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Zhanjie Song - One of the best experts on this subject based on the ideXlab platform.

  • Approximation of homogeneous random field from local averages
    Communications in Statistics - Theory and Methods, 2016
    Co-Authors: Shuo Zhang, Zhanjie Song
    Abstract:

    ABSTRACTBased on the Shannon Sampling Theorem of multivariate functions, the upper bound of approximated error of homogeneous random field by local averages in the mean square sense is established. The main result is that the approximation of weak sense stochastic process from local averages is extended to the case of random field. It is expected that one can obtain more precise local average Sampling in oceanography, meteorology, geology with this theory.

  • Truncation Error Analysis on Reconstruction of Signal From Unsymmetrical Local Average Sampling
    IEEE Transactions on Cybernetics, 2015
    Co-Authors: Yanwei Pang, Zhanjie Song, Xuelong Li
    Abstract:

    The classical Shannon Sampling Theorem is suitable for reconstructing a band-limited signal from its sampled values taken at regular instances with equal step by using the well-known sinc function. However, due to the inertia of the measurement apparatus, it is impossible to measure the value of a signal precisely at such discrete time. In practice, only unsymmetrically local averages of signal near the regular instances can be measured and used as the inputs for a signal reconstruction method. In addition, when implemented in hardware, the traditional sinc function cannot be directly used for signal reconstruction. We propose using the Taylor expansion of sinc function to reconstruct signal sampled from unsymmetrically local averages and give the upper bound of the reconstruction error (i.e., truncation error). The convergency of the reconstruction method is also presented.

  • an improved nyquist Shannon irregular Sampling Theorem from local averages
    IEEE Transactions on Information Theory, 2012
    Co-Authors: Zhanjie Song, Yanwei Pang, Bei Liu, Chunping Hou
    Abstract:

    The Nyquist–Shannon Sampling Theorem is on the reconstruction of a band-limited signal from its uniformly sampled samples. The higher the signal bandwidth gets, the more challenging the uniform Sampling may become. To deal with this problem, signal reconstruction from local averages has been studied in the literature. In this paper, we obtain an improved Nyquist–Shannon Sampling Theorem from general local averages. In practice, the measurement apparatus gives a weighted average over an asymmetrical interval. As a special case, for local averages from symmetrical interval, we show that the Sampling rate is much lower than that of a result by Grochenig. Moreover, we obtain two exact dual frames from local averages, one of which improves a result by Sun and Zhou. At the end of this paper, as an example application of local average Sampling, we consider a reconstruction algorithm: the piecewise linear approximations.

  • An Improved Nyquist–Shannon Irregular Sampling Theorem From Local Averages
    IEEE Transactions on Information Theory, 2012
    Co-Authors: Zhanjie Song, Yanwei Pang, Bei Liu, Chunping Hou
    Abstract:

    The Nyquist–Shannon Sampling Theorem is on the reconstruction of a band-limited signal from its uniformly sampled samples. The higher the signal bandwidth gets, the more challenging the uniform Sampling may become. To deal with this problem, signal reconstruction from local averages has been studied in the literature. In this paper, we obtain an improved Nyquist–Shannon Sampling Theorem from general local averages. In practice, the measurement apparatus gives a weighted average over an asymmetrical interval. As a special case, for local averages from symmetrical interval, we show that the Sampling rate is much lower than that of a result by Grochenig. Moreover, we obtain two exact dual frames from local averages, one of which improves a result by Sun and Zhou. At the end of this paper, as an example application of local average Sampling, we consider a reconstruction algorithm: the piecewise linear approximations.

  • truncation error estimate on random signals by local average
    International Conference on Computational Science, 2007
    Co-Authors: Zhanjie Song, Deyun Yang, Jianhua Zhu
    Abstract:

    Since signals are often of random characters, random signals play an important role in signal processing. We show that the bandlimited wide sense stationary stochastic process can be approximated by Shannon Sampling Theorem on local averages. Explicit truncation error bounds are given.

Xingwei Zhou - One of the best experts on this subject based on the ideXlab platform.

G.g. Walter - One of the best experts on this subject based on the ideXlab platform.

  • A Sampling Theorem for wavelet subspaces
    IEEE Transactions on Information Theory, 1992
    Co-Authors: G.g. Walter
    Abstract:

    The classical Shannon Sampling Theorem is extended to the subspaces used in the multiresolution analysis in wavelet theory. Under weak hypotheses, these subspaces are first shown to have a Riesz basis formed from the reproducing kernels. These in turn are used to construct the Sampling sequences. Examples are given. >

  • ICASSP - Positive hybrid Sampling in wavelet subspaces
    2000 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings (Cat. No.00CH37100), 1
    Co-Authors: G.g. Walter
    Abstract:

    It is well known that the Shannon Sampling Theorem can be put into a wavelet context. But it has also been shown that for most wavelets, a non-negative summability function for the associated subspaces exists. Translation of these are used in a series with Sampling coefficients to get a "hybrid" series each of whose terms is non-negative. Such series converge, avoid integration, and eliminate the Gibbs phenomenon.

