel imaging via binary illumination.
Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang
2017-09-20
Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.
Comparative analysis of imaging configurations and objectives for Fourier microscopy.
Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid
2015-11-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.
Ballooning modes or Fourier modes in a toroidal plasma?
International Nuclear Information System (INIS)
Connor, J.W.; Taylor, J.B.
1987-01-01
The relationship between two different descriptions of eigenmodes in a torus is investigated. In one the eigenmodes are similar to Fourier modes in a cylinder and are highly localized near a particular rational surface. In the other they are the so-called ballooning modes that extend over many rational surfaces. Using a model that represents both drift waves and resistive interchanges the transition from one of these structures to the other is investigated. In this simplified model the transition depends on a single parameter which embodies the competition between toroidal coupling of Fourier modes (which enhances ballooning) and variation in frequency of Fourier modes from one rational surface to another (which diminishes ballooning). As the coupling is increased each Fourier mode acquires a sideband on an adjacent rational surface and these sidebands then expand across the radius to form the extended mode described by the conventional ballooning mode approximation. This analysis shows that the ballooning approximation is appropriate for drift waves in a tokamak but not for resistive interchanges in a pinch. In the latter the conventional ballooning effect is negligible but they may nevertheless show a ballooning feature. This is localized near the same rational surface as the primary Fourier mode and so does not lead to a radially extended structure
Propagation of the initial value perturbation in a cylindrical lined duct carrying a gas flow
Directory of Open Access Journals (Sweden)
Agneta M. BALINT
2013-03-01
Full Text Available For the homogeneous Euler equation linearized around a non-slipping mean flow andboundary conditions corresponding to the mass-spring-damper impedance, smooth initial dataperturbations with compact support are considered. The propagation of this type of initial dataperturbations in a straight cylindrical lined duct is investigated. Such kind of investigations is missingin the existing literature. The mathematical tools are the Fourier transform with respect to the axialspatial variable and the Laplace transform with respect to the time variable. The functionalframework and sufficient conditions are researched that the so problem be well-posed in the sense ofHadamard and the Briggs-Bers stability criteria can be applied.
Antenna design for propagating spin wave spectroscopy in ferromagnetic thin films
Zhang, Yan; Yu, Ting; Chen, Ji-lei; Zhang, You-guang; Feng, Jian; Tu, Sa; Yu, Haiming
2018-03-01
In this paper, we investigate the characteristics of antenna for propagating-spin-wave-spectroscopy (PSWS) experiment in ferromagnetic thin films. Firstly, we simulate the amplitude and phase distribution of the high-frequency magnetic field around antenna by high frequency structure simulator (HFSS). And then k distribution of the antenna is obtained by fast Fourier transformation (FFT). Furthermore, three kinds of antenna designs, i.e. micro-strip line, coplanar waveguide (CPW), loop, are studied and compared. How the dimension parameter of antenna influence the corresponding high-frequency magnetic field amplitude and k distribution are investigated in details.
DEFF Research Database (Denmark)
Chen, Yaohui; de Lasson, Jakob Rosenkrantz; Gregersen, Niels
2015-01-01
We derive and validate a set of coupled Bloch wave equations for analyzing the reflection and transmission properties of active semiconductor photonic crystal waveguides. In such devices, slow-light propagation can be used to enhance the material gain per unit length, enabling, for example......, the realization of short optical amplifiers compatible with photonic integration. The coupled wave analysis is compared to numerical approaches based on the Fourier modal method and a frequency domain finite element technique. The presence of material gain leads to the build-up of a backscattered field, which...
Propagation engineering in radio links design
Ghasemi, Abdollah; Ghasemi, Farshid
2013-01-01
Propagation Engineering in Radio Link Design covers the basic principles of radiowaves propagation in a practical manner. This fundamental understanding enables the readers to design radio links efficiently. This book elaborates on new achievements as well as recently developed propagation models. This is in addition to a comprehensive overview of fundamentals of propagation in various scenarios. It examines theoretical calculations, approaches and applied procedures needed for radio links design. The authors study and analysis of the main propagation phenomena and its mechanisms based on the recommendations of International Telecommunications Union, (ITU). The book has been organized in 9 chapters and examines the role of antennas and passive reflectors in radio services, propagation mechanisms related to radar, satellite, short distance, broadcasting and trans-horizon radio links, with two chapters devoted to radio noise and main parameters of radio link design. The book presents some 278 illustration...
Progress in front propagation research
Fort, Joaquim; Pujol, Toni
2008-08-01
We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined.
Singularities formation, structure, and propagation
Eggers, J
2015-01-01
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.
Progress in front propagation research
Energy Technology Data Exchange (ETDEWEB)
Fort, Joaquim [Departament de Fisica, Campus de Montilivi, Universitat de Girona, 17071 Girona, Catalonia (Spain); Pujol, Toni [Departament de Mecanica, Campus de Montilivi, Universitat de Girona, 17071 Girona, Catalonia (Spain)
2008-08-15
We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined.
Front propagation in flipping processes
International Nuclear Information System (INIS)
Antal, T; Ben-Avraham, D; Ben-Naim, E; Krapivsky, P L
2008-01-01
We study a directed flipping process that underlies the performance of the random edge simplex algorithm. In this stochastic process, which takes place on a one-dimensional lattice whose sites may be either occupied or vacant, occupied sites become vacant at a constant rate and simultaneously cause all sites to the right to change their state. This random process exhibits rich phenomenology. First, there is a front, defined by the position of the leftmost occupied site, that propagates at a nontrivial velocity. Second, the front involves a depletion zone with an excess of vacant sites. The total excess Δ k increases logarithmically, Δ k ≅ ln k, with the distance k from the front. Third, the front exhibits ageing-young fronts are vigorous but old fronts are sluggish. We investigate these phenomena using a quasi-static approximation, direct solutions of small systems and numerical simulations
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
Fourier analysis of the parametric resonance in neutrino oscillations
International Nuclear Information System (INIS)
Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe
2009-01-01
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.
Spectrums Transform Operators in Bases of Fourier and Walsh Functions
Directory of Open Access Journals (Sweden)
V. V. Syuzev
2017-01-01
Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel
Some applications of Fourier's great discovery for beginners
International Nuclear Information System (INIS)
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency ω = 2π/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students should be familiar with this subject. A suitable device for demonstrating spectra of electrical signals is a digital storage oscilloscope. Spectra of various waveforms and of AM and FM signals are demonstrated, as well as AM signals from a broadcasting station. Changes in the signals filtered by frequency-selective circuits are seen by comparing the spectra of the input and output voltages. All the experiments are suitable for undergraduate laboratories and usable as classroom demonstrations. (paper)
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
On the Alignment of Shapes Represented by Fourier Descriptors
DEFF Research Database (Denmark)
Sjöstrand, Karl; Ericsson, Anders; Larsen, Rasmus
2006-01-01
The representation of shapes by Fourier descriptors is a time-honored technique that has received relatively little attention lately. Nevertheless, it has many benefits and is applicable for describing a range of medical structures in two dimensions. Delineations in medical applications often...... consist of continuous outlines of structures, where no information of correspondence between samples exist. In this article, we discuss an alignment method that works directly with the functional representation of Fourier descriptors, and that is optimal in a least-squares sense. With corresponding...... represented by common landmarks can be constructed in an automatic fashion. If the aligned Fourier descriptors are inverse transformed from the frequency domain to the spatial domain, a set of roughly aligned landmarks are obtained. The positions of these are then adjusted along the contour of the objects...
International conference Fourier Analysis and Pseudo-Differential Operators
Turunen, Ville; Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations
2014-01-01
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. This collection of 20 refereed articles is based on selected talks given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
Fixed-point error analysis of Winograd Fourier transform algorithms
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Special affine Fourier transformation in frequency-domain
Cai, L. Z.
2000-11-01
Special affine Fourier transformation (SAFT) can be considered as an extension of the fractional Fourier transformation (FRT) and the most general linear mapping in phase space. A general formula for SAFT in frequency-domain is derived, which gives a direct relationship between the input and output spatial frequency spectra of a light field. It shows that the SAFT has similar and symmetric feature in both space- and frequency-domains. As its special cases, Collins formula in frequency-domain, the spatial frequency representations of the almost-FRT, almost-Fresnel and almost-Fourier transformations are explicitly obtained. These formulae may provide a tool for investigating the performance of a lossless optical system including small deformations in both domains in a unified way within the framework of linear theory.
Shape Recognition in Presence of Occlusion from Fourier Plane Processing
Pohit, Mausumi; Goel, Alpana
2011-10-01
A new technique for recognition of objects in presence of occlusion is presented in this paper. The Fourier spectrum of a partially occluded shape differs from that of the whole object shape thereby decreasing the 2D correlation between two images. The present method is based on 1D correlation of Fourier Spectrum slices taken from the 2D Fourier Transform of the reference and the test object. For small occlusion, some of the slices are affected depending on the nature of occlusion. Responses of the rest of the slices are unaffected. This study shows that this method not only identify the object in presence of occlusion but at the same time has good discrimination capability.
