Showing papers on "Fourier transform published in 2002"
TL;DR: The method, experimental setup, data processing, and images are discussed and it is shown that this technique might be as powerful as other optical coherence tomography techniques in the ophthalmologic imaging field.
Abstract: We present what is to our knowledge the first in vivo tomograms of human retina obtained by Fourier domain optical coherence tomography. We would like to show that this technique might be as powerful as other optical coherence tomography techniques in the ophthalmologic imaging field. The method, experimental setup, data processing, and images are discussed.
1,067 citations
Book•
01 Jan 2002
TL;DR: In this paper, the authors present a model of polymer chains and the dynamics of dilute polymer solutions, including the Fourier Transform and the Delta Function. And they present a series of related works.
Abstract: Preface. Models of Polymer Chains. Thermodynamics of Dilute Polymer Solutions. Dynamics of Dilute Polymer Solutions. Thermodynamics and Dynamics of Semidilute Solutions. References. Further Readings. Appendix A1: Delta Function. Appendix A2: Fourier Transform. Appendix A3: Integrals. Appendix A4: Series. Index.
593 citations
TL;DR: A generic Fourier descriptor (GFD) is proposed to overcome the drawbacks of existing shape representation techniques by applying two-dimensional Fourier transform on a polar-raster sampled shape image.
Abstract: Shape description is one of the key parts of image content description for image retrieval. Most of the existing shape descriptors are usually either application dependent or non-robust, making them undesirable for generic shape description. In this paper, a generic Fourier descriptor (GFD) is proposed to overcome the drawbacks of existing shape representation techniques. The proposed shape descriptor is derived by applying two-dimensional Fourier transform on a polar-raster sampled shape image. The acquired shape descriptor is application independent and robust. Experimental results show that the proposed GFD outperforms common contour-based and region-based shape descriptors.
534 citations
TL;DR: In this article, the Fourier transform Raman (FT-Raman) and Fourier Transform Infrared (FTIR) spectra of polyvinylidene fluoride (PVDF) membranes with different porous structures were obtained by the phase inversion process using different casting solvents.
363 citations
01 Jan 2002
TL;DR: In this paper, the authors review the development and understanding of the nonlinear Fourier analysis of measured space and time series, based upon a generalization of linear Fourier Analysis referred to as the inverse scattering transform (IST) and its generalizations.
Abstract: Publisher Summary The Fourier transform has provided one of the most important mathematical tools for understanding the dynamics of linear wave trains that are presumed to be governed by linear partial differential equations with a well-defined dispersion relation. The aim of this chapter is to review the development and understanding of the nonlinear Fourier analysis of measured space and time series. The approach is based upon a generalization of linear Fourier analysis referred to as the inverse scattering transform (IST) and its generalizations. From a mathematical point of view, IST solves particular “integrable” nonlinear partial differential wave equations such as the Korteweg-de Vries (KdV), the nonlinear Schrodinger (NLS) and the Kadomtsev–Petviashvili (KP) equations. Because of the mathematical complexity of these theories of nonlinear wave propagation, one cannot expect to bridge all the physical possibilities for the analysis of nonlinear wave data in a single review. The chapter closes with a brief introduction to the application of the inverse scattering transform as a time series analysis tool.
357 citations
TL;DR: In this article, a stable, efficient approach to inverse Q filtering based on the theory of wavefield downward continuation is presented. But it is implemented in a layered manner, assuming a depth-dependent, layered-earth Q model.
Abstract: Stability and efficiency are two issues of general concern in inverse Q filtering. This paper presents a stable, efficient approach to inverse Q filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a depth-dependent, layered-earth Q model. For each individual constant Q layer, the seismic wavefield recorded at the surface is first extrapolated down to the top of the current layer and a constant Q inverse filter is then applied to the current layer. When extrapolating within the overburden, instead of applying wavefield downward continuation directly, a reversed, upward continuation system is solved to obtain a stabilized solution. Within the current constant Q layer, the amplitude compensation operator, which is a 2-D function of traveltime and frequency, is approximated optimally as the product of two 1-D functions depending, respectively, on time and frequency. The constant Q inverse filter that compensates simultaneously for phase and amplitude effects is then implemented efficiently in the Fourier domain.
