Article

Optimum block adaptive filtering algorithms using the preconditioning technique

Dept. of Comput. Sci., Korea Adv. Inst. of Sci. & Technol., Seoul
IEEE Transactions on Signal Processing (Impact Factor: 2.81). 04/1997; DOI: 10.1109/78.558502
Source: IEEE Xplore

ABSTRACT We propose three block adaptive algorithms using the
preconditioning technique. The Toeplitz-preconditioned optimum block
adaptive (TOBA) algorithm employs a preconditioner assumed to be
Toeplitz, the symmetric successive overrelaxation (SSOR)-preconditioned
optimum block adaptive (SOBA) algorithm uses a product of triangular
matrices as a preconditioner, and the circulant-preconditioned OBA
(COBA) algorithm is based on a circulant preconditioner. It is also
shown that their tracking properties and convergence rates are superior
to those of the OBA algorithm, the self-orthogonizing block adaptive
filter (SOBAF), and the normalized frequency-domain OBA (NFOBA)
algorithm

0 Bookmarks
 · 
32 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The solution of symmetric positive definite Toeplitz systems Ax = b by the preconditioned conjugate gradient (PCG) method was recently proposed by Strang (1986) and analyzed by Chan (1989) and Chan and Strang (1989). The convergence rate of the PCG method depends on the choice of preconditioners for the given Toeplitz matrices. The authors present a general approach to the design of Toeplitz preconditioners based on the idea to approximate a partially characterized linear deconvolution with circular deconvolutions. All resulting preconditioners can therefore be inverted via various fast transform algorithms with O ( N log N ) operations. For a wide class of problems, the PCG method converges in a finite number of iterations independent of N so that the computational complexity for solving these Toeplitz systems is O ( N log N )
    IEEE Transactions on Signal Processing 02/1992; · 2.81 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We describe an implementation of the generalized Schur algorithm for the superfast solution of real positive denite Toeplitz systems of order n + 1, where n = 2 . Our implementation uses the split-radix fast Fourier transform algorithms for real data of Duhamel. We are able to obtain the nth Szeg} o polynomial using fewer than 8n log22 n real arithmetic operations without explicit use of the bit-reversal permutation. Since Levinson's algorithm requires slightly more than 2n2 operations to obtain this polynomial, we achieve crossover with Levinson's algorithm at n = 256.
    Siam Journal on Matrix Analysis and Applications - SIAM J MATRIX ANAL APPLICAT. 01/1988; 9(1).
  • [Show abstract] [Hide abstract]
    ABSTRACT: Three fast and flexible block transform-domain gradient adaptive digital filters (ADF's) for finite impulse response (FIR) adaptive filtering are presented. The proposed ADF's employ a two-dimensional optimum block algorithm (OBA) in order to obtain a time-varying convergence factor which is optimized in a least square (LS) sense for fast and accurate adaptation, and to allow one to choose an appropriate transform size for smaller block delay and more efficient use of a hardware. In the first one of the proposed ADF's, the multidelay frequency-domain OBA (MFOBA), the two-dimensional OBA is realized with the conventional fast Fourier transform (FFT). In the second one, the normalized MFOBA (NMFOBA), a robust normalization method significantly improves its convergence speed for colored input signals. In the third one, the Fermat number transform (FNT) based realization (MFOBA/FNT), the desirable properties of the FNT (e.g., no roundoff errors, no multiplication and no complex basis functions) are utilized to yield an ideal structure for an efficient hardware implementation. By computer simulation, it is shown that these ADF's are faster than other transform-domain adaptive algorithms
    IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing 06/1994;