Fourier domain asymmetric cryptosystem for privacy protected multimodal biometric security
Choudhury, Debesh
2016-04-01
We propose a Fourier domain asymmetric cryptosystem for multimodal biometric security. One modality of biometrics (such as face) is used as the plaintext, which is encrypted by another modality of biometrics (such as fingerprint). A private key is synthesized from the encrypted biometric signature by complex spatial Fourier processing. The encrypted biometric signature is further encrypted by other biometric modalities, and the corresponding private keys are synthesized. The resulting biometric signature is privacy protected since the encryption keys are provided by the human, and hence those are private keys. Moreover, the decryption keys are synthesized using those private encryption keys. The encrypted signatures are decrypted using the synthesized private keys and inverse complex spatial Fourier processing. Computer simulations demonstrate the feasibility of the technique proposed.
A Temporal Millimeter Wave Propagation Model for Tunnels Using Ray Frustum Techniques and FFT
Directory of Open Access Journals (Sweden)
Choonghyen Kwon
2014-01-01
Full Text Available A temporal millimeter wave propagation model for tunnels is presented using ray frustum techniques and fast Fourier transform (FFT. To directly estimate or simulate effects of millimeter wave channel properties on the performance of communication services, time domain impulse responses of demodulated signals should be obtained, which needs rather large computation time. To mitigate the computational burden, ray frustum techniques are used to obtain frequency domain transfer function of millimeter wave propagation environment and FFT of equivalent low pass signals are used to retrieve demodulated waveforms. This approach is numerically efficient and helps to directly estimate impact of tunnel structures and surfaces roughness on the performance of millimeter wave communication services.
Chen, Jilei; Stueckler, Tobias; Zhang, Youguang; Zhao, Weisheng; Yu, Haiming; Chang, Houchen; Liu, Tao; Wu, Mingzhong; Liu, Chuanpu; Liao, Zhimin; Yu, Dapeng; Fert Beijing research institute Team; Colorado State University Team; Peking University Collaboration
Magnonics offers a new way to transport information using spin waves free of charge current and could lead to a new paradigm in the area of computing. Forward volume (FV) mode spin wave with perpendicular magnetized configuration is suitable for spin wave logic device because it is free of non-reciprocity effect. Here, we study FV mode spin wave propagation in YIG thin film with an ultra-low damping. We integrated differently designed antenna i.e., coplanar waveguide and micro stripline with different dimensions. The k vectors of the spin waves defined by the design of the antenna are calculated using Fourier transform. We show FV mode spin wave propagation results by measuring S12 parameter from vector network analyzer and we extract the group velocity of the FV mode spin wave as well as its dispersion relations.
Guided Wave Propagation Study on Laminated Composites by Frequency-Wavenumber Technique
Tian, Zhenhua; Yu, Lingyu; Leckey, Cara A. C.
2014-01-01
Toward the goal of delamination detection and quantification in laminated composites, this paper examines guided wave propagation and wave interaction with delamination damage in laminated carbon fiber reinforced polymer (CFRP) composites using frequency-wavenumber (f-kappa) analysis. Three-dimensional elastodynamic finite integration technique (EFIT) is used to acquire simulated time-space wavefields for a CFRP composite. The time-space wavefields show trapped waves in the delamination region. To unveil the wave propagation physics, the time-space wavefields are further analyzed by using two-dimensional (2D) Fourier transforms (FT). In the analysis results, new f-k components are observed when the incident guided waves interact with the delamination damage. These new f-kappa components in the simulations are experimentally verified through data obtained from scanning laser Doppler vibrometer (SLDV) tests. By filtering the new f-kappa components, delamination damage is detected and quantified.
PROPAGATION-BASED CONSTRAINT SOLVER IN IMS
Directory of Open Access Journals (Sweden)
I.Ol. Blynov
2012-03-01
Full Text Available Article compiling the main ideas of creating propagation-based constraint solver, theoretical basis of constraint programming and its implementation in IMS (Insertion Modeling System
Neural network construction via back-propagation
International Nuclear Information System (INIS)
Burwick, T.T.
1994-06-01
A method is presented that combines back-propagation with multi-layer neural network construction. Back-propagation is used not only to adjust the weights but also the signal functions. Going from one network to an equivalent one that has additional linear units, the non-linearity of these units and thus their effective presence is then introduced via back-propagation (weight-splitting). The back-propagated error causes the network to include new units in order to minimize the error function. We also show how this formalism allows to escape local minima
Terrestrial propagation of long electromagnetic waves
Galejs, Janis; Fock, V A
2013-01-01
Terrestrial Propagation of Long Electromagnetic Waves deals with the propagation of long electromagnetic waves confined principally to the shell between the earth and the ionosphere, known as the terrestrial waveguide. The discussion is limited to steady-state solutions in a waveguide that is uniform in the direction of propagation. Wave propagation is characterized almost exclusively by mode theory. The mathematics are developed only for sources at the ground surface or within the waveguide, including artificial sources as well as lightning discharges. This volume is comprised of nine chapte
Propagation handbook for wireless communication system design
Crane, Robert K
2003-01-01
PROPAGATION PHENOMENA AFFECTING WIRELESS SYSTEMS Types of SystemsDesign Criteria Antenna Considerations Propagation Effects Propagation Models Model Verification Statistics and RiskList of Symbols ReferencesPROPAGATION FUNDAMENTALSMaxwell's EquationsPlane Waves Spherical Waves Reflection and Refraction Geometrical OpticsRay TracingScalar Diffraction Theory Geometrical Theory of Diffraction List of Symbols ReferencesABSORPTION Molecular Absorption Absorption on a Slant Path ACTS Statistics List of Symbols ReferencesREFRACTION Ray BendingPath Delay ScintillationList of Symbols ReferencesATTENUAT
Stochastic and epistemic uncertainty propagation in LCA
DEFF Research Database (Denmark)
Clavreul, Julie; Guyonnet, Dominique; Tonini, Davide
2013-01-01
When performing uncertainty propagation, most LCA practitioners choose to represent uncertainties by single probability distributions and to propagate them using stochastic methods. However, the selection of single probability distributions appears often arbitrary when faced with scarce information...... manner and apply it to LCA. A case study is used to show the uncertainty propagation performed with the proposed method and compare it to propagation performed using probability and possibility theories alone.Basic knowledge on the probability theory is first recalled, followed by a detailed description...
Aspects of HF radio propagation
Directory of Open Access Journals (Sweden)
Stephane Saillant
2009-06-01
Full Text Available
radio systems. From the point of view Working Group 2 of the COST 296 Action, interest lies with effects associated
with propagation via the ionosphere of signals within the HF band. Several aspects are covered in this paper:
a The directions of arrival and times of flight of signals received over a path oriented along the trough have
been examined and several types of propagation effects identified. Of particular note, combining the HF observations
with satellite measurements has identified the presence of irregularities within the floor of the trough that
result in propagation displaced from the great circle direction. An understanding of the propagation effects that
result in deviations of the signal path from the great circle direction are of particular relevance to the operation
of HF radiolocation systems.
b Inclusion of the results from the above mentioned measurements into a propagation model of the northerly
ionosphere (i.e. those regions of the ionosphere located poleward of, and including, the mid-latitude trough
and the use of this model to predict the coverage expected from transmitters where the signals impinge on the
northerly ionosphere
Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.
Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda
2017-09-13
This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.
From Fourier Series to Rapidly Convergent Series for Zeta(3)
DEFF Research Database (Denmark)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions on this such ......The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions...
A Fourier Optical Model for the Laser Doppler Velocimeter
DEFF Research Database (Denmark)
Lading, Lars
1972-01-01
The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. ldquodifferential moderdquo and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions. The particles are represented...... filtering ability vanishes as the aperture size converges towards zero. The results based on fourier optics are compared with the rough estimates obtainable by using the "antenna formular" for heterodyning (ArΩr≈λ2)....
Fourier analysis of the aerodynamic behavior of cup anemometers
International Nuclear Information System (INIS)
Pindado, Santiago; Pérez, Imanol; Aguado, Maite
2013-01-01
The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force. (paper)
Fourier transform infrared spectra applications to chemical systems
Ferraro, John R
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
Neutron Diffraction Measurements using the Cairo Fourier Diffractometer facility
International Nuclear Information System (INIS)
Maayof, R.M.A.; Elkady, A.S.
1999-01-01
The paper presents neutron diffraction investigations of different polycrystalline materials, performed at room temperature, using the Cairo Fourier Diffractometer Facility (CFDF),recently installed at one of the ET-RR-1 reactor horizontal channels. The neutron diffraction patterns were measured using the CFDF while its Fourier chopper was rotating with modulation frequency 136 KHz ;leading to-7us for the FWHM of the time resolution function. The diffraction patterns were analysed by a special program (MRIA), adapted especially to the CFDF conditions. The reliability of the C DF results was confirmed from comparison of the measured diffraction patterns with similar ones obtained from neutron and x-ray measurements
Quantitative aspects of near-infrared Fourier transform Raman spectroscopy
Walder, F. T.; Smith, M. J.
