Dimensional Fourier Research Articles

Longitudinal momentum densities in transverse plane for nucleons

We present a study of longitudinal momentum densities ($p^+ \rm densities$) in the transverse impact parameter space for $u$ and $d$ quarks in both unpolarized and transversely polarized nucleons by taking a two dimensional Fourier transform of the gravitational form factors with respect to the momentum transfer in the transverse direction. The gravitational form factors are obtained by the second moments of GPDs. Here we consider the GPDs of two different soft-wall models in AdS/QCD correspondence.

Some Applications of One and Two- Dimensional Fourier Series and Transforms

Some Applications of One and Two- Dimensional Fourier Series and Transforms

An Automated Algorithm for Measurement of Surgical Tip Excursion in Ultrasonic Vibration Using the Spatial 2-Dimensional Fourier Transform in an Optical Image

The International Electrotechnical Commission (IEC) has defined a standard IEC 61847 (First Edition, 1998) for characterization of ultrasonic surgical systems. This standard prescribes several methods for measurement of primary tip vibration excursion. The first method described in the standard uses an optical microscope and relies on the motion blur of a vibrating object as it is imaged at low frame rates (e.g. 30 Hz) of conventional video equipment. This is a widely used method, that predates the standard, in ultrasonic surgical instrument design, and it is one of the key parameters that surgeons who use these devices are aware of. It is relatively easily measured using a microscope system. Although this method is widespread, the accuracy of this method is highly dependent on multiple factors such as operator training, microscope lighting and modulation of surgical tip motion. It is also a manual and time consuming measurement such that a continuous measurement that describes dynamics at the scale of micro-seconds becomes impossible. Here we describe an algorithm to automate this measurement so that it can be done at high speed without operator training, reducing human error and operator variation. The algorithm derives from techniques used in motion blur estimation and reduction in the image processing literature. A 2 dimensional spatial Fourier transform is computed from the microscope image of an ultrasonically vibrating tip. A peak detection algorithm is used along with pre-processing to reduce noise. Separation of peaks in the Fourier domain is used to estimate tip excursion. We present data that shows an error of about 1% between manual and automated methods, when measurements are in the range of 300 microns and about 20% when the measurements are in the range of 30 microns.

Further Highly Hydroxylated Steroids from the Vietnamese Starfish Archaster typicus.

Eight highly hydroxylated steroids (1-8), including three new compounds as sodium salts of (24S)-5α-cholestane-3β,4β,5,6α,7β,8,14,15α,24-nonaol 6-sulfate (1), (24E)-5α-cholest-24-ene-26-yde-3β,6α,8,14,15α-pentaol 15-sulfate (2), and 5α-cholest-3β,6α,8,14,15α,24,25,26-octaol 15-sulfate (3), were isolated and elucidated from the methanol extract of the Vietnamese starfish Archaster typicus. The structure elucidation was done by spectroscopic methods including one and two dimensional (1D-, 2D-)NMR and Fourier transform ion cyclotron resonance (FT-ICR)-MS. The isolated compounds can be used as chemical markers for taxonomic identification of the starfish A. typicus.

The force function of two rigid celestial bodies in Delaunay–Andoyer variables

Two new expansions of the force function of two rigid celestial bodies of finite size and arbitrary shape are obtained in Delaunay–Andoyer variables with any degree of accuracy, in the form of a partial sum of an eight dimensional Fourier series. These expansions of the force function contain products of expressions for the momenta and Stokes constants in terms of sines and cosines, whose arguments are linear combinations of the Delaunay and Andoyer angular variables. These representations of the force function are compact and convenient for applications in various problems in celestial mechanics and astrodynamics.

FPGA Implementation of Underwater Image Enhancement using Nonlinear Filtering

Background/Motivation: Optical image captured by autonomous underwater vehicles need to be preprocessed as they suffer from various adversary underwater conditions and require low power devices such as FPGA. Methods/ Statistical Analysis: Underwater image degradation due to non uniform illumination is corrected by non linear filtering and is implemented in FPGA. Two dimensional Fast Fourier Transform (FFT) and its inverse along with logarithmic computation were implemented in FPGA as a part of filter implementation. One dimensional row wise and column wise FFT were computed first and then combined to form two dimensional FFT. Findings: FPGA’s can be used for implementing architectures that require high level parallelism such as image processing algorithms due to its inherent parallelism. Frequency based filtering method which is employed for preprocessing an underwater image successfully provided good histogram compared to the original one. Device utilization for implementing structure was estimated. Novel method of FFT implementation, its inverse and logarithmic computation was used in this work. The method can be applied to digital signal processing applications that can be implemented in FPGA. Application/Improvements: Automation of image preprocessing is required in unmanned underwater vehicles used for cable detection, navigation etc. These vehicles are to be provided with low power devices such as FPGAs for long run in underwater applications.

