A class of new fundamental functions with compact support called many-knot spline is introduced. The two-scale relation for the fundamental functions is investigated, and the higher order accuracy spline approximation...A class of new fundamental functions with compact support called many-knot spline is introduced. The two-scale relation for the fundamental functions is investigated, and the higher order accuracy spline approximation scheme is constructed by using the available degrees of freedom which come from additional knots. The technique has been efficiently applied to the problems such as time-frequency analysis, computer aided geometric design, and digital signal processing.展开更多
The operational procedures for efficiently reconstructing the two-dimensional image of a body by the filtered back projection are described in this paper. The projections are interpolated for four times of original pr...The operational procedures for efficiently reconstructing the two-dimensional image of a body by the filtered back projection are described in this paper. The projections are interpolated for four times of original projection by zero-padding the original projection in frequency-domain and then inverse fast Fourier transform (FFT) is taken to improve accuracy. Nearest interpolation is applied to decrease operation time. Projection dependence of next pixel at the same row is used. For each row of image, the first pixel projection once for each angle is pre-computed, other pixel projection of this row can be found by iteration. Therefore, the pre-interpolation process only has to be performed once for each row, rather than individually for each pixel. It greatly reduces the amount of computation. Compared with original implementation, the speed of reconstruction image is nearly improved by five times. The image accuracy is still preserved.展开更多
Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s 1.We call f the ...Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s 1.We call f the generator of the operators In and It.It is well known that there are many results on operators In and It.But there remain some important problems to be further explored.For application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative operators.In this paper,we focus on the available generator in the class of spline functions.We shall see that not all spline functions can be used to construct available generators.Fortunately,we do find a spline function in S,of degree m-1,where m is even and S is a class of splines.But for odd m the problem is still open.Results on spline functions in this paper are new.展开更多
We make the split of the integral fractional Laplacian as(−△)^(s)u=(−△)(−△)^(s−1)u,where s∈(0,1/2)∪(1/2,1).Based on this splitting,we respectively discretize the oneand two-dimensional integral fractional Laplaci...We make the split of the integral fractional Laplacian as(−△)^(s)u=(−△)(−△)^(s−1)u,where s∈(0,1/2)∪(1/2,1).Based on this splitting,we respectively discretize the oneand two-dimensional integral fractional Laplacian with the inhomogeneous Dirichlet boundary condition and give the corresponding truncation errors with the help of the interpolation estimate.Moreover,the suitable corrections are proposed to guarantee the convergence in solving the inhomogeneous fractional Dirichlet problem and an O(h^(1+α)2s))convergence rate is obtained when the solution u∈C^(1,α)(Ω_(n)^(δ)),where n is the dimension of the space,∈(max(0,2s−1),1],δis a fixed positive constant,and h denotes mesh size.Finally,the performed numerical experiments confirm the theoretical results.展开更多
A single-stage ring resonator capable of introducing six modes within the ultra-wideband(UWB)passband is presented.The sextuple-mode resonator consists of three rings and three sets of stepped-impedance open stubs.Bas...A single-stage ring resonator capable of introducing six modes within the ultra-wideband(UWB)passband is presented.The sextuple-mode resonator consists of three rings and three sets of stepped-impedance open stubs.Based on this sextuple-mode resonator,a UWB filter fed by the interdigital-coupling line(ICL)is designed.And we propose a two-round interpolation method to obtain the filter's initial dimensions.The designed filter is fabricated on a double-sided YBCO/MgO/YBCO high-temperature superconducting(HTS)thin film for demonstration.The experimental results show that this UWB filter produces eight resonances in the passband eventually,which effectively improves the in-band reflection and the band-edge steepness.Moreover,the upper stopband performance is enhanced due to the transmission zeros(TZs)generated by the stepped-impedance open stubs and the ICL structure.The measured good performance verifies the practicability of the two-round interpolation approach,which can also be extended to other odd-even-mode filter designs.展开更多
基金Project supported by the Foundation of the National High Technique Research 863-306-ZT0308-01the National Natural Science Foundation of China (Grant Nos. 19671003, 69873001).
文摘A class of new fundamental functions with compact support called many-knot spline is introduced. The two-scale relation for the fundamental functions is investigated, and the higher order accuracy spline approximation scheme is constructed by using the available degrees of freedom which come from additional knots. The technique has been efficiently applied to the problems such as time-frequency analysis, computer aided geometric design, and digital signal processing.
文摘The operational procedures for efficiently reconstructing the two-dimensional image of a body by the filtered back projection are described in this paper. The projections are interpolated for four times of original projection by zero-padding the original projection in frequency-domain and then inverse fast Fourier transform (FFT) is taken to improve accuracy. Nearest interpolation is applied to decrease operation time. Projection dependence of next pixel at the same row is used. For each row of image, the first pixel projection once for each angle is pre-computed, other pixel projection of this row can be found by iteration. Therefore, the pre-interpolation process only has to be performed once for each row, rather than individually for each pixel. It greatly reduces the amount of computation. Compared with original implementation, the speed of reconstruction image is nearly improved by five times. The image accuracy is still preserved.
基金supported by National Natural Science Foundation of China (Grant No.10671062,60972126)
文摘Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s 1.We call f the generator of the operators In and It.It is well known that there are many results on operators In and It.But there remain some important problems to be further explored.For application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative operators.In this paper,we focus on the available generator in the class of spline functions.We shall see that not all spline functions can be used to construct available generators.Fortunately,we do find a spline function in S,of degree m-1,where m is even and S is a class of splines.But for odd m the problem is still open.Results on spline functions in this paper are new.
基金supported by the National Natural Science Foundation of China(Grant No.12071195)the AI and Big Data Funds(Grant No.2019620005000775)+1 种基金by the Fundamental Research Funds for the Central Universities(Grant Nos.lzujbky-2021-it26,lzujbky-2021-kb15)NSF of Gansu(Grant No.21JR7RA537).
文摘We make the split of the integral fractional Laplacian as(−△)^(s)u=(−△)(−△)^(s−1)u,where s∈(0,1/2)∪(1/2,1).Based on this splitting,we respectively discretize the oneand two-dimensional integral fractional Laplacian with the inhomogeneous Dirichlet boundary condition and give the corresponding truncation errors with the help of the interpolation estimate.Moreover,the suitable corrections are proposed to guarantee the convergence in solving the inhomogeneous fractional Dirichlet problem and an O(h^(1+α)2s))convergence rate is obtained when the solution u∈C^(1,α)(Ω_(n)^(δ)),where n is the dimension of the space,∈(max(0,2s−1),1],δis a fixed positive constant,and h denotes mesh size.Finally,the performed numerical experiments confirm the theoretical results.
基金the National Natural Science Foundation of China(Grant No.61471094).
文摘A single-stage ring resonator capable of introducing six modes within the ultra-wideband(UWB)passband is presented.The sextuple-mode resonator consists of three rings and three sets of stepped-impedance open stubs.Based on this sextuple-mode resonator,a UWB filter fed by the interdigital-coupling line(ICL)is designed.And we propose a two-round interpolation method to obtain the filter's initial dimensions.The designed filter is fabricated on a double-sided YBCO/MgO/YBCO high-temperature superconducting(HTS)thin film for demonstration.The experimental results show that this UWB filter produces eight resonances in the passband eventually,which effectively improves the in-band reflection and the band-edge steepness.Moreover,the upper stopband performance is enhanced due to the transmission zeros(TZs)generated by the stepped-impedance open stubs and the ICL structure.The measured good performance verifies the practicability of the two-round interpolation approach,which can also be extended to other odd-even-mode filter designs.