303 citations
TL;DR: In this paper, the Fourier Transform and Discrete Fourier Analysis (DFT) are used to analyze the inner product spaces of the Daubechies Wavelet. But they do not consider the multiresolution analysis.
Abstract: 0. Inner Product Spaces. 1. Fourier Series. 2. The Fourier Transform. 3. Discrete Fourier Analysis. 4. Wavelet Analysis. 5. Multiresolution Analysis. 6. The Daubechies Wavelets. 7. Other Wavelet Topics. Appendix A. Technical Matters. Appendix B. Matlab Routines. Bibliography.
293 citations
TL;DR: In this paper, the quality factor of a dipole defect mode in free-standing membranes is expressed in terms of the Fourier transforms of its field components and the reduction in radiation loss can be achieved by suppressing the mode's wavevector components within the light cone.
Abstract: We express the quality factor of a mode in terms of the Fourier transforms of its field components and prove that the reduction in radiation loss can be achieved by suppressing the mode's wavevector components within the light cone. Although this is intuitively clear, our analytical proof gives us insight into how to achieve the Q factor optimization, without the mode delocalization. We focus on the dipole defect mode in free-standing membranes and achieve Q > 10/sup 4/, while preserving the mode volume of the order of one half of the cubic wavelength of light in the material. The derived expressions and conclusions can be used in the optimization of the Q factor for any type of defect in planar photonic crystals.
272 citations
TL;DR: In this article, the DC-FFT algorithm was used to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy, and a set of general formulas of the frequency response function for the elastic field was derived and verified.
Abstract: The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green's, function for the cases with known Green's functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC- FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.
265 citations
TL;DR: In this article, the authors present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration, where the observation time is much greater than the time resolution of the individual data points.
Abstract: In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time resolution of the individual data points. We begin by reviewing the operational characteristics of Fourier transforms (FTs) of time series data, including power spectral statistics, discussing some of the differences between analyses of binned data, sampled data, and event data, and briefly discuss algorithms for calculating discrete Fourier transforms (DFTs) of very long time series. We then discuss the response of DFTs to periodic signals, and present techniques to recover Fourier amplitude "lost" during simple traditional analyses if the periodicities change frequency during the observation. These techniques include Fourier interpolation which allows us to correct the response for signals that occur between Fourier frequency bins. We then present techniques for estimating additional signal properties such as the signal's centroid and duration in time, the first and second derivatives of the frequency, the pulsed fraction, and an overall estimate of the significance of a detection. Finally, we present a recipe for a basic but thorough Fourier analysis of a time series for well-behaved pulsations.
250 citations
Journal Article•
TL;DR: Simulation results indicate that the energy of LFM signal will be collected effectively when the fractional order is matching with its modulation slope and in weak signals detection of underwater acoustic domain, the authors can get high anti-Doppler performance using the Fractional fourier transform algorithm.
Abstract: Based on the concept of the fractional fourier transform, its digital computation is given through computer simulation. In terms of linear frequency modulation (LFM) signal, the relation between fractional order and modulation slope is analyzed and the performance comparison with matched filter is given. Moreover, the separation of LFM signal and noise is realized in low signal-to-noise ratio through simulation. Simulation results indicate that the energy of LFM signal will be collected effectively when the fractional order is matching with its modulation slope. In weak signals detection of underwater acoustic domain, we can get high anti-Doppler performance using the Fractional fourier transform algorithm.
Proceedings Article•
01 Jan 2002
TL;DR: Different FDs are studied and a Java retrieval framework is built to compare shape retrieval performance using different FDs in terms of computation complexity, robustness, convergence speed and retrieval performance.
Abstract: Shape is one of the primary low level image features in Content Based Image Retrieval (CBIR). Many shape representations and retrieval methods exist. However, most of those methods either do not well capture shape features or are difficult to do normalization (making matching difficult). Among them, methods based Fourier descriptors (FDs) achieve both good representation (perceptually meaningful) and easy normalization. Besides, FDs are easy to derive and compact in terms of representation. Design of FDs focuses on how to derive Fourier invariants from Fourier coefficients and how to obtain Fourier coefficients from shape signatures. Different Fourier invariants and shape signatures have been exploited to derive FDs. In this paper, we study different FDs and build a Java retrieval framework to compare shape retrieval performance using different FDs in terms of computation complexity, robustness, convergence speed and retrieval performance. The retrieval performance of the different FDs is compared using a standard shape database.
