The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Jose C. Principe - One of the best experts on this subject based on the ideXlab platform.
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Crosscorrelation estimation using teacher forcing hebbian learning and its application
Proceedings of International Conference on Neural Networks (ICNN'96), 1996Co-Authors: Chuan Wang, Jose C. PrincipeAbstract:This paper proposes a new network architecture to compute the temporal Crosscorrelation function between two signals, either stationary or local stationary. We show that the weights of a multi-FIR-like filter trained with a teacher forcing Hebbian rule encode the Crosscorrelation function between the input and the desired response. This temporal correlation idea is applied to the blind sources separation problem. And experimental results are also given to show the validation of the idea.
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ICNN - Crosscorrelation estimation using teacher forcing Hebbian learning and its application
Proceedings of International Conference on Neural Networks (ICNN'96), 1Co-Authors: Chuan Wang, Jose C. PrincipeAbstract:This paper proposes a new network architecture to compute the temporal Crosscorrelation function between two signals, either stationary or local stationary. We show that the weights of a multi-FIR-like filter trained with a teacher forcing Hebbian rule encode the Crosscorrelation function between the input and the desired response. This temporal correlation idea is applied to the blind sources separation problem. And experimental results are also given to show the validation of the idea.
Daniel J Katz - One of the best experts on this subject based on the ideXlab platform.
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Crosscorrelation of Rudin–Shapiro-like polynomials
Applied and Computational Harmonic Analysis, 2020Co-Authors: Daniel J Katz, Sangman Lee, Stanislav A. TrunovAbstract:Abstract We consider the class of Rudin–Shapiro-like polynomials, whose L 4 norms on the complex unit circle were studied by Borwein and Mossinghoff. The polynomial f ( z ) = f 0 + f 1 z + ⋯ + f d z d is identified with the sequence ( f 0 , f 1 , … , f d ) of its coefficients. From the L 4 norm of a polynomial, one can easily calculate the autocorrelation merit factor of its associated sequence, and conversely. In this paper, we study the Crosscorrelation properties of pairs of sequences associated to Rudin–Shapiro-like polynomials. We find an explicit formula for the Crosscorrelation merit factor. A computer search is then used to find pairs of Rudin–Shapiro-like polynomials whose autocorrelation and Crosscorrelation merit factors are simultaneously high. Pursley and Sarwate proved a bound that limits how good this combined autocorrelation and Crosscorrelation performance can be. We find infinite families of polynomials whose performance approaches quite close to this fundamental limit.
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sequence pairs with lowest combined autocorrelation and Crosscorrelation
arXiv: Information Theory, 2017Co-Authors: Daniel J Katz, Eli MooreAbstract:For a pair $(f,g)$ of sequences of length $\ell$ whose terms are in $\{-1,1\}$, Pursley and Sarwate established a lower bound on a combined measure of Crosscorrelation and autocorrelation for $f$ and $g$. They showed that the sum of the mean square Crosscorrelation between $f$ and $g$ and the geometric mean of $f$'s mean square autocorrelation and $g$'s mean square autocorrelation must be at least $1$. For randomly selected binary sequences, this quantity is typically about $2$. In this paper, we show that Pursley and Sarwate's bound is met precisely when $(f,g)$ is a Golay complementary pair. This result generalizes to sequences whose terms are arbitrary complex numbers.
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Crosscorrelation of Rudin-Shapiro-Like Polynomials
arXiv: Information Theory, 2017Co-Authors: Daniel J Katz, Sangman Lee, Stanislav A. TrunovAbstract:We consider the class of Rudin-Shapiro-like polynomials, whose $L^4$ norms on the complex unit circle were studied by Borwein and Mossinghoff. The polynomial $f(z)=f_0+f_1 z + \cdots + f_d z^d$ is identified with the sequence $(f_0,f_1,\ldots,f_d)$ of its coefficients. From the $L^4$ norm of a polynomial, one can easily calculate the autocorrelation merit factor of its associated sequence, and conversely. In this paper, we study the Crosscorrelation properties of pairs of sequences associated to Rudin-Shapiro-like polynomials. We find an explicit formula for the Crosscorrelation merit factor. A computer search is then used to find pairs of Rudin-Shapiro-like polynomials whose autocorrelation and Crosscorrelation merit factors are simultaneously high. Pursley and Sarwate proved a bound that limits how good this combined autocorrelation and Crosscorrelation performance can be. We find infinite families of polynomials whose performance approaches quite close to this fundamental limit.
