Analysis of some two dimensional functions using two dimensional Fourier transforms: Image reconstruction and physical significance

2017 ◽  
Author(s):  
G. K. Jagatheswari ◽  
Gajanan V Honnavar ◽  
Murugesan R
Keyword(s):  
Image Reconstruction ◽  
Fourier Transforms ◽  
Physical Significance ◽  
Two Dimensional

Data Acquisition and Processing of Weak Low-Frequency Magnetic Signals

2011 ◽  
Vol 65 ◽  
pp. 299-302 ◽  
Author(s):  
Shou Qiang Men ◽  
Christian Resagk
Keyword(s):  
Magnetic Field ◽  
Data Acquisition ◽  
Fourier Transforms ◽  
Low Frequency ◽  
Fast Fourier Transforms ◽  
Two Dimensional ◽  
Calibration System ◽  
Magnetic Field Sensors ◽  
Data Acquisition And Processing

A simple calibration system for magnetic field sensors was designed, and experiments were carried out to calibrate two-dimensional fluxgate sensors and a sensor ring composed of eight fluxgate sensors. Fast Fourier Transforms and trapezoidal numerical integrals were applied to deal with the raw signals. It is found that it is not suitable to apply fast Fourier Transforms only to deal with signals with several peaks close to each other, but trapezoidal numerical integrals should also be used in combination with the FFT method.

Diffraction by a half plane perpendicular to the distinguished axis of a gyrotropic medium (oblique incidence)

1981 ◽  
Vol 59 (3) ◽  
pp. 403-424 ◽  
Author(s):  
S. Przeździecki ◽  
R. A. Hurd
Keyword(s):  
Half Plane ◽  
Fourier Transforms ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Second Order ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Electromagnetic Plane Wave

An exact, closed form solution is found for the following half plane diffraction problem. (I) The medium surrounding the half plane is gyrotropic. (II) The scattering half plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The direction of propagation of the incident electromagnetic plane wave is arbitrary (skew) with respect to the edge of the half plane. The result presented is a generalization of a solution for the same problem with incidence normal to the edge of the half plane (two-dimensional case).The fundamental, distinctive feature of the problem is that it constitutes a boundary value problem for a system of two coupled second order partial differential equations. All previously solved electromagnetic diffraction problems reduced to boundary value problems for either one or two uncoupled second order equations. (Exception: the two-dimensional case of the present problem.) The problem is formulated in terms of the (generalized) scalar Hertz potentials and leads to a set of two coupled Wiener–Hopf equations. This set, previously thought insoluble by quadratures, yields to the Wiener–Hopf–Hilbert method.The three-dimensional solution is synthesized from appropriate solutions to two-dimensional problems. Peculiar waves of ghost potentials, which correspond to zero electromagnetic fields play an essential role in this synthesis. The problem is two-moded: that is, superpositions of both ordinary and extraordinary waves are necessary for the spectral representation of the solution. An important simplifying feature of the problem is that the coupling of the modes is purely due to edge diffraction, there being no reflection coupling. The solution is simple in that the Fourier transforms of the potentials are just algebraic functions. Basic properties of the solution are briefly discussed.

Scattering of a Rayleigh Wave by an Elastic Quarter Space

1985 ◽  
Vol 52 (3) ◽  
pp. 664-668 ◽  
Author(s):  
A. K. Gautesen
Keyword(s):  
Steady State ◽  
Surface Wave ◽  
Fourier Transforms ◽  
Two Dimensional ◽  
Rayleigh Surface Wave ◽  
State Problem ◽  
Free Surfaces ◽  
Linear Elastic ◽  
Quarter Space ◽  
Steady State Problem

We study the two-dimensional, steady-state problem of the scattering of waves in a homogeneous, isotropic, linear-elastic quarter space. We derive decoupled equations for the Fourier transforms of the normal and tangential displacements on the free surfaces. For incidence of a Rayleigh surface wave, we plot the amplitudes and phases of the surface waves reflected and transmitted by the corner. These curves were obtained numerically.

scholarly journals Analytic time-of-flight positron emission tomography reconstruction: two-dimensional case

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Gengsheng L. Zeng ◽  
Ya Li ◽  
Qiu Huang
Keyword(s):  
Positron Emission Tomography ◽  
Image Reconstruction ◽  
Iterative Algorithm ◽  
Emission Tomography ◽  
Two Dimensional ◽  
Profile Function ◽  
Positron Emission ◽  
Pet Image Reconstruction ◽  
2D Filter ◽  
Tof Pet

AbstractIn a positron emission tomography (PET) scanner, the time-of-flight (TOF) information gives us rough event position along the line-of-response (LOR). Using the TOF information for PET image reconstruction is able to reduce image noise. The state-of-the-art TOF PET image reconstruction uses iterative algorithms. Analytical image reconstruction algorithm exits for TOF PET which emulates the iterative Landweber algorithm. This paper introduces such an algorithm, focusing on two-dimensional (2D) reconstruction. The proposed algorithm is in the form of backprojection filtering, in which the backprojection is performed first, and then a 2D filter is applied to the backprojected image. For the list-mode data, the backprojection is carried out in the event-by-event fashion, and a profile function may be used along the projection LOR. The 2D filter depends on the TOF timing resolution as well as the backprojection profile function. In order to emulate the iterative algorithm effects, a Fourier-domain window function is suggested. This window function has a parameter, k, which corresponds to the iteration number in an iterative algorithm.

Two-dimensional image reconstruction from zero sheets

1993 ◽  
Vol 18 (23) ◽  
pp. 2053 ◽  
Author(s):  
B. L. Satherley ◽  
C. R. Parker
Keyword(s):  
Image Reconstruction ◽  
Two Dimensional ◽  
Dimensional Image ◽  
Two Dimensional Image

An Asymptotic Analysis of Mixing Loss

1995 ◽  
Vol 117 (3) ◽  
pp. 367-374 ◽  
Author(s):  
G. Fritsch ◽  
M. B. Giles
Keyword(s):  
Asymptotic Analysis ◽  
Compressible Flow ◽  
Control Volume ◽  
Physical Significance ◽  
Pressure Waves ◽  
Two Dimensional ◽  
Asymptotic Approach ◽  
Transonic Turbine ◽  
Steady Simulation ◽  
Interface Mixing

The objective of this paper is to establish, in a rigorous mathematical manner, a link between the dissipation of unsteadiness in a two-dimensional compressible flow and the resulting mixing loss. A novel asymptotic approach and a control-volume argument are central to the analysis. It represents the first work clearly identifying the separate contributions to the mixing loss from simultaneous linear disturbances, i.e., from unsteady entropy, vorticity, and pressure waves. The results of the analysis have important implications for numerical simulations of turbomachinery flows; the mixing loss at the stator/rotor interface in steady simulations and numerical smoothing are discussed in depth. For a transonic turbine, the entropy rise through the stage is compared for a steady and an unsteady viscous simulation. The larger interface mixing loss in the steady simulation is pointed out and its physical significance is discussed. The asymptotic approach is then applied to the first detailed analysis of interface mixing loss. Contributions from different wave types and wavelengths are quantified and discussed.

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