Book•
06 Nov 2002TL;DR: In this paper, the z-dependence of the total field in Conical Diffraction is analyzed in terms of the axial ones of the Axial Field in the matrix notations.
Abstract: General Properties Basic Principles of the Differential Theory of Gratings Stacks of Gratings Fast Fourier Factorization (FFF) Method Maxwell Equations in Truncated Fourier Space Rigorous Coupled Wave (RCW) Method Coordinate Transformation Methods Gratings Made of Anisotropic Materials Crossed Gratings Photonic Crystals X-Ray Gratings Transmission Gratings Grating Couplers and Resonant Excitation of Guided Modes Differential Theory of Non-Periodic Media Fourier Factorization of Maxwell Equations in Nonlinear Optics Appendix I: The z-Dependence of the Total Field in Conical Diffraction Appendix II: Some Formulas about Toeplitz Matrices Appendix III: Expression of the Transverse Components of the Field in Terms of the Axial Ones Appendix IV: The Shooting Method in Matrix Notations List of Notations Index
TL;DR: In this paper, the authors have evaluated and adopted a spectral transform called the discrete cosine transform (DCT), which is a widely used transform for compression of digital images such as MPEG and JPEG, but its use for atmospheric spectral analysis has not yet received widespread attention.
Abstract: For most atmospheric fields, the larger part of the spatial variance is contained in the planetary scales. When examined over a limited area, these atmospheric fields exhibit an aperiodic structure, with large trends across the domain. Trying to use a standard (periodic) Fourier transform on regional domains results in the aliasing of largescale variance into shorter scales, thus destroying all usefulness of spectra at large wavenumbers. With the objective of solving this particular problem, the authors have evaluated and adopted a spectral transform called the discrete cosine transform (DCT). The DCT is a widely used transform for compression of digital images such as MPEG and JPEG, but its use for atmospheric spectral analysis has not yet received widespread attention. First, it is shown how the DCT can be employed for producing power spectra from two-dimensional atmospheric fields and how this technique compares favorably with the more conventional technique that consists of detrending the data before applying a periodic Fourier transform. Second, it is shown that the DCT can be used advantageously for extracting information at specific spatial scales by spectrally filtering the atmospheric fields. Examples of applications using data produced by a regional climate model are displayed. In particular, it is demonstrated how the 2D-DCT spectral decomposition is successfully used for calculating kinetic energy spectra and for separating mesoscale features from large scales.
TL;DR: It is demonstrated that the variables selected by the genetic algorithm are consistent with expert knowledge and a convincing application that the algorithm can select correct variables in an automated fashion.
KEMA1
TL;DR: The theory suggested enables one to quantitatively determine the refractive index of a weakly absorbing medium from x-ray intensity data measured in the near-field region.
Abstract: Phase-contrast x-ray computed tomography (CT) is an emerging imaging technique that can be implemented at third-generation synchrotron radiation sources or by using a microfocus x-ray source Promising results have recently been obtained in materials science and medicine At the same time, the lack of a mathematical theory comparable with that of conventional CT limits the progress in this field Such a theory is now suggested, establishing a fundamental relation between the three-dimensional Radon transform of the object function and the two-dimensional Radon transform of the phase-contrast projection A reconstruction algorithm is derived in the form of a filtered backprojection The filter function is given in the space and spatial-frequency domains The theory suggested enables one to quantitatively determine the refractive index of a weakly absorbing medium from x-ray intensity data measured in the near-field region The results of computer simulations are discussed
TL;DR: In this article, the Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR) was used for image current detection of coherently excited ICR motion, and the detected signal magnitude and peak shape may be understood from idealized behavior: single ion, zero-pressure, spatially uniform magnetic field, three-dimensional axial quadrupolar electrostatic trapping potential, and spatially, uniform resonant alternating electric field.
TL;DR: To solve the problem whereby weak targets are shadowed by the sidelobes of strong ones, a new implementation of the CLEAN technique is proposed based on filtering in the fractional Fourier domain, and strong moving targets and weak ones can be detected iteratively.
