Numerical method for fourier transform of support function of SAR azimuth synthesis

2017 ◽  
Author(s):  
Yury M. Meleshin ◽  
Marat S. Khasanov ◽  
Dmitry V. Prikhodko ◽  
Vitaly I. Oreshkin
Keyword(s):  
Fourier Transform ◽  
Numerical Method ◽  
Support Function

Exact Green’s functions using leaking modes for axisymmetric boreholes in solid elastic media

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 609-620 ◽  
Author(s):  
R. A. W. Haddon
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Elastic Wave ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Elastic Media ◽  
Complex Frequency ◽  
Residue Theory

By choosing appropriate paths of integration in both the complex frequency ω and complex wavenumber k planes, exact Green’s functions for elastic wave propagation in axisymmetric fluid‐filled boreholes in solid elastic media are expressed completely as sums of modes. There are no contributions from branch line integrals. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out partly by using the fast Fourier transform (FFT) and partly by using another numerical method. Provided that the number of points in the FFT can be taken sufficiently large, there are no restrictions on distance. The method is fast, accurate, and easy to apply.

Analysis of Rubber Friction by the Fast Fourier Transform

1978 ◽  
Vol 6 (2) ◽  
pp. 89-113 ◽  
Author(s):  
R. A. Schapery
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Plane Strain ◽  
Contact Problems ◽  
Fast Fourier Transform Algorithm ◽  
Periodic Arrays ◽  
Rubber Friction

Abstract A numerical method for solving contact problems is developed and then used to predict friction (without adhesion) between rubber in plane strain and periodic arrays of parabolic and triangular substrate asperities; the numerical method itself, which is based on the fast Fourier transform algorithm, is not limited to these asperity shapes. Also, effects of superposing two and more scales of texture are described. Some generalizations and related applications, such as analysis of tire traction, are then discussed.

Multi-Asset Option Pricing Based on Exponential Lévy Process

2013 ◽  
Vol 380-384 ◽  
pp. 4537-4540
Author(s):  
Nan Liu ◽  
Mei Ling Wang ◽  
Xue Bin Lü
Keyword(s):  
Differential Equation ◽  
Fourier Transform ◽  
Option Pricing ◽  
Numerical Method ◽  
Martingale Measure ◽  
Esscher Transform ◽  
Equivalent Martingale Measure ◽  
Integro Differential Equation ◽  
Equivalent Martingale ◽  
The Fourier Transform

The multi-dimensional Esscher transform was used to find a locally equivalent martingale measure to price the options based on multi-asset. An integro-differential equation was driven for the prices of multi-asset options. The numerical method based on the Fourier transform was used to calculate some special multi-asset options in exponential Lévy models. As an example we give the calculation of extreme options.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

FR-IR Molecular Microanalysis System

1990 ◽  
Vol 48 (2) ◽  
pp. 270-271
Author(s):  
John A. Reffner ◽  
William T. Wihlborg
Keyword(s):  
Fourier Transform ◽  
Fourier Transform Infrared ◽  
Integrated System ◽  
Morphological Examination ◽  
Fully Integrated ◽  
Ir Microscopy ◽  
Normal Functions ◽  
Infrared Microspectroscopy ◽  
Infrared Spectral ◽  
Ft Ir

The IRμs™ is the first fully integrated system for Fourier transform infrared (FT-IR) microscopy. FT-IR microscopy combines light microscopy for morphological examination with infrared spectroscopy for chemical identification of microscopic samples or domains. Because the IRμs system is a new tool for molecular microanalysis, its optical, mechanical and system design are described to illustrate the state of development of molecular microanalysis. Applications of infrared microspectroscopy are reviewed by Messerschmidt and Harthcock.Infrared spectral analysis of microscopic samples is not a new idea, it dates back to 1949, with the first commercial instrument being offered by Perkin-Elmer Co. Inc. in 1953. These early efforts showed promise but failed the test of practically. It was not until the advances in computer science were applied did infrared microspectroscopy emerge as a useful technique. Microscopes designed as accessories for Fourier transform infrared spectrometers have been commercially available since 1983. These accessory microscopes provide the best means for analytical spectroscopists to analyze microscopic samples, while not interfering with the FT-IR spectrometer’s normal functions.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

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