scholarly journals Fractional Fourier series expansion for finite signals and dual extension to discrete-time fractional Fourier transform

1999 ◽  
Vol 47 (10) ◽  
pp. 2883-2888 ◽  
Author(s):  
Soo-Chang Pei ◽  
Min-Hung Yeh ◽  
Tzyy-Liang Luo
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Series Expansion ◽  
Discrete Time ◽  
Fractional Fourier Transform ◽  
Fourier Series Expansion ◽  
Dual Extension

scholarly journals GREEN'S FUNCTION OF A FINITE CHAIN AND THE DISCRETE FOURIER TRANSFORM

2006 ◽  
Vol 20 (05) ◽  
pp. 593-605 ◽  
Author(s):  
SERGIU COJOCARU
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Green’S Function ◽  
Discrete Fourier Transform ◽  
Series Expansion ◽  
Green's Function ◽  
Basis Set ◽  
Fourier Series Expansion ◽  
Open Boundary ◽  
Open Boundary Conditions

Unlike the Fourier series expansion, the discrete Fourier transform is defined on a finite basis set of harmonic functions. The first approach is widely used in condensed matter to describe the thermodynamic limit of various lattice models, while the latter did not receive sufficient development that would allow to address finite lattices. In the present paper a general expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived for the first time via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Although the final expressions are completely equivalent to Bethe ansatz, the examples allow us to clarify the differences between the two approaches. On the other hand, it is explained why the well known results obtained by Fourier series expansion were incomplete and thus provides a deeper understanding of the approach.

A Wiener–Hopf theory for a semi-infinite dielectric slab

1990 ◽  
Vol 68 (11) ◽  
pp. 1348-1351
Author(s):  
G. Mitsioulis
Keyword(s):  
Fourier Transform ◽  
Wave Equation ◽  
Fourier Series ◽  
Boundary Conditions ◽  
Series Expansion ◽  
Field Distribution ◽  
Wave Number ◽  
Fourier Series Expansion ◽  
System Of Equations ◽  
Dielectric Slab

We investigate the field distribution around a semi-infinite dielectric slab. The wave equation is transformed, through a Fourier transform, to the wave number domain. The boundary conditions are imposed and we end up with an equation of the Wiener–Hopf type. Certain functions are factorized and we find a system of equations for the unknown coefficients of the Fourier series expansion for the field at the mouth of the slab.

A SIMPLE MODEL FOR ORIENTATIONAL ORDERING OF A SILVER MONOLAYER ELECTRODEPOSITED ON A C(0001) SURFACE

1995 ◽  
Vol 02 (04) ◽  
pp. 489-494 ◽  
Author(s):  
E.E. MOLA ◽  
A.G. APPIGNANESSI ◽  
J.L. VICENTE ◽  
L. VAZQUEZ ◽  
R.C. SALVAREZZA ◽  
...  
Keyword(s):  
Experimental Data ◽  
Fourier Series ◽  
Simple Model ◽  
Series Expansion ◽  
Unit Cell ◽  
Fourier Series Expansion ◽  
Crystal Formation ◽  
Substrate Potential ◽  
Weber Type ◽  
Orientational Ordering

The model for the angular orientational energy (AOE) has been extended to hexagonal submonolayer domains of Ag electrodeposited at a constant overpotential on a C(0001) surface. These domains which are characterized by an epitaxy angle θ=15±5° and an Ag−Ag distance d Ag−Ag =0.330± 0.016 nm, can be considered as precursors of 3D Ag crystal formation, according to a Volmer-Weber type mechanism. Calculations are based upon a simple Hamiltonian evaluated by introducing the concept of the commensurable unit cell. A Fourier series expansion for the substrate potential was used. Results from the model predict the existence of a commensurable cell in agreement with the experimental data derived from STM imaging.

Predicting Apple Firmness and Soluble Solids Content Based on Hyperspectral Scattering Imaging Using Fourier Series Expansion

2017 ◽  
Vol 60 (4) ◽  
pp. 1053-1062
Author(s):  
Wei Wang ◽  
Min Huang ◽  
Qibing Zhu
Keyword(s):  
Fourier Series ◽  
Least Squares ◽  
Series Expansion ◽  
Fourier Coefficients ◽  
Expansion Method ◽  
Soluble Solids ◽  
Fourier Series Expansion ◽  
Support Vector ◽  
Soluble Solids Content ◽  
Solids Content

Abstract. This article reports on using a Fourier series expansion method to extract features from hyperspectral scattering profiles for apple fruit firmness and soluble solids content (SSC) prediction. Hyperspectral scattering images of ‘Golden Delicious’ (GD), ‘Jonagold’ (JG), and ‘Delicious’ (RD) apples, harvested in 2009 and 2010, were acquired using an online hyperspectral imaging system over the wavelength region of 500 to 1000 nm. The moment method and Fourier series expansion method were used to analyze the scattering profiles of apples. The zeroth-first order moment (Z-FOM) spectra and Fourier coefficients were extracted from each apple, which were then used for developing fruit firmness and SSC prediction models using partial least squares (PLS) and least squares support vector machine (LSSVM). The PLS models based on the Fourier coefficients improved the standard errors of prediction (SEP) by 4.8% to 19.9% for firmness and by 2.4% to 13.5% for SSC, compared with the PLS models using the Z-FOM spectra. The LSSVM models for the prediction set of Fourier coefficients achieved better SEP results, with improvements of 4.4% to 11.3% for firmness and 2.8% to 16.5% for SSC over the LSSVM models for the Z-FOM spectra data and 3.7% to 12.6% for firmness and 5.4% to 8.6% for SSC over the PLS models for the Fourier coefficients. Experiments showed that Fourier series expansion provides a simple, fast, and effective means for improving Keywords: Apples, Firmness, Fourier series expansion, Hyperspectral scattering imaging, Least squares support vector machine, Partial least squares, Soluble solids content.

Texture Evolution and Earing in Aluminium Can Sheet

2005 ◽  
Vol 495-497 ◽  
pp. 1565-1572 ◽  
Author(s):  
Jürgen Hirsch
Keyword(s):  
Fourier Series ◽  
Cold Rolling ◽  
Series Expansion ◽  
Deep Drawing ◽  
Recrystallization Texture ◽  
Texture Evolution ◽  
Processing Parameters ◽  
New Method ◽  
Fourier Series Expansion ◽  
Hot And Cold Rolling

The texture evolution during hot and cold rolling of AlMg1Mn1 can body sheet is described and the related anisotropy effects during deep drawing are analysed quantitatively. The typical textures of rolled aluminium show the transition between ß-fibre orientations and cube recrystallization texture, depending on rolling temperature and strain. These correlate with transitions between 45° and 0°/90° ear heights in deep drawn cups which are described by a new method of Fourier series expansion. Processing parameters to achieve low anisotropy are discussed.

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