Proceedings ArticleDOI
FFT-based RLS in signal processing
Robert J. Plemmons
- Vol. 3, pp 571-574
TLDR
An algorithm for fast adaptive filtering that applies a FFT (fast Fourier transform)-based iterative method and uses sliding data windows involving block updating and downdating computations and computes the tap weight filter vector in O(L log N) operations.Abstract:
An algorithm for fast adaptive filtering is proposed. The algorithm applies a FFT (fast Fourier transform)-based iterative method and uses sliding data windows involving block updating and downdating computations. The method is stable and robust, and computes the tap weight filter vector in O(L log N) operations, where the sliding window Toeplitz data matrix X is L-by-N. The complexity thus generally lies between those of the family of unstable but fast, O(N), methods and the stable but slow O(N/sup 2/) Cholesky factor updating methods. >read more
Citations
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Journal ArticleDOI
Conjugate Gradient Methods for Toeplitz Systems
Raymond H. Chan,Michael K. Ng +1 more
TL;DR: Some of the latest developments in using preconditioned conjugate gradient methods for solving Toeplitz systems are surveyed, finding that the complexity of solving a large class of $n-by-n$ ToePlitz systems is reduced to $O(n \log n)$ operations.
Journal ArticleDOI
Analysis of conjugate gradient algorithms for adaptive filtering
Pi Sheng Chang,Alan N. Willson +1 more
TL;DR: Two approaches to the implementation of the conjugate gradient algorithm for filtering where several modifications to the original CG method are proposed are presented and it is shown that in finite word-length computation and close to steady state, the algorithms' behaviors are similar to the steepest descent algorithm.
Journal ArticleDOI
Galerkin Projection Methods for Solving Multiple Linear Systems
Tony F. Chan,Michael K. Ng +1 more
TL;DR: A theoretical error bound is given for the approximation obtained from a projection process onto a Krylov subspace generated from solving a previous linear system and numerical results for multiple linear systems arising from image restorations and recursive least squares computations are reported to illustrate the effectiveness of the method.
Proceedings ArticleDOI
Adaptive filtering using modified conjugate gradient
Pi Sheng Chang,Alan N. Willson +1 more
TL;DR: In this article, an adaptive filtering algorithm is described that uses the modified Conjugate Gradient (CG) algorithm, which has the ability to perform sample-by-sample updating of the filter coefficients more efficiently than previously described CG methods.
Proceedings ArticleDOI
Analysis of conjugate gradient algorithms for adaptive filtering
Pi Sheng Chang,Alan N. Willson +1 more
TL;DR: It is shown that, close to steady-state, the Conjugate Gradient algorithms' behaviors are similar to the Steepest Descent algorithm, where the stalling phenomenon is also observed and the algorithms are numerically stable.
References
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Book
Adaptive Filter Theory
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
Book
Discrete-Time Signal Processing
TL;DR: In this paper, the authors provide a thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete time Fourier analysis.
Journal ArticleDOI
An Optimal Circulant Preconditioner for Toeplitz Systems
TL;DR: The new preconditioner is easy to compute and in preliminary numerical experiments performs better than Strang's preconditionser in terms of reducing the condition number of $C^{ - 1} A$ and comparably in Terms of clustering the spectrum around unity.