Abstract: As a useful signal processing technique, the fractional Fourier transform (FrFT) is largely unknown to the radar signal processing community. In this correspondence, the FrFT is applied to airborne synthetic aperture radar (SAR) slow-moving target detection. For airborne SAR, the echo from a ground moving target can be regarded approximately as a chirp signal, and the FrFT is a way to concentrate the energy of a chirp signal. Therefore, the FrFT presents a potentially effective technique for ground moving target detection in airborne SAR. Compared with the common Wigner-Ville distribution (WVD) algorithm, the FrFT is a linear operator, and will not be influenced by cross-terms even if multiple moving targets exist. Moreover, to solve the problem whereby weak targets are shadowed by the sidelobes of strong ones, a new implementation of the CLEAN technique is proposed based on filtering in the fractional Fourier domain. In this way strong moving targets and weak ones can be detected iteratively. This combined method is demonstrated by using raw clutter data combined with simulated moving targets.
01 Aug 2002
TL;DR: The letter defines an IFR estimation algorithm and theoretically analyzes it and is seen to be asymptotically optimal at the center of the data record for high signal-to-noise ratios.
Abstract: This letter introduces a two-dimensional bilinear mapping operator referred to as the cubic phase (CP) function. For first-, second-, or third-order polynomial phase signals, the energy of the CP function is concentrated along the frequency rate law of the signal. The function, thus, has an interpretation as a time-frequency rate representation. The peaks of the CP function yield unbiased estimates of the instantaneous (angular) frequency rate (IFR) and, hence, can be used as the basis for an IFR estimation algorithm. The letter defines an IFR estimation algorithm and theoretically analyzes it. The estimation is seen to be asymptotically optimal at the center of the data record for high signal-to-noise ratios. Simulations are provided to verify the theoretical claims.
TL;DR: In this paper, a new method for numerical simulation of potential flows with a free surface of two-dimensional fluid, based on combination of the conformal mapping and Fourier Transform is proposed.
Abstract: New method for numerical simulation of potential flows with a free surface of two-dimensional fluid, based on combination of the conformal mapping and Fourier Transform is proposed. The method is efficient for study of strongly nonlinear effects in gravity waves including wave breaking and formation of rogue waves.
TL;DR: In this article, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier Transform (DFT) is introduced, where the lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures.
Abstract: A concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible. The lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures where the dynamic range of the lifting coefficients can be controlled by proper choices of lifting factorizations. Split-radix FFT is used to illustrate the approach for the case of 2/sup N/-point FFT, in which case, an upper bound of the minimal dynamic range of the internal nodes, which is required by the reversibility of the transform, is presented and confirmed by a simulation. The transform can be implemented by using only bit shifts and additions but no multiplication. A method for minimizing the number of additions required is presented. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts. Finally, they are applied to noise reduction applications, where the IntFFT provides significantly improvement over the FxpFFT at low power and maintains similar results at high power.
TL;DR: In this paper, a combinatorial version of harmonic analysis on configuration spaces over Riemannian manifolds is developed based on the use of a lifting operator which can be considered as a kind of (combinatorial) Fourier transform in the configuration space analysis.
Abstract: We develop a combinatorial version of harmonic analysis on configuration spaces over Riemannian manifolds. Our constructions are based on the use of a lifting operator which can be considered as a kind of (combinatorial) Fourier transform in the configuration space analysis. The latter operator gives us a natural lifting of the geometry from the underlying manifold onto the configuration space. Properties of correlation measures for given states (i.e. probability measures) on configuration spaces are studied including a characterization theorem for correlation measures.
TL;DR: The eigenfunctions of the LCT are derived and it is shown that there are usually varieties of input functions that can cause the self-imaging phenomena in optics.
Abstract: The linear canonical transform (the LCT) is a useful tool for optical system analysis and signal processing. It is parameterized by a 2/spl times/2 matrix {a, b, c, d}. Many operations, such as the Fourier transform (FT), fractional Fourier transform (FRFT), Fresnel transform, and scaling operations are all the special cases of the LCT. We discuss the eigenfunctions of the LCT. The eigenfunctions of the FT, FRFT, Fresnel transform, and scaling operations have been known, and we derive the eigenfunctions of the LCT based on the eigenfunctions of these operations. We find, for different cases, that the eigenfunctions of the LCT also have different forms. When |a+d| 2, the eigenfunctions become the chirp multiplication and chirp convolution of self-similar functions (fractals). Besides, since many optical systems can be represented by the LCT, we can thus use the eigenfunctions of the LCT derived in this paper to discuss the self-imaging phenomena in optics. We show that there are usually varieties of input functions that can cause the self-imaging phenomena for an optical system.