Three fundamental behaviors of vibrational spectroscopy data manipulation routinely associated with Fourier transform infrared (FTIR) spectroscopy are evaluated for near-infrared (NIR) Fourier transform Raman spectroscopy. Spectral reproducibility, spectral subtraction and sensitivity are examined relative to the NIR FT-Raman experiment. Quantitative predictive ability is compared for identical sets of samples containing mixtures of the three xylene isomers. Partial least-squares analysis is used to compare predictive ability. IR performance is found to be better than Raman, though the potential for method development using NIR FT-Raman is shown to be quite promising.
On L1-convergence of Walsh-Fourier series
Directory of Open Access Journals (Sweden)
C. W. Onneweer
1978-01-01
Full Text Available Let G denote the dyadic group, which has as its dual group the Walsh(-Paley functions. In this paper we formulate a condition for functions in L1(G which implies that their Walsh-Fourier series converges in L1(G-norm. As a corollary we obtain a Dini-Lipschitz-type theorem for L1(G convergence and we prove that the assumption on the L1(G modulus of continuity in this theorem cannot be weakened. Similar results also hold for functions on the circle group T and their (trigonometric Fourier series.
Application of Fourier analysis to multispectral/spatial recognition
Hornung, R. J.; Smith, J. A.
1973-01-01
One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
An introduction to Lebesgue integration and Fourier series
Wilcox, Howard J
1995-01-01
This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects.The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate
Neural network signature verification using Haar wavelet and Fourier transforms
McCormack, Daniel K. R.; Brown, B. M.; Pedersen, John F.
1993-08-01
This paper discusses the use of neural network's for handwritten signature verification using the Fourier and Haar wavelet transforms as methods of encoding signature images. Results will be presented that discuss a neural network's ability to generalize to unseen signatures using wavelet encoded training data. These results will be discussed with reference to both Backpropagation networks and Cascade-Correlation networks. Backpropagation and Cascade- Correlation networks are used to compare and contrast the generalization ability of Haar wavelet and Fourier transform encoded signature data.
Fourier transform infrared spectra applications to chemical systems
Ferraro, John R
1978-01-01
Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems presents the chemical applications of the Fourier transform interferometry (FT-IR).The book contains discussions on the applications of FT-IR in the fields of chromatography FT-IR, polymers and biological macromolecules, emission spectroscopy, matrix isolation, high-pressure interferometry, and far infrared interferometry. The final chapter is devoted to the presentation of the use of FT-IR in solving national technical problems such as air pollution, space exploration, and energy related subjects.Researc
Energy Technology Data Exchange (ETDEWEB)
Rodriguez Z, G.; Rodriguez V, R.; Luna C, A. [Centro de Investigaciones en Optica, Apartado Postal 948, 37000 Leon, Guanajuato (Mexico)
1999-05-01
The introduction of tomography as an advanced topic to be included in a Fourier optics course at graduated level is proposed. It is shown a possible presentation sequence which features the use of typical Fourier optics techniques, as well as some well known opto-mechanical devices as examples. Finally, a simplified apparatus which illustrates the central Fourier theorem as an experimental project on Fourier optics is described. Corresponding experimental results are also shown. (Author)
Fourier analysis and signal processing by use of the Moebius inversion formula
Reed, Irving S.; Yu, Xiaoli; Shih, Ming-Tang; Tufts, Donald W.; Truong, T. K.
1990-01-01
A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.
Front propagation in a regular vortex lattice: Dependence on the vortex structure.
Beauvier, E; Bodea, S; Pocheau, A
2017-11-01
We investigate the dependence on the vortex structure of the propagation of fronts in stirred flows. For this, we consider a regular set of vortices whose structure is changed by varying both their boundary conditions and their aspect ratios. These configurations are investigated experimentally in autocatalytic solutions stirred by electroconvective flows and numerically from kinematic simulations based on the determination of the dominant Fourier mode of the vortex stream function in each of them. For free lateral boundary conditions, i.e., in an extended vortex lattice, it is found that both the flow structure and the front propagation negligibly depend on vortex aspect ratios. For rigid lateral boundary conditions, i.e., in a vortex chain, vortices involve a slight dependence on their aspect ratios which surprisingly yields a noticeable decrease of the enhancement of front velocity by flow advection. These different behaviors reveal a sensitivity of the mean front velocity on the flow subscales. It emphasizes the intrinsic multiscale nature of front propagation in stirred flows and the need to take into account not only the intensity of vortex flows but also their inner structure to determine front propagation at a large scale. Differences between experiments and simulations suggest the occurrence of secondary flows in vortex chains at large velocity and large aspect ratios.
Front propagation in a regular vortex lattice: Dependence on the vortex structure
Beauvier, E.; Bodea, S.; Pocheau, A.
2017-11-01
We investigate the dependence on the vortex structure of the propagation of fronts in stirred flows. For this, we consider a regular set of vortices whose structure is changed by varying both their boundary conditions and their aspect ratios. These configurations are investigated experimentally in autocatalytic solutions stirred by electroconvective flows and numerically from kinematic simulations based on the determination of the dominant Fourier mode of the vortex stream function in each of them. For free lateral boundary conditions, i.e., in an extended vortex lattice, it is found that both the flow structure and the front propagation negligibly depend on vortex aspect ratios. For rigid lateral boundary conditions, i.e., in a vortex chain, vortices involve a slight dependence on their aspect ratios which surprisingly yields a noticeable decrease of the enhancement of front velocity by flow advection. These different behaviors reveal a sensitivity of the mean front velocity on the flow subscales. It emphasizes the intrinsic multiscale nature of front propagation in stirred flows and the need to take into account not only the intensity of vortex flows but also their inner structure to determine front propagation at a large scale. Differences between experiments and simulations suggest the occurrence of secondary flows in vortex chains at large velocity and large aspect ratios.
Radio Channel Modelling Using Stochastic Propagation Graphs
DEFF Research Database (Denmark)
Pedersen, Troels; Fleury, Bernard Henri
2007-01-01
In this contribution the radio channel model proposed in [1] is extended to include multiple transmitters and receivers. The propagation environment is modelled using random graphs where vertices of a graph represent scatterers and edges model the wave propagation between scatterers. Furthermore...
Diagnostics for the ATA beam propagation experiments
International Nuclear Information System (INIS)
Fessenden, T.J.; Atchison, W.L.; Barletta, W.A.
1981-11-01
This report contains a discussion of the diagnostics required for the beam propagation experiment to be done with the ATA accelerator. Included are a list of the diagnostics needed; a description of the ATA experimental environment; the status of beam diagnostics available at Livermore including recent developments, and a prioritized list of accelerator and propagation diagnostics under consideration or in various stages of development
Content Propagation in Online Social Networks
Blenn, N.
2014-01-01
This thesis presents methods and techniques to analyze content propagation within online social networks (OSNs) using a graph theoretical approach. Important factors and different techniques to analyze and describe content propagation, starting from the smallest entity in a network, representing a
The ACTS propagation terminal delivery and support
Stutzman, Warren L.
1993-01-01
Viewgraphs on the Advanced Communications Technology Satellite (ACTS) propagation terminal delivery and support are included. Topics covered include: the ACTS propagation terminal (APT) development program; terminal overview; physical units; test results; status of terminals and schedule; shipping cartons; and site support.
Topology optimization of wave-propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....
Uncertainty Propagation in an Ecosystem Nutrient Budget.
New aspects and advancements in classical uncertainty propagation methods were used to develop a nutrient budget with associated error for a northern Gulf of Mexico coastal embayment. Uncertainty was calculated for budget terms by propagating the standard error and degrees of fr...
Transhorizon Radiowave Propagation due to Evaporation Dueting
Indian Academy of Sciences (India)
waves to propagate beyond the horizon. Over the years, much research has been undertaken to explain the mecha- nism of radiowave propagation in evaporation ducts. Background Theory. The lowest part of the earth's atmosphere is called the tropo- sphere. Typically, the troposphere extends from the surface of the.
In vitro propagation of Irvingia gabonensis
African Journals Online (AJOL)
GREGO
2007-04-16
Apr 16, 2007 ... Full-grown plantlets were obtained and work is in progress on mass propagation. ... subsequent mass propagation to produce seedlings for farmers, and to improve food security and ... Shooting and rooting were observed, and full grown plantlets were obtained. ¼ MS +0.2 mg KIN. +0.1 mg NAA. Rooting ...
Diagnostics for the ATA beam propagation experiments
Energy Technology Data Exchange (ETDEWEB)
Fessenden, T.J.; Atchison, W.L.; Barletta, W.A.
1981-11-01
This report contains a discussion of the diagnostics required for the beam propagation experiment to be done with the ATA accelerator. Included are a list of the diagnostics needed; a description of the ATA experimental environment; the status of beam diagnostics available at Livermore including recent developments, and a prioritized list of accelerator and propagation diagnostics under consideration or in various stages of development.
A vector model for error propagation
Energy Technology Data Exchange (ETDEWEB)
Smith, D.L.; Geraldo, L.P.
1989-03-01
A simple vector model for error propagation, which is entirely equivalent to the conventional statistical approach, is discussed. It offers considerable insight into the nature of error propagation while, at the same time, readily demonstrating the significance of uncertainty correlations. This model is well suited to the analysis of error for sets of neutron-induced reaction cross sections. 7 refs., 1 fig.
