Volume 4, pp. 14-36, 1996.
LMS-Newton adaptive filtering using FFT-based conjugate gradient iterations
Michael K. Ng and Robert J. Plemmons
Abstract
In this paper, we propose a new fast Fourier transform (FFT) based
LMS-Newton (LMSN) adaptive filter algorithm. At each adaptive time
step , the th-order filter coefficients are updated by using the
inverse of an -by- Hermitian, positive definite, Toeplitz operator
. By applying the cyclic displacement formula for
the inverse of a Toeplitz operator, can be constructed using
the solution vector of the Toeplitz system , where
is the last unit vector.
We apply the FFT–based preconditioned conjugate
gradient (PCG) method with the Toeplitz matrix as preconditioner
to solve such
systems at the step .
As both matrix vector products and
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 is near to
1. The method converges very quickly, and the filter coefficients can be
updated in operations per adaptive filter input.
Preliminary numerical results are reported in order to illustrate
the effectiveness of the method.
Full Text (PDF) [486 KB],
BibTeX
Key words
LMS-Newton adaptive filter algorithm, finite impulse response filter, Toeplitz matrix, circulant matrix, preconditioned conjugate gradient method, fast Fourier transform.
AMS subject classifications
65F10.
Links to the cited ETNA articles