01 Jan 2002
TL;DR: In this paper, Hardy-type operators are used to define fractional integrals on the line and one-sided maximal functions on the measure spaces. But they do not specify the number of numbers to be added to the fractional integral functions.
Abstract: Preface. Acknowledgments. Basic notation. 1. Hardy-type operators. 2. Fractional integrals on the line. 3. One-sided maximal functions. 4. Ball fractional integrals. 5. Potentials on RN. 6. Fractional integrals on measure spaces. 7. Singular numbers. 8. Singular integrals. 9. Multipliers of Fourier transforms. 10. Problems. References. Index.
TL;DR: In this article, a new algorithm to eliminate the error caused by this decaying component in the Fourier algorithm has been proposed, and three simplified methods are proposed to alleviate the computation burden.
Abstract: The impact of exponentially decaying direct component on the Fourier algorithm is theoretically investigated first in this paper. A new algorithm to eliminate the error caused by this decaying component in the Fourier algorithm has been proposed. Furthermore, three simplified methods are proposed to alleviate the computation burden. The performance of the Fourier algorithm improved with these methods along with the least error squares algorithm is evaluated using a simple network and a real power system modeled by EMTP. The evaluation results are presented and discussed.
TL;DR: In this paper, the authors compare several algorithms for successfully extending a nonperiodic function f(x) into the fog even when the analytic extension is singular, and the best third-kind extension requires singular value decomposition with iterative refinement but achieves accuracy close to machine precision.
Book•
08 Mar 2002
TL;DR: In this article, the authors present a mathematical representation of a sum of sinusoidal signals and their properties, including the Fourier Transform and the Spectrum, as well as its properties and properties.
Abstract: 1. Introduction. Mathematical Representation of Signals. Mathematical Representation of Systems. Thinking about Systems. 2. Sinusoids. Tuning Fork Experiment. Review of Sine and Cosine Functions. Sinusoidal Signals. Sampling and Plotting Sinusoids. Complex Exponentials and Phasors. Phasor Addition. Physics of the Tuning Fork. Time Signals: More Than Formulas. 3. Spectrum Representation. The Spectrum of a Sum of Sinusoids. Beat Notes. Periodic Waveforms. More Periodic Signals. Fourier Series Analysis and Synthesis. Time-Frequency Spectrum. Frequency Modulation: Chirp Signals. 4. Sampling and Aliasing. Sampling. Spectrum View of Sampling and Reconstruction. Strobe Demonstration. Discrete-to-Continuous Conversion. The Sampling Theorem. 5. FIR Filters. Discrete-Time Systems. The Running Average Filter. The General FIR Filter. Implementation of FIR Filters. Linear Time-Invariant (LTI) Systems. Convolution and LTI Systems. Cascaded LTI Systems. Example of FIR Filtering. 6. Frequency Response of FIR Filters. Sinusoidal Response of FIR Systems. Superposition and the Frequency Response. Steady State and Transient Response. Properties of the Frequency Response. Graphical Representation of the Frequency Response. Cascaded LTI Systems. Running-Average Filtering. Filtering Sampled Continuous-Time Signals. 7. z-Transforms. Definition of the z-Transform. The z-Transform and Linear Systems. Properties of the z-Transform. The z-Transform as an Operator. Convolution and the z-Transform. Relationship between the z -Domain and the w-Domain. Useful Filters. Practical Bandpass Filter Design. Properties of Linear Phase Filters. 8. IIR Filters. The General IIR Difference Equation. Time-Domain Response. System Function of an IIR Filter. Poles and Zeros. Frequency Response of an IIR Filter. Three Domains. The Inverse z-Transform and Some Applications. Steady-State Response and Stability. Second-Order Filters. Frequency Response of Second-Order IIR Filter. Example of an IIR Lowpass Filter. 9. Continuous-Time Signals and LTI Systems. Continuous-Time Signals. The Unit Impulse. Continuous-Time Systems. Linear Time-Invariant Systems. Impulse Responses of Basic LTI Systems. Convolution of Impulses. Evaluating Convolution Integrals. Properties of LTI Systems. Using Convolution to Remove Multipath Distortion. 10. The Frequency Response. The Frequency Response Function for LTI Systems. Response to Real Sinusoidal Signals. Ideal Filters. Application of Ideal Filters. Time-Domain or Frequency-Domain? 