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Article: LMS-newton adaptive filtering using FFT-based conjugate gradient iterations
Title | LMS-newton adaptive filtering using FFT-based conjugate gradient iterations |
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Authors | |
Keywords | Fast fourier transform Toeplitz matrix Circulant matrix Preconditioned conjugate gradient method Lms-newton adaptive filter algorithm Finite impulse response filter |
Issue Date | 1996 |
Publisher | Kent State University, Institute of Computational Mathematics. The Journal's web site is located at http://etna.mcs.kent.edu/ |
Citation | Electronic Transactions on Numerical Analysis, 1996, v. 4, p. 14-36 How to Cite? |
Abstract | In this paper, we propose a new fast Fourier transform (FFT) based LMS-Newton (LMSN) adaptive filter algorithm. At each adaptive time step t, the rath-order filter coefficients are updated by using the inverse of an n-ky-n Hermitian, positive definite, Toeplitz operator T(t). By applying the cyclic displacement formula for the inverse of a Toeplitz operator, T(£) can be constructed using the solution vector of the Toeplitz system T(t)u(t) = en, where en is the last unit vector. We apply the FFT-based preconditioned conjugate gradient (PCG) method with the Toeplitz matrix T(t -1) as preconditioner to solve such systems at the step t. As both matrix vector products T(t)v and T(i -l)-1v can be computed by circular convolutions, FFTs are used throughout the computations. Under certain practical assumptions in signal processing applications, we prove that with probability 1 that the condition number of the preconditioned matrix T(t -1)~ T(t) is near to 1. The method converges very quickly, and the filter coefficients can be updated in O(n logra) operations per adaptive filter input. Preliminary numerical results are reported in order to illustrate the effectiveness of the method. Copyright ©1996, Kent State University. |
Persistent Identifier | http://hdl.handle.net/10722/276477 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 0.685 |
DC Field | Value | Language |
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dc.contributor.author | Michael, K. N.G. | - |
dc.contributor.author | Plemmons, Robert J. | - |
dc.date.accessioned | 2019-09-18T08:33:43Z | - |
dc.date.available | 2019-09-18T08:33:43Z | - |
dc.date.issued | 1996 | - |
dc.identifier.citation | Electronic Transactions on Numerical Analysis, 1996, v. 4, p. 14-36 | - |
dc.identifier.issn | 1068-9613 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276477 | - |
dc.description.abstract | In this paper, we propose a new fast Fourier transform (FFT) based LMS-Newton (LMSN) adaptive filter algorithm. At each adaptive time step t, the rath-order filter coefficients are updated by using the inverse of an n-ky-n Hermitian, positive definite, Toeplitz operator T(t). By applying the cyclic displacement formula for the inverse of a Toeplitz operator, T(£) can be constructed using the solution vector of the Toeplitz system T(t)u(t) = en, where en is the last unit vector. We apply the FFT-based preconditioned conjugate gradient (PCG) method with the Toeplitz matrix T(t -1) as preconditioner to solve such systems at the step t. As both matrix vector products T(t)v and T(i -l)-1v can be computed by circular convolutions, FFTs are used throughout the computations. Under certain practical assumptions in signal processing applications, we prove that with probability 1 that the condition number of the preconditioned matrix T(t -1)~ T(t) is near to 1. The method converges very quickly, and the filter coefficients can be updated in O(n logra) operations per adaptive filter input. Preliminary numerical results are reported in order to illustrate the effectiveness of the method. Copyright ©1996, Kent State University. | - |
dc.language | eng | - |
dc.publisher | Kent State University, Institute of Computational Mathematics. The Journal's web site is located at http://etna.mcs.kent.edu/ | - |
dc.relation.ispartof | Electronic Transactions on Numerical Analysis | - |
dc.subject | Fast fourier transform | - |
dc.subject | Toeplitz matrix | - |
dc.subject | Circulant matrix | - |
dc.subject | Preconditioned conjugate gradient method | - |
dc.subject | Lms-newton adaptive filter algorithm | - |
dc.subject | Finite impulse response filter | - |
dc.title | LMS-newton adaptive filtering using FFT-based conjugate gradient iterations | - |
dc.type | Article | - |
dc.description.nature | link_to_OA_fulltext | - |
dc.identifier.scopus | eid_2-s2.0-0011618933 | - |
dc.identifier.volume | 4 | - |
dc.identifier.spage | 14 | - |
dc.identifier.epage | 36 | - |
dc.identifier.eissn | 1068-9613 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 1068-9613 | - |