The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Xingwei Zhou - One of the best experts on this subject based on the ideXlab platform.
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An Average Sampling Theorem for Bandlimited Stochastic Processes
IEEE Transactions on Information Theory, 2007Co-Authors: Zhanjie Song, Xingwei Zhou, Wenchang Sun, Zhengxin HouAbstract:In this correspondence, we give an average Sampling Theorem for bandlimited stochastic processes which shows that many average Sampling Theorems have their counterparts for stochastic signals.
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Sampling Theorem for wavelet subspaces: error estimate and irregular Sampling
IEEE Transactions on Signal Processing, 2000Co-Authors: Wenchang Sun, Xingwei ZhouAbstract:The error estimate is useful in the application of the Sampling Theorem. For the classical Shannon Sampling Theorem, various errors are widely studied, but for the Sampling Theorem in general wavelet subspaces, only the aliasing error is studied. In this paper, we study three other errors: truncation error, amplitude error, and time-jitter error. With the same technique, a result on irregular Sampling is improved.
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On the Sampling Theorem for wavelet subspaces
The Journal of Fourier Analysis and Applications, 1999Co-Authors: Xingwei Zhou, Wenchang SunAbstract:In [13], Walter extended the classical Shannon Sampling Theorem to some wavelet subspaces. For any closed subspace V0/L2 (R), we present a necessary and sufficient condition under which there is a Sampling expansion for everyf e V0-Several examples are given.
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Sampling Theorem for multiwavelet subspaces
Chinese Science Bulletin, 1999Co-Authors: Wenchang Sun, Xingwei ZhouAbstract:Sampling Theorem on multiwavelet subspaces is established. Necessary and sufficient conditions are obtained. The result covers the Shannon’s Sampling Theorem and the early results on the Sampling Theorem for wavelet subspaces.
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Frames and Sampling Theorem
Science in China Series A: Mathematics, 1998Co-Authors: Wenchang Sun, Xingwei ZhouAbstract:The Sampling problem on a closed subspace Vo of L2(ℝ) is studied. For the regular Sampling, a necessary and sufficient condition on the Sampling Theorem is presented and the Sampling problem proposed by Walter is completely solved. Moreover, a representation formula for the derived function is given. The irregular Sampling is studied. The results improve the ones of Walter and Liu’s.
Wenchang Sun - One of the best experts on this subject based on the ideXlab platform.
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Average Sampling Theorem
SCIENTIA SINICA Mathematica, 2015Co-Authors: Haiye Huo, Wenchang SunAbstract:The Sampling Theorem is one of the fundamental and powerful tools in signal processing, which is widely used in digital signal processing, wireless communication, and many other elds. Recently, the classical Shannon Sampling Theorem has been extended from bandlimited functions to shift invariant subspaces, and from Sampling function values to Sampling local averages. In this paper, we simply review the development of the Sampling theory with a focus on some recent advances in average Sampling, multi-channel Sampling and average Sampling for stochastic processes. We also introduce some results on approximation errors.
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An Average Sampling Theorem for Bandlimited Stochastic Processes
IEEE Transactions on Information Theory, 2007Co-Authors: Zhanjie Song, Xingwei Zhou, Wenchang Sun, Zhengxin HouAbstract:In this correspondence, we give an average Sampling Theorem for bandlimited stochastic processes which shows that many average Sampling Theorems have their counterparts for stochastic signals.
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Sampling Theorem for wavelet subspaces: error estimate and irregular Sampling
IEEE Transactions on Signal Processing, 2000Co-Authors: Wenchang Sun, Xingwei ZhouAbstract:The error estimate is useful in the application of the Sampling Theorem. For the classical Shannon Sampling Theorem, various errors are widely studied, but for the Sampling Theorem in general wavelet subspaces, only the aliasing error is studied. In this paper, we study three other errors: truncation error, amplitude error, and time-jitter error. With the same technique, a result on irregular Sampling is improved.
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On the Sampling Theorem for wavelet subspaces
The Journal of Fourier Analysis and Applications, 1999Co-Authors: Xingwei Zhou, Wenchang SunAbstract:In [13], Walter extended the classical Shannon Sampling Theorem to some wavelet subspaces. For any closed subspace V0/L2 (R), we present a necessary and sufficient condition under which there is a Sampling expansion for everyf e V0-Several examples are given.