Fourier transform distribution function of relaxation times; application and limitations
Boukamp, Bernard A.
2015-01-01
A simple Fourier transform (FT) method is presented for obtaining a Distribution Function of Relaxation Times (DFRT) for electrochemical impedance spectroscopy (EIS) data. By using a special data extension procedure the FT is performed over the range from -∞ ≤ lnω ≤ + ∞. The integration procedure is
Fourier coefficientes computation in two variables, a distributional version
Directory of Open Access Journals (Sweden)
Carlos Manuel Ulate R.
2015-01-01
Full Text Available The present article, by considering the distributional summations of Euler-Maclaurin and a suitable choice of the distribution, results in repre- sentations for the Fourier coefficients in two variables are obtained. These representations may be used for the numerical evaluation of coefficients.
Multipliers for the absolute Euler summability of Fourier series
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
(Math. Sci.), Vol. 111, No. 2, May 2001, pp. 203–219. Printed in India. Multipliers for the absolute Euler summability of Fourier series. PREM CHANDRA. School of Studies in Mathematics, Vikram University, Ujjain 456 010, India. MS received 30 December 1999; revised 30 October 2000. Abstract. In this paper, the author ...
Non-spectral fractal measures with Fourier frames
Lai, Chun-Kit; Wang, Yang
2015-01-01
We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. By doing so, we demonstrate the first singular fractal measure which has only finitely many mutually orthogonal exponentials (and hence it does not admit any exponential orthonormal bases), but it still admits Fourier frames.
Fourier transform infrared spectroscopic estimation of crystallinity in ...
Indian Academy of Sciences (India)
Wintec
quartz in rock samples and estimate the mining quality of quartz mineral, which is substantiated by calculating the crystallinity index. ... procedure which can be used to estimate the distribution of quartz in various rocks for mining purpose. ... coal was reported by several workers (Heaney et al. 1994). Fourier transform ...
Bilaterally symmetric Fourier approximations of the skull outlines of ...
Indian Academy of Sciences (India)
Unknown
[Sengupta P D, Sengupta D and Ghosh P 2005 Bilaterally symmetric Fourier approximations of the skull outlines of temnospondyl amphibians and their ... The outlines of the vertebrate skulls are variable and they help in recognizing the ..... Carrol R L 1988 Vertebrate paleontology and evolution (New York: Freeman) pp 698.
From Fourier Series to Rapidly Convergent Series for Zeta(3)
DEFF Research Database (Denmark)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions on this such ...
Coupling of column liquid chromatography and Fourier transform infrared spectrometry
Somsen, G.W; Gooijer, C; Velthorst, N.H; Brinkman, U.A Th
1998-01-01
This paper provides an extensive overview of the literature on the coupling of column liquid chromatography (LC) and Fourier transform infrared spectrometry (FT-IR). Flow-cell-based FT-IR detection and early solvent-elimination interfaces for LC-FT-IR are discussed in brief. A comprehensive
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit ...
Application of Migration Velocity Using Fourier Transform Approach ...
African Journals Online (AJOL)
Application of velocity by Fourier transform to process 3-D unmigrated seismic sections has been carried out in Fabi Field, Niger Delta – Nigeria. Usually, all seismic events (sections) are characterized by spikes or noise (random or coherent), multiples and shear waves so that when a seismic bed is dipping, the apparent ...
Fourier-transform infrared spectroscopic studies of dithia ...
Indian Academy of Sciences (India)
Unknown
limited region 1000–1150 cm–1.10 Therefore, in the present paper we report and analyse Fourier-trans- form infrared (FT-IR) spectra of S2TPP and its chemically prepared cation. 2. Experimental. Dithia tetraphenyl porphyrine was received from. Professor A L Verma as a gift and used without fur- ther purification. However ...
Grating-assisted superresolution of slow waves in Fourier space
DEFF Research Database (Denmark)
Thomas, N. Le; Houdré, R.; Frandsen, Lars Hagedorn
2007-01-01
with a high numerical aperture Fourier space imaging set-up. A high-resolution spectroscopy of the far-field emission diagram allows us to accurately and efficiently determine the dispersion curve and the group-index dispersion of planar photonic waveguides operating in the slow light regime....
Properties of the Simpson discrete fourier transform | Singh ...
African Journals Online (AJOL)
The Simpson discrete Fourier transform (SDFT) and its inverse are transformations relating the time and frequency domains. In this paper we state and prove the important properties of shift, circular convolution, conjugation, time reversal and Plancherel's theorem. In addition, we provide an alternative representation of the ...
Fourier transform infrared spectroscopic estimation of crystallinity in ...
Indian Academy of Sciences (India)
Wintec
Fourier transform infrared spectroscopic estimation of crystallinity in SiO2 based rocks. BHASKAR J SAIKIA. †. , G PARTHASARATHY* and N C SARMAH. †. National Geophysical Research Institute, Council of Scientific and Industrial Research, Hyderabad 500 007, India. †. Department of Physics, Dibrugarh University, ...
Grid-Independent Compressive Imaging and Fourier Phase Retrieval
Liao, Wenjing
2013-01-01
This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem. Many situations in optics, medical imaging and signal processing call…
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.
Fourier transform infrared microspectroscopy as a diagnostic tool for ...
Indian Academy of Sciences (India)
Fourier transform infrared (FTIR) microspectroscopy can be considered to be a fast and non-invasive tool for distinguishing between normal and cancerous cells and tissues without the need for laborious and invasive sampling procedures. Gastric samples from four patients (age, 65±2 years) were analysed. Samples were ...
A new analytical solution to the diffusion problem: Fourier series ...
African Journals Online (AJOL)
This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.
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...
Synthetic aperture ultrasound Fourier beamformation using virtual sources
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2016-01-01
An efficient Fourier beamformation algorithm is presented for multistatic synthetic aperture ultrasound imaging using virtual sources (FBV). The concept is based on the frequency domain wavenumber algorithm from radar and sonar and is extended to a multi-element transmit/receive configuration using...
Overcoming Spurious Regression Using time-Varying Fourier ...
African Journals Online (AJOL)
Non-stationary time series data have been traditionally analyzed in the frequency domain by assuming constant amplitudes regardless of the timelag. A new approach called time-varying amplitude method (TVAM) is presented here. Oscillations are analyzed for changes in the magnitude of Fourier Coefficients which are ...
Embedding relations connected with strong approximation of Fourier ...
Indian Academy of Sciences (India)
ing only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl. 11(4) (2008) 749–756] which is a generalization of Tikhonov's results [Anal. Math. 31 (2005) 183–194]. We also ...
Novel properties of the Fourier decomposition of the sinogram
International Nuclear Information System (INIS)
Edholm, P.R.; Lewitt, R.M.; Lindholm, B.
1986-01-01
The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency ω (continuous) and angular harmonic number n (discrete). For absolute value of ω large, the Fourier coefficients on the line n=kω of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed
Free Sixteen Harmonic Fourier Series Web App with Sound
Ruiz, Michael J.
2018-01-01
An online HTML5 Fourier synthesizer app is provided that allows students to manipulate sixteen harmonics and construct periodic waves. Students can set the amplitudes and phases for each harmonic, seeing the resulting waveforms and hearing the sounds. Five waveform presets are included: sine, triangle, square, ramp (sawtooth), and pulse train. The…
The RC Circuit: An Approach with Fourier Transforms
Indian Academy of Sciences (India)
In this article we shall mathematically analyse the Resistor-Capacitor (RC) circuit with the help of Fourier transforms(FT). This very general technique gives us a lot of insight intosolving first order differential equations with source terms dependingon time. In itself, the RC circuit is by far the mostcommonplace entity in modern ...
Fourier beamformation of multistatic synthetic aperture ultrasound imaging
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2015-01-01
A new Fourier beamformation (FB) algorithm is presented for multistatic synthetic aperture ultrasound imaging. It can reduce the number of computations by a factor of 20 compared to conventional Delay-and-Sum (DAS) beamformers. The concept is based on the wavenumber algorithm from radar and sonar...
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 ...
The linogram algorithm and direct fourier method with linograms
International Nuclear Information System (INIS)
Edholm, P.R.
1990-01-01
This text is an attempt to describe the linogram algorithm based on a somewhat simplified mathematical description of the algorithm which is also more similar to the actual digital implementation. Another algorithm with linograms, which may be called a direct fourier method is also presented. (K.A.E.)
Education and Utopia: Robert Owen and Charles Fourier
Leopold, David
2011-01-01
The aims of education, and the appropriate means of realising them, are a recurring preoccupation of utopian authors. The utopian socialists Robert Owen (1771-1858) and Charles Fourier (1772-1837) both place human nature at the core of their educational views, and both see education as central to their wider objective of social and political…
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 ...
Multipliers for the Absolute Euler Summability of Fourier Series
Indian Academy of Sciences (India)
In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with multipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.
L1-convergence of complex double Fourier series
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
L1-convergence of complex double Fourier series. KULWINDER KAUR, S S BHATIA and BABU RAM. ∗. School of Mathematics and Computer Applications, Thapar Institute of Engineering and Technology, Post Box No. 32, Patiala 147 004, India. ∗. Department of Mathematics, Maharshi Dayanand University, Rohtak, India.
