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25
Multichannel Blind Deconvolution: Fir Matrix Algebra And Separation Of Multipath Mixtures
, 1996
"... A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and mat ..."
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A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feedforward memory connections, wideband array processing, and in problems with a multiinput, multioutput network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...
Levinson and Fast Choleski Algorithms for Toeplitz and Almost Toeplitz Matrices
 Internal Report, Lab of Elec., MIT
, 1984
"... In this paper, we review Levinson and fast Choleski algorithms for solving sets of linear equations involving Toeplitz or almost Toeplitz matrices. The LevinsonTrenchZohar algorithm is first presented for solving problems involving exactly Toeplitz matrices. A fast Choleski algorithm is derived by ..."
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In this paper, we review Levinson and fast Choleski algorithms for solving sets of linear equations involving Toeplitz or almost Toeplitz matrices. The LevinsonTrenchZohar algorithm is first presented for solving problems involving exactly Toeplitz matrices. A fast Choleski algorithm is derived by a simple linear transformation. The almost Toeplitz problem is then considered and a Levinsonstyle algorithm is proposed for solving it. A set of linear transformations converts the algorithm into a fast Choleski method. Symmetric and band diagonal applications are considered. Formulas for the inverse of an almost Toeplitz matrix are derived. The relationship between the fast Choleski algorithms and a Euclidian algorithm is exploited in order to derive accelerated &quot;doubling &quot; algorithms for inverting the matrix. Finally, strategies for removing the strongly nonsingular constraint
Matrixvalued NevanlinnaPick interpolation with complexity constraint: An optimization approach
 IEEE Trans. Automatic Control
, 2003
"... Abstract. Over the last several years a new theory of NevanlinnaPick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrixvalued case, also allowing for multiple interpolation points. We parameterize a class of in ..."
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Abstract. Over the last several years a new theory of NevanlinnaPick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrixvalued case, also allowing for multiple interpolation points. We parameterize a class of interpolants consisting of “most interpolants ” of no higher degree than the central solution in terms of spectral zeros. This is a complete parameterization, and for each choice of interpolant we provide a convex optimization problem for determining it. This is derived in the context of duality theory of mathematical programming. To solve the convex optimization problem, we employ a homotopy continuation technique previously developed for the scalar case. These results can be applied to many classes of engineering problems, and, to illustrate this, we provide some examples. In particular, we apply our method to a benchmark problem in multivariate robust control. By constructing a controller satisfying all design specifications but having only half the McMillan degree of conventional H ∞ controllers, we demonstrate the efficiency of our method.
A new algorithm for optimal filtering of discretetime stationary processes
 SIAM J. Control
, 1974
"... Abstract. An algorithm (which does not involve the usual Riccatitype equation) for computing t/e gain matrices of the Kalman filter is presented. If the dimension k of the state space is much larger than that of the observation process, the number of nonlinear equations to be solved in each step is ..."
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Abstract. An algorithm (which does not involve the usual Riccatitype equation) for computing t/e gain matrices of the Kalman filter is presented. If the dimension k of the state space is much larger than that of the observation process, the number of nonlinear equations to be solved in each step is of order k rather than k as by the usual procedure. 1. Introduction. Let {x.
Relationships between digital signal processing and control and estimation theory
 Proceedings of the IEEE
, 1978
"... The purpose of this paper is to explore several current research directions in the fields of digital signal processing and modern control and estimation theory. We examine topics such as stability theory, linear prediction, and parameter identification, system synthesis and implementation, twodimens ..."
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Cited by 8 (4 self)
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The purpose of this paper is to explore several current research directions in the fields of digital signal processing and modern control and estimation theory. We examine topics such as stability theory, linear prediction, and parameter identification, system synthesis and implementation, twodimensional filtering, decentralized control and estimation, and image processing, in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines.
Computationally Efficient TwoDimensional Capon Spectrum Analysis
"... We present a computationally ecient algorithm for computing the 2D Capon spectral estimator. The implementation is based on the fact that the 2D data covariance matrix will have a ToeplitzBlockToeplitz structure, with the result that the inverse covariance matrix can be expressed in closed form ..."
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We present a computationally ecient algorithm for computing the 2D Capon spectral estimator. The implementation is based on the fact that the 2D data covariance matrix will have a ToeplitzBlockToeplitz structure, with the result that the inverse covariance matrix can be expressed in closed form by using a special case of the GohbergHeinig formula that is a function of strictly the forward 2D prediction matrix polynomials. Furthermore, we present a novel method, based on a 2D lattice algorithm, to compute the needed forward prediction matrix polynomials and discuss the dierence in the soobtained 2D spectral estimate as compared to the one obtained by using the prediction matrix polynomials given by the WhittleWigginsRobinson algorithm. Numerical simulations illustrate the clear computational gain in comparison to both the wellknown classical implementation and the method recently published by Liu et al. This work was supported in part by the Swedish Foundation for Strateg...
Assessment of linear and nonlinear EEG synchronization measures for
"... evaluating mild epileptic signal patterns ..."
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"... A decision support framework for the discrimination of children with controlled epilepsy ..."
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A decision support framework for the discrimination of children with controlled epilepsy
> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLECLICK HERE TO EDIT) < 1 A Modified Burg Algorithm Equivalent In Results to Levinson Algorithm
"... Abstract — We present a new modified BurgLike algorithm for spectral estimation and adaptive signal processing that yield the same prediction coefficients given by the Levinson algorithm for the solution of the normal equations. An equivalency proof is given for both the 1D signal and 2D signal cas ..."
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Abstract — We present a new modified BurgLike algorithm for spectral estimation and adaptive signal processing that yield the same prediction coefficients given by the Levinson algorithm for the solution of the normal equations. An equivalency proof is given for both the 1D signal and 2D signal cases. Numerical simulations illustrate the improved accuracy and stability in spectral power amplitude and localization; especially in the cases of low signal to noise ratio, and (or) augmenting the used prediction coefficients number for a relatively short data records. Also our simulations illustrate that for relatively short data records the unmodified version of Burg Algorithm fail to minimize the mean square residual error beyond certain Order, while the new algorithm continue the minimization with Order elevation. Index Terms—Adaptive Signal processing, lattice filters, image processing, multidimensional signal processing.