M. Pawlak - One of the best experts on this subject based on the ideXlab platform.

  • Signal recovery under noise for not necessarily band-limited functions
    Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252), 1998
    Co-Authors: Adam Krzyżak, M. Pawlak, Ewaryst Rafajłowicz
    Abstract:

    We consider the problem of estimating a class of smooth functions defined everywhere on a real line using reconstruction techniques motivated by the Whittaker-Shannon Sampling Theorem. Such functions may be considered as signals and are common in communication. Furthermore, they have finite energy, bounded frequency content and are often jammed by noise. We examine the expected L/sub 2/-error of a class of estimators based on Whittaker-Shannon interpolation series and smoothing. Not band-limited signals are approximated in L/sub 2/(R) by an increasing ladder of band-limited subspaces (multiresolution approach).

  • Moving average restoration of bandlimited signals from noisy observations
    IEEE Transactions on Signal Processing, 1997
    Co-Authors: Adam Krzyżak, Ewaryst Rafajłowicz, M. Pawlak
    Abstract:

    The purpose of this paper is to describe the extension of the Whittaker-Shannon Sampling Theorem to reconstruction of bandlimited functions in the presence of zero mean, uncorrelated noise. It is shown that the classical Whittaker-Shannon Sampling scheme is not consistent in the case of noisy measurements, and new reconstruction algorithms based on the moving average smoothing are proposed. The weak and strong consistency of the algorithms is established, and the rate of convergence is investigated. The theory is verified in the computer simulations.

  • Recovery of not necessarily band-limited signals from noisy observations
    2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060), 1
    Co-Authors: Adam Krzyżak, Ewaryst Rafajłowicz, M. Pawlak
    Abstract:

    The purpose of this paper is to describe the extension of the Whittaker-Shannon Sampling Theorem to the case of signals observed in the presence of noise. We introduce a class of signal recovery methods being a smooth correction of the cardinal series. Both band-limited and non band-limited signals are considered. The weak and strong L/sub 2/ consistency of the algorithms are established and the rate of convergence is investigated.

  • Moving average restoration of band-limited signals from noisy observations
    Proceedings of IEEE International Symposium on Information Theory, 1
    Co-Authors: Adam Krzyżak, Ewaryst Rafajłowicz, M. Pawlak
    Abstract:

    The purpose of this paper is to describe the extension of the Whittaker-Shannon Sampling Theorem to the reconstruction of band-limited functions in the presence of zero mean, uncorrelated noise. It is shown that the classical Whittaker-Shannon Sampling scheme is not consistent in the case of noisy measurements and a new reconstruction algorithm based on moving average smoothing is proposed. The consistency of the algorithm is established and the rate of convergence is investigated.

Chunping Hou - One of the best experts on this subject based on the ideXlab platform.

  • an improved nyquist Shannon irregular Sampling Theorem from local averages
    IEEE Transactions on Information Theory, 2012
    Co-Authors: Zhanjie Song, Yanwei Pang, Bei Liu, Chunping Hou
    Abstract:

    The Nyquist–Shannon Sampling Theorem is on the reconstruction of a band-limited signal from its uniformly sampled samples. The higher the signal bandwidth gets, the more challenging the uniform Sampling may become. To deal with this problem, signal reconstruction from local averages has been studied in the literature. In this paper, we obtain an improved Nyquist–Shannon Sampling Theorem from general local averages. In practice, the measurement apparatus gives a weighted average over an asymmetrical interval. As a special case, for local averages from symmetrical interval, we show that the Sampling rate is much lower than that of a result by Grochenig. Moreover, we obtain two exact dual frames from local averages, one of which improves a result by Sun and Zhou. At the end of this paper, as an example application of local average Sampling, we consider a reconstruction algorithm: the piecewise linear approximations.

  • An Improved Nyquist–Shannon Irregular Sampling Theorem From Local Averages
    IEEE Transactions on Information Theory, 2012
    Co-Authors: Zhanjie Song, Yanwei Pang, Bei Liu, Chunping Hou
    Abstract:

    The Nyquist–Shannon Sampling Theorem is on the reconstruction of a band-limited signal from its uniformly sampled samples. The higher the signal bandwidth gets, the more challenging the uniform Sampling may become. To deal with this problem, signal reconstruction from local averages has been studied in the literature. In this paper, we obtain an improved Nyquist–Shannon Sampling Theorem from general local averages. In practice, the measurement apparatus gives a weighted average over an asymmetrical interval. As a special case, for local averages from symmetrical interval, we show that the Sampling rate is much lower than that of a result by Grochenig. Moreover, we obtain two exact dual frames from local averages, one of which improves a result by Sun and Zhou. At the end of this paper, as an example application of local average Sampling, we consider a reconstruction algorithm: the piecewise linear approximations.