scholarly journals A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions

2011 ◽  
Vol 2011 (1) ◽  
Author(s):  
Jürgen Seiler (EURASIP Member) ◽  
André Kaup (EURASIP Member)
Keyword(s):  
Fast Algorithm ◽  
Basis Functions ◽  
Signal Extrapolation

An Algorithm for Computation of Radial-Harmonic-Fourier Moments

2010 ◽  
Vol 142 ◽  
pp. 284-288
Author(s):  
Yong Jing Jiang ◽  
Zi Liang Ping
Keyword(s):  
Theoretical Analysis ◽  
Fast Algorithm ◽  
Experimental Testing ◽  
Direct Method ◽  
Basis Functions ◽  
Straight Line

A fast algorithm for the computation of radial- harmonic-fourier moments (RHFM) is presented in this paper. This algorithm is based on some properties of the radial- harmonic-fourier (RHF) basis functions. As RHF basis functions have specific symmetry or anti-symmetry about the x-axis, the y-axis, the origin, and the straight line of y=x, we can compute one eighth range of the RHF basis functions instead of the whole. Both theoretical analysis and experimental testing show that the fast algorithm makes the time of the computation shorter than the direct method.

scholarly journals Generalized Orthogonal Discrete W Transform and Its Fast Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jichao Sun ◽  
Zhengping Zhang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fast Algorithm ◽  
Basis Functions ◽  
Real Sequence ◽  
Communication Signal ◽  
Numerical Computing ◽  
Orthogonal Transform ◽  
Generalized Orthogonal ◽  
And Storage

Based on the generalized discrete Fourier transform, the generalized orthogonal discrete W transform and its fast algorithm are proposed and derived in this paper. The orthogonal discrete W transform proposed by Zhongde Wang has only four types. However, the generalized orthogonal discrete W transform proposed by us has infinite types and subsumes a family of symmetric transforms. The generalized orthogonal discrete W transform is a real-valued orthogonal transform, and the real-valued orthogonal transform of a real sequence has the advantages of simple operation and facilitated transmission and storage. The generalized orthogonal discrete W transforms provide more basis functions with new frequencies and phases and hence lead to more powerful analysis and processing tools for communication, signal processing, and numerical computing.

scholarly journals Analysis of electromagnetic non-destructive evaluation modelling using Stratton-Chu formulation-based fast algorithm

2020 ◽  
Vol 378 (2182) ◽  
pp. 20190583
Author(s):  
Yang Bao ◽  
Jiming Song
Keyword(s):  
Fast Algorithm ◽  
Normal Component ◽  
Solution Process ◽  
Low Frequency ◽  
Iterative Solution ◽  
Basis Functions ◽  
Linear System Of Equations ◽  
Non Destructive Evaluation ◽  
Multi Stage ◽  
Non Destructive

The eddy current non-destructive evaluation (NDE) modelling using Stratton-Chu formulation-based fast algorithm is analysed. Stratton-Chu formulations, which have no low frequency breakdown issue, are selected for modelling electromagnetic NDE problems with low frequency and high conductivity approximations. As the main contribution of this article, the robustness and efficiency of the approximations, which result in big savings in both memory and CPU time, are validated and analysed using examples from practical EC testing. The boundary element method (BEM) is used to discretize the integral equations into a linear system of equations: the first order Rao-Wilton-Glisson (RWG) vector basis functions with the flat triangle meshes of the object and pulse basis functions are selected to expand the equivalent surface currents and the normal component of magnetic fields, respectively. Then the multilevel adaptive cross approximation (MLACA) algorithm is applied to accelerate the iterative solution process. The performance and efficiency of adaptively applying a multi-stage (level) algorithm based on the criteria concluded for the operators are shown. This article is part of the theme issue ‘Advanced electromagnetic non-destructive evaluation and smart monitoring’.

scholarly journals Expansions of Functions Based on Rational Orthogonal Basis with Nonnegative Instantaneous Frequencies

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaona Cui ◽  
Suxia Yao
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Fast Algorithm ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Almost Everywhere ◽  
Integrable Functions ◽  
Instantaneous Frequencies ◽  
Square Integrable Functions

We consider in this paper expansions of functions based on the rational orthogonal basis for the space of square integrable functions. The basis functions have nonnegative instantaneous frequencies so that the expansions make physical sense. We discuss the almost everywhere convergence of the expansions and develop a fast algorithm for computing the coefficients arising in the expansions by combining the characterization of the coefficients with the fast Fourier transform.

Spectral analysis with a minimal basis functions approach for quantification of ligand-receptor dynamic PET study

2005 ◽  
Vol 25 (1_suppl) ◽  
pp. S634-S634 ◽  
Author(s):  
Yun Zhou ◽  
Weiguo Ye ◽  
James R Brasic ◽  
Mohab Alexander ◽  
John Hilton ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Basis Functions ◽  
Dynamic Pet ◽  
Minimal Basis

Optimization of Perfect Reconstruction Cosine-Modulated Filter Banks: Fast Algorithm

2001 ◽  
Vol 56 (12) ◽  
pp. 8 ◽  
Author(s):  
Oscar G. Ibarra-Manzano ◽  
Yuriy V. Shkvarko ◽  
Rene Jaime-Rivas ◽  
Jose A. Andrade-Lucio ◽  
Gordana Jovanovic-Dolecek
Keyword(s):  
Fast Algorithm ◽  
Filter Banks ◽  
Perfect Reconstruction

Material Identification in Presence of Metal for Baggage Screening

2020 ◽  
Vol 2020 (14) ◽  
pp. 294-1-294-8
Author(s):  
Sandamali Devadithya ◽  
David Castañón
Keyword(s):  
Atomic Number ◽  
Effective Atomic Number ◽  
Simulated Data ◽  
Dual Energy ◽  
Basis Functions ◽  
Total Variation Regularization ◽  
Ct Scanner ◽  
Edge Preserving ◽  
Baggage Screening ◽  
Dual Energy Imaging

Dual-energy imaging has emerged as a superior way to recognize materials in X-ray computed tomography. To estimate material properties such as effective atomic number and density, one often generates images in terms of basis functions. This requires decomposition of the dual-energy sinograms into basis sinograms, and subsequently reconstructing the basis images. However, the presence of metal can distort the reconstructed images. In this paper we investigate how photoelectric and Compton basis functions, and synthesized monochromatic basis (SMB) functions behave in the presence of metal and its effect on estimation of effective atomic number and density. Our results indicate that SMB functions, along with edge-preserving total variation regularization, show promise for improved material estimation in the presence of metal. The results are demonstrated using both simulated data as well as data collected from a dualenergy medical CT scanner.

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