Fourier-transform Infrared Characterization of Kaolin, Granite ...
African Journals Online (AJOL)
Fourier-transform Infrared Characterization of Kaolin, Granite, Bentonite and Barite. ... Diazonium salts at the peak region frequency of 3200-3100cm-1, organic substance at peak region of 2900-2700cm-1, by comparing the spectra obtained with those ... Keywords: characterization; clays; infrared; minerals; spectroscopy ...
Optimal Fourier Inversion in Semi-analytical Option Pricing
R. Lord (Roger); Ch. Kahl
2006-01-01
textabstractAt the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane
From Fourier Series to Rapidly Convergent Series for Zeta(3)
DEFF Research Database (Denmark)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions...
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
Holograms; security holograms; optical security; extended fractional Fourier transforms. PACS Nos 42.40.-i; 42.40. ... cost-effective scheme for the development of security hologram, we noticed that two reference beams holography [10] can ..... couragement, support and for permission to publish this work. They wish to thank.
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
Construction of a pulsed nozzle fourier transform microwave ...
Indian Academy of Sciences (India)
Administrator
Construction of a pulsed nozzle fourier transform microwave spectrometer to study the lithium bond. A P TIWARI 1, B J MUKKADA 1, E ARUNAN 1 and P C MATHIAS 2. 1Department of Inorganic and Physical Chemistry, Indian Institute of. Science, Bangalore 560 012, India. 2Sophisticated Instruments Facility, Indian Institute ...
Discrete frequency identification using the HP 5451B Fourier analyser
International Nuclear Information System (INIS)
Holland, L.; Barry, P.
1977-01-01
The frequency analysis by the HP5451B discrete frequency Fourier analyser is studied. The advantages of cross correlation analysis to identify discrete frequencies in a background noise are discussed in conjuction with the elimination of aliasing and wraparound error. Discrete frequency identification is illustrated by a series of graphs giving the results of analysing 'electrical' and 'acoustical' white noise and sinusoidal signals [pt
Quantifying complex shapes: elliptical fourier analysis of octocoral sclerites.
Carlo, Joseph M; Barbeitos, Marcos S; Lasker, Howard R
2011-06-01
Species descriptions of most alcyonacean octocorals rely heavily on the morphology of sclerites, the calcium carbonate spicules embedded in the soft tissue. Sclerites provide taxonomic characters for species delineation but require qualitative descriptions, which introduce ambiguities in recognizing morphological features. Elliptical Fourier analysis of the outline of sclerites was used to quantify the morphology of eight species of gorgoniid octocoral in the genus Pseudopterogorgia. Sclerites from one to seven colonies of each species were compared. Scaphoids and spindles were examined separately; rods and octoradiates were excluded from the analyses because of their morphologic similarity across all species. Discriminant analysis of elliptical Fourier descriptors (EFDs) was used to determine whether the elliptical Fourier analysis could be used to identify the specimens. Sclerites were highly variable even within a single colony. Correct species assignments of individual sclerites were greater than 50% for both scaphoids and spindles. Species assignments based on averages of the EFDs for each colony approached 90%. Elliptical Fourier analysis quantifies morphological differences between species and measures colony variance in sclerite size and shape among colonies and species. Phylogenetic analysis based on EFDs did not capture monophyletic groups. The quantification of complex shapes such as sclerites provides an important tool in alpha taxonomy but may be less useful in phylogenetic analyses.
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.
An introduction to non-harmonic Fourier series
Young, Robert M
2001-01-01
An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.
Quaternion Fourier transforms for signal and image processing
Ell, Todd A; Sangwine, Stephen J
2014-01-01
Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book's attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.
Bilaterally symmetric Fourier approximations of the skull outlines of ...
Indian Academy of Sciences (India)
Unknown
2000; Steyer 2003) to study shape changes through onto- geny. However, in all the cases only the complete or nearly- ..... (iii) Energy-phase summary of Fourier coefficients. After analysing several samples we find the following .... luga-land in northern Russia; Ann. Soc. Pal. Russie 8 49–76. Romer A S 1947 Review of the ...
Fourier ptychographic microscopy at telecommunication wavelengths using a femtosecond laser
Ahmed, Ishtiaque; Alotaibi, Maged; Skinner-Ramos, Sueli; Dominguez, Daniel; Bernussi, Ayrton A.; de Peralta, Luis Grave
2017-12-01
We report the implementation of the Fourier Ptychographic Microscopy (FPM) technique, a phase retrieval technique, at telecommunication wavelengths using a low-coherence ultrafast pulsed laser source. High quality images, near speckle-free, were obtained with the proposed approach. We demonstrate that FPM can also be used to image periodic features through a silicon wafer.
A functional program for the Fast Fourier Transform
Vries, F.-J. de
This paper is written as a contribution to the Parallel Reduction Machine Project. Its purpose is to present a functional program for a well-known application of the fundamental algorithmic method Fast Fourier Transform for multiplication of polynomials. This in order to verify experimentally two
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
Abstract. This paper describes a simple method for making dual beam encoded ex- tended 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 ...
International Nuclear Information System (INIS)
Kroon, John J.; Becker, Peter A.
2014-01-01
Accreting black hole sources show a wide variety of rapid time variability, including the manifestation of time lags during X-ray transients, in which a delay (phase shift) is observed between the Fourier components of the hard and soft spectra. Despite a large body of observational evidence for time lags, no fundamental physical explanation for the origin of this phenomenon has been presented. We develop a new theoretical model for the production of X-ray time lags based on an exact analytical solution for the Fourier transform describing the diffusion and Comptonization of seed photons propagating through a spherical corona. The resulting Green's function can be convolved with any source distribution to compute the associated Fourier transform and time lags, hence allowing us to explore a wide variety of injection scenarios. We show that thermal Comptonization is able to self-consistently explain both the X-ray time lags and the steady-state (quiescent) X-ray spectrum observed in the low-hard state of Cyg X-1. The reprocessing of bremsstrahlung seed photons produces X-ray time lags that diminish with increasing Fourier frequency, in agreement with the observations for a wide range of sources
Accelerated radial Fourier-velocity encoding using compressed sensing
International Nuclear Information System (INIS)
Hilbert, Fabian; Han, Dietbert
2014-01-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Accelerated radial Fourier-velocity encoding using compressed sensing.
Hilbert, Fabian; Wech, Tobias; Hahn, Dietbert; Köstler, Herbert
2014-09-01
Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. We imaged the femoral artery of healthy volunteers with ECG-triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6-fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity distribution in vessels in the order of the voxel size. Thus
Accelerated radial Fourier-velocity encoding using compressed sensing
Energy Technology Data Exchange (ETDEWEB)
Hilbert, Fabian; Han, Dietbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wech, Tobias; Koestler, Herbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wuerzburg Univ. (Germany). Comprehensive Heart Failure Center (CHFC)
2014-10-01
Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity
Lightninig Induced Sferics Correlated with Whistler Propagation
Compston, A. J.; Said, R.; Linscott, I.; Inan, U. S.; Parrot, M.
2011-12-01
Lightning discharges generate broadband electromagnetic pulses, known as sferics, that efficiently propagate through the Earth-ionosphere waveguide. Some sferic energy can escape the Earth-ionosphere waveguide and propagate in a whistler mode, enabled by Earth's magnetic field, through the ionosphere. In this presentation, we correlate lightning discharge location and time data from the National Lightning Detection Network (NLDN) in the United States with burst mode electric field measurements from the DEMETER spacecraft to quantify and model whistler propagation through the ionosphere. Using the International Reference Ionosphere (IRI) model for electron density and the International Geomagnetic Reference Field (IGRF) model for magnetic field, we compare measured propagation with the Full Wave Method (FWM) finite element numerical code developed by N. G. Lehtinen and U. S. Inan. While a few studies have analyzed whistler propagation through the ionosphere using spacecraft measurements, spacecraft data have yet to be compared with the FWM as we have done here.
Propagation of SLF/ELF electromagnetic waves
Pan, Weiyan
2014-01-01
This book deals with the SLF/ELF wave propagation, an important branch of electromagnetic theory. The SLF/ELF wave propagation theory is well applied in earthquake electromagnetic radiation, submarine communication, thunderstorm detection, and geophysical prospecting and diagnostics. The propagation of SLF/ELF electromagnetic waves is introduced in various media like the earth-ionospheric waveguide, ionospheric plasma, sea water, earth, and the boundary between two different media or the stratified media. Applications in the earthquake electromagnetic radiation and the submarine communications are also addressed. This book is intended for scientists and engineers in the fields of radio propagation and EM theory and applications. Prof. Pan is a professor at China Research Institute of Radiowave Propagation in Qingdao (China). Dr. Li is a professor at Zhejiang University in Hangzhou (China).
Seismic waves modeling with the Fourier pseudo-spectral method on massively parallel machines.