Sample Image Watermarking Study

Digital watermarking is the powerful solution to copyright protection of digital media. Digital watermarking is nothing but the process of embedding information as watermark, in to the digital content which is to be protected from unauthenticated copying. Digital watermarking is having some other applications as copyright protection, fingerprinting, owner identification etc. Application of watermarks is depending upon the types of watermarks classification such as fragile, robust, visible and invisible. The main requirements of digital watermarks are integrity, robustness and complexity. This paper presents the measure of recovered image quality in terms of signal to noise ratio and similarity ratio, two dimensional discrete cosines transform (DCT2) watermarking and two dimensional fast Fourier transform (FFT2) watermarking methods.

Approximated Pricing of Swaptions in General Interest Rate Models

The accurate pricing of swaption contracts is fundamental in interest rate markets, but modelling swaption payo may be relevant also beyond the standard setting. For example Basel III accords introduced the Credit Value Adjustment (C.V.A.) charge for over the counter contracts. It is interesting that for the most simple and popular kind of interest rate derivative, i.e. interest rate swap, the (unilateral) C.V.A. can be estimated as a portfolio of forward start European swaptions. We propose new bounds on the prices of European-style swaptions for a wide class of interest rate models. These bounds are computable whenever the joint characteristic function of the state variables is known in closed form or can be obtained numerically via some e cient procedure. In particular our lower bound involves the computation of one dimensional Fourier transform independently from the swap length.This allows a reduction of the computational cost, mainly when we have to price swaptions written on long-maturity swaps. We also show that methods put forward by Singleton and Umantsev [19] and Kim [13] are particular cases of our general framework. Indeed, we prove that their

Telugu Handwritten Isolated Characters Recognition using Two Dimensional Fast Fourier Transform and Support Vector Machine

Research in character recognition is an old application in the area of pattern recognition and has attracted many researchers during the last few decades. Handwritten character recognition (HCR) is of two types namely, Online and Offline. The recognition accuracy for HCR is less than 60% as per the literature survey. Also the non existence of standard database for Indian languages is another reason for motivation of this work. This work describes Offline HCR by extracting features using 2D FFT and using the support vector machines for Telugu documents. The best percentage recognition accuracy for Telugu handwritten characters is 71%.

A numerical model for the scattering of elastic waves from a non-axisymmetric defect in a pipe

Ultrasonic guided waves are used in the non-destructive testing of pipelines. This involves launching an elastic wave along the wall of the pipe and then capturing the returning wave scattered by a defect. Numerical study of wave scattering is often computationally expensive because the shortest wavelength is often very small compared to the size of the pipe in the ultrasonic frequency range. Furthermore, the number of the scattered wave modes from a non-axisymmetric defect in the pipe can be large and separation of these modes is difficult in a conventional finite element method. Accordingly, this article presents a model suitable for studying elastic wave propagation in waveguides with an arbitrary cross-section in the time and frequency domain. A weighted residual formulation is used to deliver an efficient hybrid numerical formulation, which is applied to a long pipeline containing a defect of arbitrary shape. The problem is solved first in the frequency domain and then extended to the time domain using an inverse Fourier transform. To separate the scattered wave modes in the time domain, a technique is proposed whereby measurement locations are arranged axially along the pipe and a two dimensional Fourier transform is used to present data in the wavenumber−frequency domain. This enables the separation of highly dispersive modes and the recovery of modal amplitudes. This has the potential to reveal more information about the characteristics of a defect and so may help in distinguishing between different type of defects, such a cracks or regions of corrosion, typically found in pipelines.

Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple

The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. A toolbox of functions for the computation of two dimensional Fourier transforms in polar coordinates with symbolic computer algebra (Maple) was developed. The implementation of the 2D Fourier transform in polar coordinates within the toolbox is a combination of two significantly simpler transforms. A modular approach is used along with the idea of lookup tables to help avoid the issue of indeterminate results when attempting to directly evaluate the transform. This concept helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

Implementation Oriened Phase based IRIS Recognition

Phase based image matching is one of the technique which is used for iris recognition. In this technique phase component present in Two dimensional (2D) Discrete Fourier Transform (DFT) of given images are used to determine similarity between two images. This technique can be used for developing applications such as access control system. But here problem is size of iris database. As number of individuals using such application will go on increasing, size of iris database will also go on increasing. This paper discusses the method which is used to address this problem. In this paper 2D Fourier phase code (2D FPC) is used to represent iris information. Instead of storing whole iris image, only 2D FPC is stored in the database which reduces size of required database significantly. This method is evaluated with CASIA iris image database (version 1.0). General Terms Pattern Recognition, Security.

