The letter deals with the development of a simplified fastleast-squares algorithm which is free of roundoff error accumulation. The simplified algorithm requires 9N MADPR (multiplications and divisions per recursion)...
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The letter deals with the development of a simplified fastleast-squares algorithm which is free of roundoff error accumulation. The simplified algorithm requires 9N MADPR (multiplications and divisions per recursion) rather than 10N MADPR as in the fastleastsquares or fast Kalman (FLS) case where N is the order of predictor. The superiority of SFLS over FLS and LMS approaches is illustrated by prediction gain performance curves for various speech signals.
In this paper, a fast affine projection algorithm (FAPA), for the two-dimensional (2-D) adaptive linear filtering and prediction, is presented. The derivation of the proposed algorithm is based on the spatial shift-in...
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In this paper, a fast affine projection algorithm (FAPA), for the two-dimensional (2-D) adaptive linear filtering and prediction, is presented. The derivation of the proposed algorithm is based on the spatial shift-invariant properties of the 2-D discrete time signals. The proposed algorithm has low computational complexity, comparable to that of the 2-D LMS algorithm. The performance of the proposed scheme is comparable to that of the higher complexity 2-D RLS algorithms. The convergence speed and the tracking ability of the proposed 2-D FAPA algorithm are illustrated by computer simulation. (c) 2005 Elsevier B.V. All rights reserved.
Low displacement rank theory underlies many fastalgorithms designed for structured covariance matrices. Some of these have gained notoriety for their numerical instability problems, particularly fastleast-squares al...
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Low displacement rank theory underlies many fastalgorithms designed for structured covariance matrices. Some of these have gained notoriety for their numerical instability problems, particularly fast least-squares algorithms. Recent studies have shown that instability is not inherent to fastalgorithms, but rather comes from the violation of backward consistency constraints. This paper thus details the connection between covariance matrices of a given displacement inertia and lossless rational matrices, as well as the role of this connection in numerically consistent algorithms. This basic connection allows displacement structures to be parametrized via a sequence of rotation angles obtained from a lossless system. The utility of this approach is that, irrespective of errors in the rotation parameter set, they remain consistent with a positive definite matrix of a prescribed displacement inertia. This property in turn may be rephrased as meaningful forms of backward consistency in numerical algorithms. The rotation parameters then take the form of Givens or Jacobi angles applied to data, in contrast to classical approaches which directly manipulate dyadic decompositions of the displacement structure. The concepts are illustrated in popular signal processing applications. In particular, these connections lend clear insight into the stable computation of reflection coefficients of Toeplitz, systems, and also serve to resolve the numerical instability problem of fast least-squares algorithms.
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