Klin, Peter
2015-04-01
The Fourier pseudo-spectral method (FPSM) is an approach for the 3D numerical modeling of the wave propagation, which is based on the discretization of the spatial domain in a structured grid and relies on global spatial differential operators for the solution of the wave equation. This last peculiarity is advantageous from the accuracy point of view but poses difficulties for an efficient implementation of the method to be run on parallel computers with distributed memory architecture. The 1D spatial domain decomposition approach has been so far commonly adopted in the parallel implementations of the FPSM, but it implies an intensive data exchange among all the processors involved in the computation, which can degrade the performance because of communication latencies. Moreover, the scalability of the 1D domain decomposition is limited, since the number of processors can not exceed the number of grid points along the directions in which the domain is partitioned. This limitation inhibits an efficient exploitation of the computational environments with a very large number of processors. In order to overcome the limitations of the 1D domain decomposition we implemented a parallel version of the FPSM based on a 2D domain decomposition, which allows to achieve a higher degree of parallelism and scalability on massively parallel machines with several thousands of processing elements. The parallel programming is essentially achieved using the MPI protocol but OpenMP parts are also included in order to exploit the single processor multi - threading capabilities, when available. The developed tool is aimed at the numerical simulation of the seismic waves propagation and in particular is intended for earthquake ground motion research. We show the scalability tests performed up to 16k processing elements on the IBM Blue Gene/Q computer at CINECA (Italy), as well as the application to the simulation of the earthquake ground motion in the alluvial plain of the Po river (Italy).
Scaling analysis of affinity propagation
Furtlehner, Cyril; Sebag, Michèle; Zhang, Xiangliang
2010-06-01
We analyze and exploit some scaling properties of the affinity propagation (AP) clustering algorithm proposed by Frey and Dueck [Science 315, 972 (2007)]. Following a divide and conquer strategy we setup an exact renormalization-based approach to address the question of clustering consistency, in particular, how many cluster are present in a given data set. We first observe that the divide and conquer strategy, used on a large data set hierarchically reduces the complexity O(N2) to O(N(h+2)/(h+1)) , for a data set of size N and a depth h of the hierarchical strategy. For a data set embedded in a d -dimensional space, we show that this is obtained without notably damaging the precision except in dimension d=2 . In fact, for d larger than 2 the relative loss in precision scales such as N(2-d)/(h+1)d . Finally, under some conditions we observe that there is a value s∗ of the penalty coefficient, a free parameter used to fix the number of clusters, which separates a fragmentation phase (for ss∗ ) of the underlying hidden cluster structure. At this precise point holds a self-similarity property which can be exploited by the hierarchical strategy to actually locate its position, as a result of an exact decimation procedure. From this observation, a strategy based on AP can be defined to find out how many clusters are present in a given data set.
Correspondence propagation with weak priors.
Wang, Huan; Yan, Shuicheng; Liu, Jianzhuang; Tang, Xiaoou; Huang, Thomas S
2009-01-01
For the problem of image registration, the top few reliable correspondences are often relatively easy to obtain, while the overall matching accuracy may fall drastically as the desired correspondence number increases. In this paper, we present an efficient feature matching algorithm to employ sparse reliable correspondence priors for piloting the feature matching process. First, the feature geometric relationship within individual image is encoded as a spatial graph, and the pairwise feature similarity is expressed as a bipartite similarity graph between two feature sets; then the geometric neighborhood of the pairwise assignment is represented by a categorical product graph, along which the reliable correspondences are propagated; and finally a closed-form solution for feature matching is deduced by ensuring the feature geometric coherency as well as pairwise feature agreements. Furthermore, our algorithm is naturally applicable for incorporating manual correspondence priors for semi-supervised feature matching. Extensive experiments on both toy examples and real-world applications demonstrate the superiority of our algorithm over the state-of-the-art feature matching techniques.
Sonic Boom Pressure Signature Uncertainty Calculation and Propagation to Ground Noise
West, Thomas K., IV; Bretl, Katherine N.; Walker, Eric L.; Pinier, Jeremy T.
2015-01-01
The objective of this study was to outline an approach for the quantification of uncertainty in sonic boom measurements and to investigate the effect of various near-field uncertainty representation approaches on ground noise predictions. These approaches included a symmetric versus asymmetric uncertainty band representation and a dispersion technique based on a partial sum Fourier series that allows for the inclusion of random error sources in the uncertainty. The near-field uncertainty was propagated to the ground level, along with additional uncertainty in the propagation modeling. Estimates of perceived loudness were obtained for the various types of uncertainty representation in the near-field. Analyses were performed on three configurations of interest to the sonic boom community: the SEEB-ALR, the 69o DeltaWing, and the LM 1021-01. Results showed that representation of the near-field uncertainty plays a key role in ground noise predictions. Using a Fourier series based dispersion approach can double the amount of uncertainty in the ground noise compared to a pure bias representation. Compared to previous computational fluid dynamics results, uncertainty in ground noise predictions were greater when considering the near-field experimental uncertainty.
Failure propagation tests and analysis at PNC
International Nuclear Information System (INIS)
Tanabe, H.; Miyake, O.; Daigo, Y.; Sato, M.
1984-01-01
Failure propagation tests have been conducted using the Large Leak Sodium Water Reaction Test Rig (SWAT-1) and the Steam Generator Safety Test Facility (SWAT-3) at PNC in order to establish the safety design of the LMFBR prototype Monju steam generators. Test objectives are to provide data for selecting a design basis leak (DBL), data on the time history of failure propagations, data on the mechanism of the failures, and data on re-use of tubes in the steam generators that have suffered leaks. Eighteen fundamental tests have been performed in an intermediate leak region using the SWAT-1 test rig, and ten failure propagation tests have been conducted in the region from a small leak to a large leak using the SWAT-3 test facility. From the test results it was concluded that a dominant mechanism was tube wastage, and it took more than one minute until each failure propagation occurred. Also, the total leak rate in full sequence simulation tests including a water dump was far less than that of one double-ended-guillotine (DEG) failure. Using such experimental data, a computer code, LEAP (Leak Enlargement and Propagation), has been developed for the purpose of estimating the possible maximum leak rate due to failure propagation. This paper describes the results of the failure propagation tests and the model structure and validation studies of the LEAP code. (author)
Underwater Acoustic Propagation in the Philippine Sea: Intensity Fluctuations
White, Andrew W.
In the spring of 2009, broadband transmissions from a ship-suspended source with a 284 Hz center frequency were received on a moored and navigated vertical array of hydrophones over a range of 107 km in the Philippine Sea. During a 60-hour period over 19 000 transmissions were carried out. The observed wavefront arrival structure reveals four distinct purely refracted acoustic paths: one with a single upper turning point near 80 m depth, two with a pair of upper turning points at a depth of roughly 300 m, and one with three upper turning points at 420 m. Individual path intensity, defined as the absolute square of the center frequency Fourier component for that arrival, was estimated over the 60-hour duration and used to compute scintillation index and log-intensity variance. Monte Carlo parabolic equation simulations using internal-wave induced sound speed perturbations obeying the Garrett-Munk internal-wave en- ergy spectrum were in agreement with measured data for the three deeper-turning paths but differed by as much as a factor of four for the near surface-interacting path. Estimates of the power spectral density and temporal autocorrelation function of intensity were attempted, but were complicated by gaps in the measured time-series. Deep fades in intensity were observed in the near surface-interacting path. Hypothesized causes for the deep fades were examined through further acoustic propagation modeling and analysis of various available oceanographic measurements.
Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.
Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong
2018-02-13
Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.
Spatial correlation in 3D MIMO channels using fourier coefficients of power spectrums
Nadeem, Qurrat-Ul-Ain
2015-03-01
In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for the standardized three-dimensional (3D) multiple-input multiple-output (MIMO) channel. This novel SCF is developed for a uniform linear array of antennas with non-isotropic antenna patterns. The proposed method resorts to the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials to obtain a closed-form expression for the SCF for arbitrary angular distributions and antenna patterns. The resulting expression depends on the underlying angular distributions and antenna patterns through the Fourier Series (FS) coefficients of power azimuth and elevation spectrums. The novelty of the proposed method lies in the SCF being valid for any 3D propagation environment. Numerical results validate the proposed analytical expression and study the impact of angular spreads on the correlation. The derived SCF will help evaluate the performance of correlated 3D MIMO channels in the future. © 2015 IEEE.
Bifurcations and chaos in convection taking non-Fourier heat-flux
Layek, G. C.; Pati, N. C.
2017-11-01
In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.
Network propagation in the cytoscape cyberinfrastructure.
Directory of Open Access Journals (Sweden)
Daniel E Carlin
2017-10-01
Full Text Available Network propagation is an important and widely used algorithm in systems biology, with applications in protein function prediction, disease gene prioritization, and patient stratification. However, up to this point it has required significant expertise to run. Here we extend the popular network analysis program Cytoscape to perform network propagation as an integrated function. Such integration greatly increases the access to network propagation by putting it in the hands of biologists and linking it to the many other types of network analysis and visualization available through Cytoscape. We demonstrate the power and utility of the algorithm by identifying mutations conferring resistance to Vemurafenib.