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Aperiodic Crosscorrelation of Sequences Derived from Characters
arXiv: Information Theory, 2016Co-Authors: Daniel J KatzAbstract:It is shown that pairs of maximal linear recursive sequences (m-sequences) typically have mean square aperiodic Crosscorrelation on par with that of random sequences, but that if one takes a pair of m-sequences where one is the reverse of the other, and shifts them appropriately, one can get significantly lower mean square aperiodic Crosscorrelation. Sequence pairs with even lower mean square aperiodic Crosscorrelation are constructed by taking a Legendre sequence, cyclically shifting it, and then cutting it (approximately) in half and using the halves as the sequences of the pair. In some of these constructions, the mean square aperiodic Crosscorrelation can be lowered further if one truncates or periodically extends (appends) the sequences. Exact asymptotic formulae for mean squared aperiodic Crosscorrelation are proved for sequences derived from additive characters (including m-sequences and modified versions thereof) and multiplicative characters (including Legendre sequences and their relatives). Data is presented that shows that sequences of modest length have performance that closely approximates the asymptotic formulae.
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Aperiodic Crosscorrelation of Sequences Derived From Characters
IEEE Transactions on Information Theory, 2016Co-Authors: Daniel J KatzAbstract:It is shown that the pairs of maximal linear recursive sequences ( $m$ -sequences) typically have mean square aperiodic Crosscorrelation on par with that of random sequences, but that if one takes a pair of $m$ -sequences where one is the reverse of the other, and shifts them appropriately, one can get significantly lower mean square aperiodic Crosscorrelation. Sequence pairs with even lower mean square aperiodic Crosscorrelation are constructed by taking a Legendre sequence, cyclically shifting it, and then cutting it (approximately) in half and using the halves as the sequences of the pair. In some of these constructions, the mean square aperiodic Crosscorrelation can be lowered further if one truncates or periodically extends (appends) the sequences. Exact asymptotic formulas for mean squared aperiodic Crosscorrelation are proved for sequences derived from additive characters (including $m$ -sequences and modified versions thereof) and multiplicative characters (including Legendre sequences and their relatives). Data are presented that show that the sequences of modest length have performance that closely approximates the asymptotic formulas.
Chuan Wang - One of the best experts on this subject based on the ideXlab platform.
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Crosscorrelation estimation using teacher forcing hebbian learning and its application
Proceedings of International Conference on Neural Networks (ICNN'96), 1996Co-Authors: Chuan Wang, Jose C. PrincipeAbstract:This paper proposes a new network architecture to compute the temporal Crosscorrelation function between two signals, either stationary or local stationary. We show that the weights of a multi-FIR-like filter trained with a teacher forcing Hebbian rule encode the Crosscorrelation function between the input and the desired response. This temporal correlation idea is applied to the blind sources separation problem. And experimental results are also given to show the validation of the idea.
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ICNN - Crosscorrelation estimation using teacher forcing Hebbian learning and its application
Proceedings of International Conference on Neural Networks (ICNN'96), 1Co-Authors: Chuan Wang, Jose C. PrincipeAbstract:This paper proposes a new network architecture to compute the temporal Crosscorrelation function between two signals, either stationary or local stationary. We show that the weights of a multi-FIR-like filter trained with a teacher forcing Hebbian rule encode the Crosscorrelation function between the input and the desired response. This temporal correlation idea is applied to the blind sources separation problem. And experimental results are also given to show the validation of the idea.
