Real time digital recording and numerical reconstruction of a temporal digital hologram sequence have become feasible in recent years.They provide a new measurement method which enjoys the valuable advantages of being...Real time digital recording and numerical reconstruction of a temporal digital hologram sequence have become feasible in recent years.They provide a new measurement method which enjoys the valuable advantages of being full-field,noncontact and high precision.In this paper,a combined method of temporal digital hologram sequence and windowed Fourier transform is proposed to measure the kinematic parameters of random vibration.A series of holograms are recorded by CCD camera and the original phase can be reconstructed by Fresnel reconstruction algorithm.The three-dimensional windowed Fourier transform is used to filter noise in phase and extract the instantaneous kinematic parameters of the specimen,such as the displacement,velocity and acceleration.An experiment is conducted on a chloroprene rubber latex membrane.Results demonstrate that the proposed method determines the vibration parameters precisely and enjoys many merits.展开更多
Let g（x） ∈L<sup>2</sup>（R） and （ω） be the Fourier transform of g（x）.Define g<sub>mn</sub>（x）=e<sup>imx</sup>g（x- 2πn）.In this paper we shall give a sufficient and nec...Let g（x） ∈L<sup>2</sup>（R） and （ω） be the Fourier transform of g（x）.Define g<sub>mn</sub>（x）=e<sup>imx</sup>g（x- 2πn）.In this paper we shall give a sufficient and necessary condition under which {g<sub>mn</sub>（x）} constitutes an orthonormal basis of L<sup>2</sup>（R） for compactly supported g（x） or （ω）.展开更多
This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators , s.t. are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB)...This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators , s.t. are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of T n L 2(R). Furthermore, it shows the orthogonal spaces decomposition of . Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6].展开更多
The coherent states approximation for one-dimensional multi-phased wave functions is considered in this paper.The wave functions are assumed to oscillate on a characteristic wave length O(∈)withǫ≪1.A parameter recove...The coherent states approximation for one-dimensional multi-phased wave functions is considered in this paper.The wave functions are assumed to oscillate on a characteristic wave length O(∈)withǫ≪1.A parameter recovery algorithm is first developed for single-phased wave function based on a moment asymptotic analysis.This algorithm is then extended to multi-phased wave functions.If cross points or caustics exist,the coherent states approximation algorithm based on the parameter recovery will fail in some local regions.In this case,we resort to the windowed Fourier transform technique,and propose a composite coherent states approximation method.Numerical experiments show that the number of coherent states derived by the proposedmethod is much less than that by the directwindowed Fourier transform technique.展开更多
基金supported by the National Natural Science Foundation of China (10772171 and 10732080)the National Basic Research Program of China (2007CB936803)
文摘Real time digital recording and numerical reconstruction of a temporal digital hologram sequence have become feasible in recent years.They provide a new measurement method which enjoys the valuable advantages of being full-field,noncontact and high precision.In this paper,a combined method of temporal digital hologram sequence and windowed Fourier transform is proposed to measure the kinematic parameters of random vibration.A series of holograms are recorded by CCD camera and the original phase can be reconstructed by Fresnel reconstruction algorithm.The three-dimensional windowed Fourier transform is used to filter noise in phase and extract the instantaneous kinematic parameters of the specimen,such as the displacement,velocity and acceleration.An experiment is conducted on a chloroprene rubber latex membrane.Results demonstrate that the proposed method determines the vibration parameters precisely and enjoys many merits.
基金This work is supported by the National Natural Science Foundation of China(No.19801005)the Project of New Stars of Science and Technology of Beijing a Grant of Young Fellow of Educational Ministry.
文摘Let g（x） ∈L<sup>2</sup>（R） and （ω） be the Fourier transform of g（x）.Define g<sub>mn</sub>（x）=e<sup>imx</sup>g（x- 2πn）.In this paper we shall give a sufficient and necessary condition under which {g<sub>mn</sub>（x）} constitutes an orthonormal basis of L<sup>2</sup>（R） for compactly supported g（x） or （ω）.
基金Research supported by 973 Project G1999075105 and NNFS of China,Nos.90104004 and 69735020
文摘This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators , s.t. are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of T n L 2(R). Furthermore, it shows the orthogonal spaces decomposition of . Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6].
基金The authors thank Prof.Shi Jin for introducing this research project to them.They are also grateful to Prof.Xuguang Lu for the helpful discussion on asymptotic analysis,and the anonymous referees for their valuable constructive suggestions.D.Yin was supported by the National Natural Science Foundation of China under Grant No.10901091C.Zheng was supported by the National Natural Science Foundation of China under Grant No.10971115.
文摘The coherent states approximation for one-dimensional multi-phased wave functions is considered in this paper.The wave functions are assumed to oscillate on a characteristic wave length O(∈)withǫ≪1.A parameter recovery algorithm is first developed for single-phased wave function based on a moment asymptotic analysis.This algorithm is then extended to multi-phased wave functions.If cross points or caustics exist,the coherent states approximation algorithm based on the parameter recovery will fail in some local regions.In this case,we resort to the windowed Fourier transform technique,and propose a composite coherent states approximation method.Numerical experiments show that the number of coherent states derived by the proposedmethod is much less than that by the directwindowed Fourier transform technique.