Pole solutions for flame front propagation
Kupervasser, Oleg
2015-01-01
This book deals with solving mathematically the unsteady flame propagation equations. New original mathematical methods for solving complex non-linear equations and investigating their properties are presented. Pole solutions for flame front propagation are developed. Premixed flames and filtration combustion have remarkable properties: the complex nonlinear integro-differential equations for these problems have exact analytical solutions described by the motion of poles in a complex plane. Instead of complex equations, a finite set of ordinary differential equations is applied. These solutions help to investigate analytically and numerically properties of the flame front propagation equations.
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.
Matrix-Vector Based Fast Fourier Transformations on SDR Architectures
Directory of Open Access Journals (Sweden)
Y. He
2008-05-01
Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.
Meso-optical Fourier transform microscope with double focusing
International Nuclear Information System (INIS)
Batusov, Yu.A.; Soroko, L.M.; Tereshchenko, V.V.
1992-01-01
The meso-optical Fourier transform microscope (MFTM) with double focusing for particle tracks of low ionization level in the nuclear emulsion is described. It is shown experimentally that this device enables one to get high concentration of information about the position of the particle track in the nuclear emulsion and thus to increase the signal-to-noise ratio. It is shown that spreading of the meso-optical image of the particle track in the sagittal section of the MFTM can be eliminated completely in the frame of the diffraction limit. The number of the additional degrees of freedom in this new MFTM system along depth coordinate is equal to 20 in comparison to single degree of freedom in the Fourier transform microscope of the direct observation. 10 refs.; 15 figs
Fourier-based magnetic induction tomography for mapping resistivity
International Nuclear Information System (INIS)
Puwal, Steffan; Roth, Bradley J.
2011-01-01
Magnetic induction tomography is used as an experimental tool for mapping the passive electromagnetic properties of conductors, with the potential for imaging biological tissues. Our numerical approach to solving the inverse problem is to obtain a Fourier expansion of the resistivity and the stream functions of the magnetic fields and eddy current density. Thus, we are able to solve the inverse problem of determining the resistivity from the applied and measured magnetic fields for a two-dimensional conducting plane. When we add noise to the measured magnetic field, we find the fidelity of the measured to the true resistivity is quite robust for increasing levels of noise and increasing distances of the applied and measured field coils from the conducting plane, when properly filtered. We conclude that Fourier methods provide a reliable alternative for solving the inverse problem.
Discrete Fourier Transform Analysis in a Complex Vector Space
Dean, Bruce H.
2009-01-01
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
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.
Time-of-flight Fourier Spectrometry with UCN
Kulin, G. V.; Frank, A. I.; Goryunov, S. V.; Geltenbort, P.; Jentschel, M.; Bushuev, V. A.; Lauss, B.; Schmidt-Wellenburg, Ph.; Panzarella, A.; Fuchs, Y.
2016-09-01
The report presents the first experience of using a time-of-flight Fourier spectrometer of ultracold neutrons (UCN). The description of the spectrometer design and first results of its testing are presented. The results of the first experiments show that the spectrometer may be used for obtaining UCN energy spectra in the energy range of 60÷200 neV with a resolution of about 5 neV. The application of TOF Fourier spectrometry technique allowed us to obtain the energy spectra from the diffraction of monochromatic ultracold neutrons on a moving grating. Lines of 0, +1 and +2 diffraction orders were simultaneously recorded, which had previously been impossible to be done by other methods. These results have made it possible to make a comparison with the recent theoretical calculations based on the dynamical theory of neutron diffraction on a moving phase grating.
Jones matrix treatment for optical Fourier processors with structured polarization.
Moreno, Ignacio; Iemmi, Claudio; Campos, Juan; Yzuel, Maria J
2011-02-28
We present a Jones matrix method useful to analyze coherent optical Fourier processors employing structured polarization. The proposed method is a generalization of the standard classical optical Fourier transform processor, but considering vectorial spatial functions with two complex components corresponding to two orthogonal linear polarizations. As a result we derive a Jones matrix that describes the polarization output in terms of two vectorial functions defining respectively the structured polarization input and the generalized polarization impulse response. We apply the method to show and analyze an experiment in which a regular scalar diffraction grating is converted into equivalent polarization diffraction gratings by means of an appropriate polarization filtering. The technique is further demonstrated to generate arbitrary structured polarizations. Excellent experimental results are presented.
An introduction to Laplace transforms and Fourier series
Dyke, Phil
2014-01-01
Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...
Absolute Measurement of Tilts via Fourier Analysis of Interferograms
Toland, Ronald W.
2004-01-01
The Fourier method of interferogram analysis requires the introduction of a constant tilt into the interferogram to serve as a carrier signal for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.
A time Fourier analysis of zonal averaged ozone heating rates
Wang, P.-H.; Wu, M.-F.; Deepak, A.; Hong, S.-S.
1981-01-01
A time-Fourier analysis is presented for the yearly variation of the zonal averaged ozone heating rates in the middle atmosphere based on a model study. The ozone heating rates are determined by utilizing two-dimensional ozone distributions, the altitude and latitude, and by including the effect of the curved earth's atmosphere. In addition, assumptions are introduced to the yearly variations of the ozone distributions due to the lack of sufficient existing ozone data. Among other results, it is shown that the first harmonic component indicates that the heating rates are completely out of phase between the northern and southern hemispheres. The second Fourier component shows a symmetric pattern with respect to the equator, as well as five distinct local extreme values of the ozone heating rate. The third harmonic component shows a pattern close to that of the first component except in the regions above 70 deg between 45-95 km in both hemispheres.
Spectrometer calibration for spectroscopic Fourier domain optical coherence tomography
Szkulmowski, Maciej; Tamborski, Szymon; Wojtkowski, Maciej
2016-01-01
We propose a simple and robust procedure for Fourier domain optical coherence tomography (FdOCT) that allows to linearize the detected FdOCT spectra to wavenumber domain and, at the same time, to determine the wavelength of light for each point of detected spectrum. We show that in this approach it is possible to use any measurable physical quantity that has linear dependency on wavenumber and can be extracted from spectral fringes. The actual values of the measured quantity have no importance for the algorithm and do not need to be known at any stage of the procedure. As example we calibrate a spectral OCT spectrometer using Doppler frequency. The technique of spectral calibration can be in principle adapted to of all kind of Fourier domain OCT devices. PMID:28018723
On frame properties for Fourier-like systems
DEFF Research Database (Denmark)
Christensen, Ole; Osgooei, Elnaz
2013-01-01
structure. An attractive class of frames is formed by letting the window functions be trigonometric polynomials, restricted to compact intervals. We prove, under weak conditions, that such systems generate a frame with a dual that is also generated by a trigonometric polynomial. For polynomial windows......, a result of this type does not hold. Throughout the paper the results are related to the well established theory for Gabor systems.......Fourier-like systems are formed by multiplying a class of exponentials with a set of window functions. Via the Fourier transform they are equivalent to shift-invariant systems. We present sufficient and easily verifiable conditions for such systems to form a frame with a dual frame having the same...
Fourier-positivity constraints on QCD dipole models
Directory of Open Access Journals (Sweden)
Bertrand G. Giraud
2016-09-01
Full Text Available Fourier-positivity (F-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position space r. They are Bessel transforms of positive transverse momentum dependent gluon distributions. Using mathematical F-positivity constraints on the limit r→0 behavior of the dipole amplitudes, we identify the common origin of the violation of F-positivity for various, however phenomenologically convenient, dipole models. It is due to the behavior r2+ϵ, ϵ>0 softer, even slightly, than color transparency. F-positivity seems thus to conflict with the present dipole formalism when it includes a QCD running coupling constant α(r.
Fractional fourier-based filter for denoising elastograms.
Subramaniam, Suba R; Hon, Tsz K; Georgakis, Apostolos; Papadakis, George
2010-01-01
In ultrasound elastography, tissue axial strains are obtained through the differentiation of axial displacements. However, the application of the gradient operator amplifies the noise present in the displacement rendering unreadable axial strains. In this paper a novel denoising scheme based on repeated filtering in consecutive fractional Fourier transform domains is proposed for the accurate estimation of axial strains. The presented method generates a time-varying cutoff threshold that can accommodate the discrete non-stationarities present in the displacement signal. This is achieved by means of a filter circuit which is composed of a small number of ordinary linear low-pass filters and appropriate fractional Fourier transforms. We show that the proposed method can improve the contrast-to-noise ratio (CNR(e)) of the elastogram outperforming conventional low-pass filters.
Group-based sparse representation for Fourier ptychography microscopy
Zhang, Yongbing; Cui, Ze; Zhang, Jian; Song, Pengming; Dai, Qionghai
2017-12-01
Fourier ptychography microscopy (FPM), which employs alternative projection between spatial and Fourier domains to stitch low-resolution images captured under angularly varying illumination, reconstructs one image with high-resolution and wide field of view (FOV) to bypass the limitation of the space-bandwidth product (SBP) of the traditional optical system. However, system noises such as pupil aberrations, LEDs misalignment and so on, are inevitably introduced in the process of capturing low-resolution images. To address this problem, we propose a new method to insert the Group-based sparse representation (GSR) into the convergence-related metric of FPM as the regularization term in this paper. We have carried out the experiments over both synthetic and real captured images, and the results demonstrate that the proposed method is able to have promising performance while inhibiting the noises efficiently.
High resolution integral holography using Fourier ptychographic approach.