11. Continuous-Time Fourier Transform. Definition of the Fourier Transform. The Fourier Transform and the Spectrum. Existence and Convergence of the Fourier Transform. Examples of Fourier Transform Pairs. Properties of Fourier Transform Pairs. The Convolution Property. Basic LTI Systems. The Multiplication Property. Table of Fourier Transform Properties and Pairs. Using the Fourier Transform for Multipath Analysis. 12. Filtering, Modulation, and Sampling. Linear Time-Invariant Systems. Sinewave Amplitude Modulation. Sampling and Reconstruction. 13. Computing the Spectrum. Finite Fourier Sum. Too Many Fourier Transforms? Time-windowing. Analysis of a Sum of Sinusoids. Discrete Fourier Transform. Spectrum Analysis of Finite-Length Signals. Spectrum Analysis of Periodic Signals. The Spectrogram. The Fast Fourier Transform (FFT). Appendix A: Complex Numbers. Notation for Complex Numbers. Euler's Formula. Algebraic Rules for Complex Numbers. Geometric Views of complex Operations. Powers and Roots. Appendix B: Programming in MATLAB. MATLAB Help. Matrix Operations and Variables. Plots and Graphics. Programming Constructs. MATLAB Scripts. Writing a MATLAB Function. Programming Tips. Appendix C: Laboratory Projects. Introduction to MATLAB. Encoding and Decoding Touch-Tone Signals. Two Convolution GUIs. Appendix D: CD-ROM Demos. Index.
TL;DR: In this article, Kjartansson's constant-Q model is solved in the time domain using a new modeling algorithm based on fractional derivatives, which can handle complex geometries.
Abstract: Kjartansson’s constant-Q model is solved in the time-domain using a new modeling algorithm based on fractional derivatives. Instead of time derivatives of order 2, Kjartansson’s model requires derivatives of order 2y, with 0 < y < 1/2, in the dilatation-stress formulation. The derivatives are computed with the Griinwald-Letnikov and central-difference approximations, which are finite-difference extensions of the standard finite-difference operators for derivatives of integer order. The modeling uses the Fourier method to compute the spatial derivatives, and therefore can handle complex geometries. A synthetic cross-well seismic experiment illustrates the capabilities of this novel modeling algorithm.
Posted Content•
TL;DR: In this paper, the authors present three examples of ''unknown shift'' problems that can be solved efficiently on a quantum computer using the quantum Fourier transform and define the hidden coset problem, which generalizes the hidden shift problem and the hidden subgroup problem.
Abstract: Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to capture shift structure has received far less attention in the context of quantum computation.
In this paper, we present three examples of ``unknown shift'' problems that can be solved efficiently on a quantum computer using the quantum Fourier transform. We also define the hidden coset problem, which generalizes the hidden shift problem and the hidden subgroup problem. This framework provides a unified way of viewing the ability of the Fourier transform to capture subgroup and shift structure.
16 Nov 2002
TL;DR: The high-resolution direct numerical simulations of incompressible turbulence with numbers of grid points up to 40963 have been executed on the Earth Simulator, based on the Fourier spectral method, and yields an energy spectrum exhibiting a wide inertial subrange, in contrast to previous DNSs with lower resolutions, and therefore provides valuable data for the study of the universal features of turbulence at large Reynolds number.
Abstract: The high-resolution direct numerical simulations (DNSs) of incompressible turbulence with numbers of grid points up to 40963 have been executed on the Earth Simulator (ES). The DNSs are based on the Fourier spectral method, so that the equation for mass conservation is accurately solved. In DNS based on the spectral method, most of the computation time is consumed in calculating the three-dimensional (3D) Fast Fourier Transform (FFT), which requires huge-scale global data transfer and has been the major stumbling block that has prevented truly high-performance computing. By implementing new methods to efficiently perform the 3D-FFT on the ES, we have achieved DNS at 16.4 Tflops on 20483 grid points. The DNS yields an energy spectrum exhibiting a wide inertial subrange, in contrast to previous DNSs with lower resolutions, and therefore provides valuable data for the study of the universal features of turbulence at large Reynolds number.