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

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

Temperature Fluctuations in a Rectangular Nanochannel

We consider an incompressible fluid in a rectangular nanochannel. We solve numerically the three dimensional Fourier heat equation to get the steady solution for the temperature. Then we set and solve the Langevin equation for the temperature. We have developed equations in order to determine relaxation time of the temperature fluctuations, τT = 4.62 × 10−10 s. We have performed a spectral analysis of the thermal fluctuations, with the result that temporal correlations are in the one-digit ps range, and the thermal noise excites the thermal modes in the two-digit GHz range. Also we observe long-range spatial correlation up to more than half the size of the cell, 600 nm; the wave number, q, is in the 10 6 m −1 range. We have also determined two thermal relaxation lengths in the z direction: l1 = 1.18 nm and l2 = 9.86 nm.

Multipole Matrix of Green Function of Laplace Equation

Multipole matrix elements of Green function of Laplace equation are calculated. The multipole matrix elements of Green function in electrostatics describe potential on a sphere which is produced by a charge distributed on the surface of a different (possibly overlapping) sphere of the same radius. The matrix elements are defined by double convolution of two spherical harmonics with the Green function of Laplace equation. The method we use relies on the fact that in the Fourier space the double convolution has simple form. Therefore we calculate the multipole matrix from its Fourier transform. An important part of our considerations is simplification of the three dimensional Fourier transformation of general multipole matrix by its rotational symmetry to the one-dimensional Hankel transformation.

Case study of guided wave propagation in a one-side water-immersed steel plate

This paper presents a case study of guided waves in a steel plate with one side immersed in water. A hybrid sensing system that uses PZT as the guided wave actuator and a scanning laser vibrometer as the guided wave receiver is employed to acquire the time–space wavefield data. By using the two dimensional Fourier transform, the time–space wavefield is transformed into the frequency–wavenumber domain where the wave modes and the guided wave dispersion can be determined. The study confirms the existence of quasi-Scholte wave in the one-sidedly water-immersed plate in addition to fundamental guided waves. The results also show the quasi-Scholte wave can be directly generated and measured in the immersed plate at low frequencies using the present sensing system. Through pitch–catch sensing tests, the influence of water on guided wave propagation in the one-side water-immersed plate is investigated. It is seen that the water level affects the wave propagation time linearly and can be potentially used for estimation of water level in a container.

The Radiation Problem from a Vertical Short Dipole Antenna above Flat and Lossy Ground: Novel Formulation in the Spectral Domain with Closed – Form Analytical Solution in the High Frequency Regime

In this paper we consider the problem of radiation from a vertical short Hertzian dipole above flat lossy ground, which represents the well known in the literature Sommerfeld radiation problem. The problem is formulated in a novel spectral domain approach, and by inverse three dimensional Fourier transformation the expressions for the received electric and magnetic field in the physical space are derived as one dimensional integrals over the radial component of wavevector, in cylindrical coordinates. Subsequent use of the Stationary Phase Method in the high frequency regime yields closed form analytical solutions for the received EM field vectors, which coincide with the corresponding reflected EM field originating from the image point. In this way, we conclude that the so called in the literature space wave, i.e. line of sight plus reflected EM field, represents the total solution of the Sommerfeld problem in the high frequency regime, in which case the surface wave can be ignored. Finally, numerical results in the high frequency regime are presented in this paper, in comparison with corresponding numerical results based on Norton solution of the problem, i.e. space and surface waves.

Backward heat equations with locally lipschitz source

Let be in and let , be a locally Lipschitz function with respect to the variable and . In this article, we consider the following backward heat problem with a nonlinear heat source The problem is ill-posed in the sense of Hadamard. Hence a regularization is in order. We use the -dimensional Fourier transform to construct an approximate solution for this problem. We also prove error estimates for our problem and give comments on similar problems.

Computation of two-dimensional Fourier transforms for noisy band-limited signals

In this paper, the ill-posedness of computing the two dimensional Fourier transform is discussed. A regularized algorithm for computing the two dimensional Fourier transform of band-limited signals is presented. The convergence of the regularized Fourier series is studied and compared with the Fourier series by some examples.

Understanding domain symmetry in vanadium oxide phthalocyanine monolayers on Au (111)

Understanding the growth of organic semiconductors on solid surfaces is of key importance for the field of organic electronics. Non planar phthalocyanines have shown great promise in organic photovoltaic (OPV) applications, but little of the fundamental surface characterization to understand their structure and properties has been performed. Acquiring a deeper understanding of the molecule/substrate interaction in small molecule systems is a vital step in controlling structure/property relationships. Here we characterize the vanadium oxide phthalocyanine (VOPc)/Au (111) surface using a combination of low energy electron diffraction (LEED) and scanning tunneling microscopy (STM), obtaining complex diffraction patterns which can be understood using two dimensional fast Fourier transform (2D-FFT) analysis of STM images. These measurements reveal coexistence of three symmetrically equivalent in-plane orientations with respect to the substrate, each of which is imaged simultaneously within a single area. Combining scanning probe and diffraction measurements allows symmetrically related domains to be visualized and structurally analyzed, providing fundamental information useful for the structural engineering of non-planar phthalocyanine interfaces.