Li, Zhaohui; Zhang, Jianqi; Wang, Xiaorui; Liu, Delian
2014-12-29
An innovative approach is proposed for calculating high resolution computer generated integral holograms by using the Fourier Ptychographic (FP) algorithm. The approach initializes a high resolution complex hologram with a random guess, and then stitches together low resolution multi-view images, synthesized from the elemental images captured by integral imaging (II), to recover the high resolution hologram through an iterative retrieval with FP constrains. This paper begins with an analysis of the principle of hologram synthesis from multi-projections, followed by an accurate determination of the constrains required in the Fourier ptychographic integral-holography (FPIH). Next, the procedure of the approach is described in detail. Finally, optical reconstructions are performed and the results are demonstrated. Theoretical analysis and experiments show that our proposed approach can reconstruct 3D scenes with high resolution.
Free sixteen harmonic Fourier series web app with sound
Ruiz, Michael J.
2018-03-01
An online HTML5 Fourier synthesizer app is provided that allows students to manipulate sixteen harmonics and construct periodic waves. Students can set the amplitudes and phases for each harmonic, seeing the resulting waveforms and hearing the sounds. Five waveform presets are included: sine, triangle, square, ramp (sawtooth), and pulse train. The program is free for non-commercial use and can also be downloaded for running offline.
Visible Imaging Fourier Transform Spectrometer: Design and Calibration
International Nuclear Information System (INIS)
Wishnow, E.H.; Wurtz, R.; Blais-Ouellette, S.; Cook, K.H.; Carr, D.; Lewis, I.; Grandmont, F.; Stubbs, C.W.
2002-01-01
We present details of the design, operation and calibration of an astronomical visible-band imaging Fourier transform spectrometer (IFTS). This type of instrument produces a spectrum for every pixel in the field of view where the spectral resolution is flexible. The instrument is a dual-input/dual-output Michelson interferometer coupled to the 3.5 meter telescope at the Apache Point Observatory. Imaging performance and interferograms and spectra from calibration sources and standard stars are discussed
On One Application of Fourier Analysis in Plastic Surgery
Rakhimov, Abdumalik; Zainuddin, Hishamuddin
In present paper, we discuss the spectral methods of measurement of the degree of speech and/or quality of sound by comparing the coefficient of performance indicators depending on energy distributions, ratio of energy of the fundamental tone and energy of overtones. Such a method is very efficient for string oscillation with different initial conditions and it is useful for justification of applications of Fourier analysis in plastic surgery in treatment of some medical diseases.
Vanishing dissipation limit for the Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2016-01-01
Roč. 14, č. 6 (2016), s. 1535-1551 ISSN 1539-6746 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : inviscid limit * compressible fluid * Navier–Stokes–Fourier system Subject RIV: BA - General Mathematics Impact factor: 1.425, year: 2016 http://intlpress.com/site/pub/pages/journals/items/cms/content/vols/0014/0006/a004/index.html
Dimension reduction for the full Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Březina, J.; Kreml, Ondřej; Mácha, Václav
2017-01-01
Roč. 19, č. 4 (2017), s. 659-683 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier–Stokes–Fourier system * dimension reduction * relative entropy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.106, year: 2016 https://link.springer.com/article/10.1007%2Fs00021-016-0301-6
10th International Conference on Progress in Fourier Transform Spectroscopy
Keresztury, Gábor; Kellner, Robert
1997-01-01
19 plenary lectures and 203 poster papers presented at the 10th International Conference of Fourier Transform Spectroscopy in Budapest 1995 give an overview on the state-of-the art of this technology and its wide range of applications. The reader will get information on any aspects of FTS including the latest instrumental developments, e.g. in diode array detection, time resolution FTS, microscopy and spectral mapping, double modulation and two-dimensional FTS.
Dimension reduction for the full Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Březina, J.; Kreml, Ondřej; Mácha, Václav
2017-01-01
Roč. 19, č. 4 (2017), s. 659-683 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier–Stokes–Fourier system * dimension reduction * relative entropy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.106, year: 2016 https://link. springer .com/article/10.1007%2Fs00021-016-0301-6
Fourier analysis of multi-tracer cosmological surveys
Abramo, L. Raul; Secco, Lucas F.; Loureiro, Arthur
2015-01-01
We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure. Our estimators can be used to simultaneously fit the matter power spectrum and the biases of the tracers - as well as redshift-space distortions (RSDs), non-Gaussianities (NGs), or any other effects that are manifested through differences between the clusterings of distinct species of tracers. Our estimators reduce to the one by Feld...
Neutron Fourier Diffractometer FSD for Internal Stress Analysis First Results
Aksenov, V L; Bokuchava, G D; Zhuravlev, V V; Kuzmin, E S; Bulkin, A P; Kudryashov, V A; Trounov, V A
2001-01-01
At the IBR-2 pulsed reactor (FLNP, JINR) a specialised instrument - neutron Fourier diffractometer FSD - intended for internal stress measurements in bulk materials is under construction. Internal stress studies by neutron diffraction has been successfully developed last years in leading neutron centres, including Dubna and Gatchina, due to several important advantages of this method in comparison with other techniques. In current work the operation principles and construction of the diffractometer, basic parameters and outcomes of test experiments are presented.
FTIS compact Fourier transform imaging spectrometer for remote sensing
Posselt, W.; Holota, K.; Tittel, H. O.; Rost, M.; Harnisch, B.
2017-11-01
The feasibility of a compact Fourier-Transform-Imaging-Spectrometer (FTIS) for small satellite remote sensing missions is currently being studied under ESA contract. Compared to classical hyperspectral imagers using dispersive spectrometers the major advantages of the FTIS is the compact optics module and the tolerable higher detector temperature, thus easing the instrument thermal design. The feasibility of this instrument concept will be demonstrated by breadboarding.
Approximation by weighted means of Walsh-Fourier series
Directory of Open Access Journals (Sweden)
F. Móricz
1996-01-01
Full Text Available We study the rate of approximation to functions in Lp and, in particular, in Lip(α,p by weighted means of their Walsh-Fourier series, where α>0 and 1≤p≤∞. For the case p=∞, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0,1. We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.
Lacunary Fourier series and a qualitative uncertainty principle for ...
Indian Academy of Sciences (India)
Since Ff vanishes on an open set, by Lemma 2.1, Ff vanishes identically. It follows that Trace(π( f )) is zero for π ∈ ˆG. Next, notice that any translate of f has lacunary Fourier series. If g varies in a small enough neighborhood of the identity in G, then applying the above argument to the trans- lated function g f (x) = f (gx) we ...
Fast Fourier transform analysis of rotor-bearing systems
Choy, K. C.; Gunter, E. J.; Allaire, P. E.
1978-01-01
Nonlinear transient analysis of rotor-bearing systems is becoming increasingly important in the analysis of modern-day rotating machinery to model such phenomena as oil film whirl. This paper develops an analysis technique incorporating modal analysis and fast Fourier transform techniques to analyze rotors with residual shaft bow and realistic nonlinear bearings. The technique is demonstrated on single-mass and three-mass rotor examples. Comparisons of the theoretical results with experimental data give excellent agreement.
Fourier expansions and multivariable Bessel functions concerning radiation programmes
International Nuclear Information System (INIS)
Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.
1996-01-01
The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)
Fourier transform profilometry by using digital dc subtraction
Wongjarern, J.; Widjaja, J.; Sangpech, W.; Thongdee, N.; Santisoonthornwat, P.; Traisak, O.; Chuamchaitrakool, P.; Meemon, P.
2014-06-01
A new method for eliminating unwanted background of Fourier transform profilometry (FTP) by using simple dc bias and background eliminations from the deformed grating images is proposed. The proposed method has an advantage over a conventional FTP in that the 3-D object profile can be accurately measured although original fundamental spectra are corrupted by a zeroth-order spectrum. Experimental verifications of the proposed method are presented.
Vanishing dissipation limit for the Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2016-01-01
Roč. 14, č. 6 (2016), s. 1535-1551 ISSN 1539-6746 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : inviscid limit * compressible fluid * Navier–Stokes–Fourier system Subject RIV: BA - General Mathematics Impact factor: 1.425, year: 2016 http://intlpress.com/site/pub/pages/ journals /items/cms/content/vols/0014/0006/a004/index.html
Fourier-Malliavin volatility estimation theory and practice
Mancino, Maria Elvira; Sanfelici, Simona
2017-01-01
This volume is a user-friendly presentation of the main theoretical properties of the Fourier-Malliavin volatility estimation, allowing the readers to experience the potential of the approach and its application in various financial settings. Readers are given examples and instruments to implement this methodology in various financial settings and applications of real-life data. A detailed bibliographic reference is included to permit an in-depth study. .
A Fourier space algorithm for solving quadratic assignment problems
Kondor, Risi
2010-01-01
The quadratic assignment problem (QAP) is a central problem in combinatorial optimization. Several famous computationally hard tasks, such as graph matching, partitioning, and the traveling salesman all reduce to special cases of the QAP. In this paper we propose a new approach to the QAP based on the theory of non–commutative Fourier analysis on the symmetric group. Specifically, we present a branch–and–bound algorithm that performs both the branching and the bound...