High-order spline filter: Design and application to surface metrology

2015 ◽  
Vol 40 ◽  
pp. 74-80 ◽  
Author(s):  
Hao Zhang ◽  
Yibao Yuan ◽  
Jin Hua ◽  
Yuzhu Cheng
Keyword(s):  
Filter Design ◽  
High Order ◽  
Surface Metrology ◽  
Order Spline ◽  
Spline Filter ◽  
Design And Application

A High-order Spline Filter for Surface Roughness Measurement

2006 ◽  
pp. 335-336
Author(s):  
Munetoshi Numada ◽  
Takashi Nomura ◽  
Kazuhisa Yanagi ◽  
Kazuhide Kamiya ◽  
Hatsuzo Tashiro
Keyword(s):  
Surface Roughness ◽  
High Order ◽  
Roughness Measurement ◽  
Surface Roughness Measurement ◽  
Order Spline ◽  
Spline Filter

High-order spline filter and ideal low-pass filter at the limit of its order

2007 ◽  
Vol 31 (3) ◽  
pp. 234-242 ◽  
Author(s):  
Munetoshi Numada ◽  
Takashi Nomura ◽  
Kazuhisa Yanagi ◽  
Kazuhide Kamiya ◽  
Hatsuzo Tashiro
Keyword(s):  
High Order ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Order Spline ◽  
Spline Filter

scholarly journals Reconstruction of Piecewise Smooth Multivariate Functions from Fourier Data

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 88
Author(s):  
David Levin
Keyword(s):  
Fourier Series ◽  
Fourier Coefficients ◽  
Order Approximation ◽  
High Accuracy ◽  
Rectangular Domain ◽  
High Order ◽  
Piecewise Smooth ◽  
Multidimensional Case ◽  
Order Spline ◽  
The Given

In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a method for deriving high order approximation to f using a Padé-like method. Namely, we do this by fitting some Fourier coefficients of the approximant to the given Fourier coefficients of f. Given the Fourier series coefficients of a function on a rectangular domain in Rd, assuming the function is piecewise smooth, we approximate the function by piecewise high order spline functions. First, the singularity structure of the function is identified. For example in the 2D case, we find high accuracy approximation to the curves separating between smooth segments of f. Secondly, simultaneously we find the approximations of all the different segments of f. We start by developing and demonstrating a high accuracy algorithm for the 1D case, and we use this algorithm to step up to the multidimensional case.

Modeling and Analyzing High-Order Modes in Periodic-Stub-Loaded Stripline for Wideband Filter Design

2020 ◽  
Vol 62 (2) ◽  
pp. 398-405
Author(s):  
Da Yi ◽  
Xing-Chang Wei ◽  
Rui Yang ◽  
Richard Xian-Ke Gao ◽  
Yan-Bin Yang
Keyword(s):  
Filter Design ◽  
High Order

SPECTRAL PROPERTIES OF DERIVATIVE OPERATORS IN THE BASIS-SPLINE COLLOCATION METHOD

1995 ◽  
Vol 06 (01) ◽  
pp. 143-167 ◽  
Author(s):  
J.C. WELLS ◽  
V.E. OBERACKER ◽  
M.R. STRAYER ◽  
A.S. UMAR
Keyword(s):  
Collocation Method ◽  
Spectral Properties ◽  
High Order ◽  
Collocation Methods ◽  
Finite Difference Schemes ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
The Difference ◽  
Order Spline ◽  
The One

We discuss the basis-spline collocation method for the lattice solution of boundary-value differential equations, drawing particular attention to the difference between lattice and continuous collocation methods. Spectral properties of the basis-spline lattice representation of the first and second spatial derivatives are studied for the case of periodic boundary conditions with homogeneous lattice spacing and compared to spectra obtained using traditional finite-difference schemes. Basis-spline representations are shown to give excellent resolution on small-length scales and to satisfy the chain rule with good fidelity for the lattice-derivative operators using high-order splines. Application to the one-dimensional Dirac equation shows that very high-order spline representations of the Hamiltonian on odd lattices avoid the notorious spectral-doubling problem.

Research on Improved Spline Interpolation Algorithm in Super-Resolution Reconstruction of Video Image

2013 ◽  
Vol 380-384 ◽  
pp. 3722-3725
Author(s):  
Xiang Hua Hou ◽  
Hong Hai Liu
Keyword(s):  
Spline Interpolation ◽  
Super Resolution ◽  
Cubic Spline ◽  
High Order ◽  
Experimental Results ◽  
Interpolation Algorithm ◽  
Cubic Spline Interpolation ◽  
Video Images ◽  
The Common ◽  
Order Spline

When low-spline interpolation algorithm is adopted by super-resolution reconstruction for video images, there are some defects, such as saw tooth and blur edge, if the result image is magnified. In this paper, high-order spline interpolation algorithm is introduced and it is optimized. Firstly, the common low-spline interpolation algorithms are analyzed and their shortcomings are pointed out. Then cubic spline interpolation algorithm is discussed. If the image is rotated by cubic spline interpolation algorithm, the magnified image may be not correctly displayed and the image can not be registered in super-resolution reconstruction. Finally, the cubic spline algorithm has been improved. Experimental results show that the improved cubic spline interpolation algorithm can not only eliminate the edge blur and saw tooth, but also do registration in reconstruction when image is rotating.

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