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25th Annual International Conference of the IEEE-Engineering-in-Medicine-and-Biology-Society

作者： Silva, R Zook, J Gaumond, R Penn State Univ University Pk PA 16802 USA

ISBN: (纸本)0780377893

We consider the problem of interpreting the signal recorded from an electrode, which sums currents from a large number of neurons responding asynchronously to an applied stimulus. We use a markov chain numerical simulation to establish conditions under which the action potential waveform can be extracted from the autocorrellation of the summed signal, by means of the levinson algorithm. We tested the efficacy of the algorithm in recovering the signal for two different Action Potential (AP) waveforms under different test conditions. We conclude that our system is both capable of recovering the average AP and detecting changes in its morphology.

关键词： field potential levinson algorithm multiple neurons simulation

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Receiver Function Estimated by Wiener Filtering

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Earthquake Research in China 2003年第4期17卷 386-391页

作者： Wu Qingju, Tian Xiaobo, Zhang Nailing, Li Weiping and Zeng RongshengInstitute of Geophysics, China Seismological Bureau, Beijing 100081, China Institute of Geophysics China Seismological Bureau Beijing 100081China

Wiener filtering is used to estimate receiver function in a time_domain. With the vertical component of 3_component teleseismic P waveform as the input of a Wiener filter, receiver function as the filter response, and radial and tangential components as the expected output, receiver function is estimated by minimizing the error between expected and actual outputs. Receiver function can be obtained by solving the Toeplitz equation using the levinson algorithm. The non_singularity of the Toeplitz equation ensures the stability of Wiener Deconvolution. Both synthetic and observational seismogram checks show that Wiener Deconvolution is an effective time_domain method to estimate receiver function from teleseismic P waveform.

关键词： Receiver function Wiener filter Toeplitz equation levinson algorithm

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A levinson-Galerkin algorithm for regularized trigonometric approximation

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2000年第4期22卷 1160-1183页

作者： Strohmer, T Univ Calif Davis Dept Math Davis CA 95616 USA

Trigonometric polynomials are widely used for the approximation of a smooth function from a set of nonuniformly spaced samples. If the samples are perturbed by noise, a good choice for the polynomial degree of the trigonometric approximation becomes an essential issue to avoid overfitting and underfitting of the data. Standard methods for trigonometric least squares approximation assume that the degree for the approximating polynomial is known a priori, which is usually not the case in practice. We derive a multilevel algorithm that recursively adapts to the least squares solution of suitable degree. We analyze under which conditions this multilevel approach yields the optimal solution. The proposed algorithm computes the solution in at most O (rM + M-2) operations (M being the polynomial degree of the approximation and r being the umber of samples) by solving a family of nested Toeplitz systems. It is shown how the presented method can be extended to multivariate trigonometric approximation. We demonstrate the performance of the algorithm by applying it in echocardiography to the recovery of the boundary of the left ventricle of the heart.

关键词： trigonometric approximation Toeplitz matrix levinson algorithm multilevel method

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Comparative study of joint-detection techniques for TD-CDMA based mobile radio systems

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2001年第8期19卷 1461-1475页

作者： Vollmer, M Haardt, M Götze, J Siemens AG Informat & Commun Mobile D-81359 Munich Germany Univ Dortmund Informat Proc Lab D-44221 Dortmund Germany Siemens AG Informat & Commun Mobile D-81359 Munich Germany

Third-generation mobile radio systems use time division-code division multiple access (TD-CDMA) in their time division duplex (TDD) mode. Due to the time division multiple access (TDMA) component of TD-CDMA, joint (or multi-user) detection techniques can be implemented with a reasonable complexity. Therefore, joint detection will already be implemented in the first phase of the system deployment to eliminate the intracell interference. In a TD-CDMA mobile radio system, joint-detection is performed by solving a least squares problem, where the system matrix has a block-Sylvester structure. In this paper, we present and compare several techniques that reduce the computational complexity of the joint detection task even further by exploiting this block-Sylvester structure and by incorporating different approximations. These techniques are based on the Cholesky factorization, the levinson algorithm, the Schur algorithm, and on Fourier techniques, respectively. The focus of this paper Is on Fourier techniques since they have the smallest computational complexity and achieve the same performance as the joint detection algorithm that does not use any approximations. Similar to the well-known implementation of fast convolutions, the resulting Fourier-based joint detection scheme also uses a sequence of fast Fourier transforms (FFTs) and overlapping. It is well suited for the implementation on parallel hardware architectures.

关键词： Cholesky factor fast Fourier transform joint detection levinson algorithm overlap save Schur algorithm TD-CDMA Toeplitz structure

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Maximum likelihood estimation with side information of a 1-D discrete layered medium from its noisy impulse reflection response

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2000年第7期48卷 1975-1983页

作者： Yagle, AE Joshi, RR Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA

We consider the problem of computing the maximum likelihood estimates of the reflection coefficients of a discrete 1-D layered medium from noisy observations of its impulse reflection response. We have side information in that a known subset of the reflection coefficients are known to be zero;this knowledge could come from either a priori knowledge of a homogeneous subregion inside the scattering medium or from a thresholding operation in which noisy reconstructed reflection coefficients with absolute values below a threshold are known to be zero. Our procedure converges in one or two iterations, each of which requires only setting up and solving a small system of linear equations and running the levinson algorithm, Numerical examples are provided that demonstrate not only the operation of the algorithm but also that the side information improves the reconstruction of unconstrained reflection coefficients as well as constrained ones due to the nonlinearity of the inverse scattering problem.