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Sampling Theorem for multiwavelet subspaces
Chinese Science Bulletin, 1999Co-Authors: Wenchang Sun, Xingwei ZhouAbstract:Sampling Theorem on multiwavelet subspaces is established. Necessary and sufficient conditions are obtained. The result covers the Shannon’s Sampling Theorem and the early results on the Sampling Theorem for wavelet subspaces.
James S.j. Lee - One of the best experts on this subject based on the ideXlab platform.
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The digital morphological Sampling Theorem
1988. IEEE International Symposium on Circuits and Systems, 1Co-Authors: Robert M. Haralick, Xinhua Zhuang, C. Lin, James S.j. LeeAbstract:There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing. It is for this reason that a morphological Sampling Theorem is important. The morphological Sampling Theorem described by the authors states: (1) how a digital image must be morphologically filtered before Sampling to preserve the relevant information after Sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after Sampling; and (3) the relationship between morphologically operating before Sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital Sampling Theorem is developed for the case of binary morphology. >
I.w. Selesnick - One of the best experts on this subject based on the ideXlab platform.
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Cardinal multiwavelets and the Sampling Theorem
1999 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), 1999Co-Authors: I.w. SelesnickAbstract:This paper considers the classical Shannon Sampling Theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang (1993), for an orthogonal scaling function to support such a Sampling Theorem, the scaling function must be cardinal. They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar function, which has only 1 vanishing moment and is not continuous. This paper addresses the same question, but in the multiwavelet context, where the situation is different. This paper presents the construction of orthogonal multiscaling functions that are simultaneously cardinal, of compact support, and have more than one vanishing moment. The scaling functions thereby support a Shannon-like Sampling Theorem. Such wavelet bases are appealing because the initialization of the discrete wavelet transform (prefiltering) is the identity operator-the projection of a function onto the scaling space is given by its samples.
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Interpolating multiwavelet bases and the Sampling Theorem
IEEE Transactions on Signal Processing, 1999Co-Authors: I.w. SelesnickAbstract:This paper considers the classical Sampling Theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang (1993), for an orthogonal scaling function to support such a Sampling Theorem, the scaling function must be cardinal (interpolating). They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar function, which is not continuous. This paper addresses the same question, but in the multiwavelet context, where the situation is different. This paper presents the construction of compactly supported orthogonal multiscaling functions that are continuously differentiable and cardinal. The scaling functions thereby support a Shannon-like Sampling Theorem. Such wavelet bases are appealing because the initialization of the discrete wavelet transform (prefiltering) is the identity operator.
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ICASSP - Cardinal multiwavelets and the Sampling Theorem
1999 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), 1999Co-Authors: I.w. SelesnickAbstract:This paper considers the classical Shannon Sampling Theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang (1993), for an orthogonal scaling function to support such a Sampling Theorem, the scaling function must be cardinal. They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar function, which has only 1 vanishing moment and is not continuous. This paper addresses the same question, but in the multiwavelet context, where the situation is different. This paper presents the construction of orthogonal multiscaling functions that are simultaneously cardinal, of compact support, and have more than one vanishing moment. The scaling functions thereby support a Shannon-like Sampling Theorem. Such wavelet bases are appealing because the initialization of the discrete wavelet transform (prefiltering) is the identity operator-the projection of a function onto the scaling space is given by its samples.
Robert M. Haralick - One of the best experts on this subject based on the ideXlab platform.
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The digital morphological Sampling Theorem
1988. IEEE International Symposium on Circuits and Systems, 1Co-Authors: Robert M. Haralick, Xinhua Zhuang, C. Lin, James S.j. LeeAbstract:There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing. It is for this reason that a morphological Sampling Theorem is important. The morphological Sampling Theorem described by the authors states: (1) how a digital image must be morphologically filtered before Sampling to preserve the relevant information after Sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after Sampling; and (3) the relationship between morphologically operating before Sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital Sampling Theorem is developed for the case of binary morphology. >