T. Inouye - One of the best experts on this subject based on the ideXlab platform.
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Wavelet-Crosscorrelation Analysis: Non-Stationary Analysis of Neurophysiological Signals
Brain Topography, 2005Co-Authors: Y. Mizuno-matsumoto, S. Ukai, R. Ishii, S. Date, T. Kaishima, K. Shinosaki, S. Shimojo, M. Takeda, S. Tamura, T. InouyeAbstract:Objective: Wavelet-Crosscorrelation analysis is a new application of wavelet analysis used to show the propagation of epileptiform discharges and to localize the corresponding lesions. We have shown previously that this analysis can help predict brain conditions statistically (Mizuno-Matsumoto et al. 2002). Our objective was to assess whether wavelet-Crosscorrelation analysis reveals the initiation and propagation of epileptiform activity in human patients. Methods: The data obtained from three patients with simple partial seizures (SPS) using whole-head magnetoencephalography (MEG) were analyzed by the wavelet-Crosscorrelation method. Wavelet-Crosscorrelation coefficients (WCC), the coherent structure of each possible pair of signals from 64 MEG channels for various periods, and the time lag (TL) in two related signals, were ascertained. Results: We clearly demonstrated both localization of the irritative zone and propagation of the epileptiform discharges. Conclusions: Wavelet-Crosscorrelation analysis can help reveal and visualize the dynamic changes of brain conditions. The method of this analysis can compensate for other existing methods for the analysis of MEG, electroencephalography (EEG) or Elecotrocorticography (ECoG). Significance: Our proposed method suggests that revealing and visualizing the dynamic changes of brain conditions can help clinicians and even patients themselves better understand such conditions.
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Wavelet-Crosscorrelation analysis: Non-stationary analysis of neurophysiological signals.
Brain topography, 2005Co-Authors: Y. Mizuno-matsumoto, S. Ukai, R. Ishii, S. Date, T. Kaishima, K. Shinosaki, S. Shimojo, M. Takeda, S. Tamura, T. InouyeAbstract:Objective: Wavelet-Crosscorrelation analysis is a new application of wavelet analysis used to show the propagation of epileptiform discharges and to localize the corresponding lesions. We have shown previously that this analysis can help predict brain conditions statistically (Mizuno-Matsumoto et al. 2002). Our objective was to assess whether wavelet-Crosscorrelation analysis reveals the initiation and propagation of epileptiform activity in human patients.
Stanislav A. Trunov - One of the best experts on this subject based on the ideXlab platform.
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Crosscorrelation of Rudin–Shapiro-like polynomials
Applied and Computational Harmonic Analysis, 2020Co-Authors: Daniel J Katz, Sangman Lee, Stanislav A. TrunovAbstract:Abstract We consider the class of Rudin–Shapiro-like polynomials, whose L 4 norms on the complex unit circle were studied by Borwein and Mossinghoff. The polynomial f ( z ) = f 0 + f 1 z + ⋯ + f d z d is identified with the sequence ( f 0 , f 1 , … , f d ) of its coefficients. From the L 4 norm of a polynomial, one can easily calculate the autocorrelation merit factor of its associated sequence, and conversely. In this paper, we study the Crosscorrelation properties of pairs of sequences associated to Rudin–Shapiro-like polynomials. We find an explicit formula for the Crosscorrelation merit factor. A computer search is then used to find pairs of Rudin–Shapiro-like polynomials whose autocorrelation and Crosscorrelation merit factors are simultaneously high. Pursley and Sarwate proved a bound that limits how good this combined autocorrelation and Crosscorrelation performance can be. We find infinite families of polynomials whose performance approaches quite close to this fundamental limit.
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Crosscorrelation of Rudin-Shapiro-Like Polynomials
arXiv: Information Theory, 2017Co-Authors: Daniel J Katz, Sangman Lee, Stanislav A. TrunovAbstract:We consider the class of Rudin-Shapiro-like polynomials, whose $L^4$ norms on the complex unit circle were studied by Borwein and Mossinghoff. The polynomial $f(z)=f_0+f_1 z + \cdots + f_d z^d$ is identified with the sequence $(f_0,f_1,\ldots,f_d)$ of its coefficients. From the $L^4$ norm of a polynomial, one can easily calculate the autocorrelation merit factor of its associated sequence, and conversely. In this paper, we study the Crosscorrelation properties of pairs of sequences associated to Rudin-Shapiro-like polynomials. We find an explicit formula for the Crosscorrelation merit factor. A computer search is then used to find pairs of Rudin-Shapiro-like polynomials whose autocorrelation and Crosscorrelation merit factors are simultaneously high. Pursley and Sarwate proved a bound that limits how good this combined autocorrelation and Crosscorrelation performance can be. We find infinite families of polynomials whose performance approaches quite close to this fundamental limit.