关键词： inverse scattering levinson algorithm maximum likelihood estimation

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Linear approximation in the discrete frequency domain

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2000年第1-2期126卷 255-267页

作者： Alonso, S González-Concepción, C Univ La Laguna Dept Estadist Invest Operat & Computac Tenerife Spain Univ La Laguna Dept Econ Aplicada Tenerife Spain

In this paper, a linear model in the discrete frequency domain is used. The main aim of this work is not only to deduce a filter model expression for DFT sequences of real data, but also to give an interpretation of the parameters involved in this expression. This convenient explanation is built given the relationship between the reflection coefficients used by the levinson algorithm and the dispersion of the energy of the sequence in the frequency domain. From this interpretation, the computation of the model parameters is accelerated in a levinson algorithm modified. A realistic example is presented to show these results. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 42A16;41A45;41A21.

关键词： linear prediction levinson algorithm discrete frequency domain

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Asymmetric half-plane lattice modeling based on 2-D levinson algorithm

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING 1997年第10期44卷 865-868页

作者： Nakachi, T Yamashita, K Hamada, N UNIV RYUKYUS FAC ENGNNISHIHARAOKINAWA 903JAPAN

This brief proposes a two-dimensional (2-D) levinson algorithm and a lattice filter for the general case of the Autoregressive (AR) model with an asymmetric half-plane (AHP) support, The resulting levinson algorithm and corresponding lattice filter solve the 2-D normal equation recursively, Although the 2-D signals of the model support are ordered into a one-dimensional (1-D) array, the ordering of the support signal is assigned voluntarily, The effects on the resulting model caused by different choices of support signal ordering are discussed. Finally, the validity of the proposed theory is confirmed through various simulations.

关键词： lattice filter levinson algorithm linear prediction two-dimensional signal processing

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Unitary orthogonalization processes

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1997年第1期86卷 335-345页

作者： Watkins, DS WASHINGTON STATE UNIV DEPT PURE & APPL MATHPULLMANWA 99164

All methods for solving least-squares problems involve orthogonalization in one way or another. Certain fundamental estimation and prediction problems of signal processing and time-series analysis can be formulated as least-squares problems. In these problems, the sequence that is to be orthogonalized is generated by an underlying unitary operator. A prime example of an efficient orthogonalization procedure for this class of problems is Gragg's isometric Arnoldi process, which is the abstract encapsulation of a number of concrete algorithms. In this paper, we discuss a two-sided orthogonalization process that is equivalent to Gragg's process but has certain conceptual strengths that warrant its introduction. The connections with classical algorithms of signal processing are discussed.

关键词： orthogonalization unitary operators levinson algorithm

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Further optimized look-ahead recurrences for adjacent rows in the Pade table and Toeplitz matrix factorizations

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1997年第1期86卷 219-236页

作者： Hochbruck, M UNIV TUBINGEN MATH INSTD-72076 TUBINGENGERMANY

In a recent paper, we introduced a new look-ahead algorithm for recursively computing Pade approximants. This algorithm generates a subsequence of the Pade approximants on two adjacent rows (defined by fixed numerator degree) of the Pade table. Its two basic versions reduce to the classical levinson and Schur algorithms if no look-ahead is required. In this paper, we show that the computational overhead of the look-ahead steps in the O(N-2) versions of the look-ahead levinson-and the look-ahead Schur-type algorithm can be further reduced. If the algorithms are used to solve Toeplitz systems of equations Tx = b, then the corresponding block LDU decompositions of T-1 or T, respectively, can be found with less computational effort than with any other look-ahead algorithm available today.

关键词： Pade approximation row recurrence fast algorithm sawtooth recurrence look-ahead toeplitz matrix levinson algorithm Schur algorithm biorthogonal polynomials

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Optimized look-ahead recurrences for adjacent rows in the Pade table

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BIT 1996年第2期36卷 264-286页

作者： Gutknecht, MH Hochbruck, M ETH ZENTRUM SWISS CTR SCI COMPCH-8092 ZURICHSWITZERLAND UNIV TUBINGEN INST MATHD-72076 TUBINGENGERMANY

A new look-ahead algorithm for recursively computing Pade approximants is introduced. It generates a subsequence of the Fade approximants on two adjacent rows (defined by fixed numerator degree) of the Pade table. Its two basic versions reduce to the classical levinson and Schur algorithms if no look-ahead is required. The new algorithm can be viewed as a combination of the look-ahead sawtooth and the look-ahead levinson and Schur algorithms that we proposed before, but now the look-ahead step size is minimal (as in the sawtooth version) and the computational costs are as low as in the least expensive competing algorithms (including our look-ahead levinson and Schur algorithms). The underlying recurrences Link well-conditioned basic pairs, i.e., pairs of sufficiently different neighboring Pade forms. The algorithm can be used to solve Toeplitz systems of equations Tx = b. In this application it comes in several versions: an O(N-2) levinson-type form, an O(N-2) Schur-type form, and a superfast O(Nlog(2) N) Schur-type version. As an option of the first two versions, the corresponding block LDU decompositions of T-1 or T, respectively, can be found.

关键词： Pade approximation row recurrence fast algorithm sawtooth recurrence look-ahead Toeplitz matrix levinson algorithm Schur algorithm biorthogonal polynomials

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