A fast ARMA transversal RLS filter algorithm

Ardalan, S.H.; Faber, Lukas

doi:10.1109/29.1531

Cited by 17 publications

(4 citation statements)

References 11 publications

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“…The procedure starts from the last row of , moves upwards, and guarantees the upper triangular structure and the positivedefiniteness of the resulting factor. It is now straightforward that inversion of (53) and (56) leads to (15) and (16).…”

Section: Discussionmentioning

confidence: 99%

“…where is the Cholesky factor of It is clear from (14) that the time update of requires the time update of The latter is achieved by employing (for a proof see Appendix A) (15) and (16), shown at the bottom of the page, where and are quantities related to the backward and forward problems, respectively (Appendix A). According to (56) of Appendix A, the orthogonal matrix satisfies the equation (17) Matrix can be split up into blocks as…”

Section: Block Multichannel Fast Qrd Algorithmmentioning

confidence: 99%

“…It is clear from the discussion in Appendix A that if is the "part" of that annihilates , then consists of elementary Givens rotation matrices and satisfies (18) Furthermore, it is straightforward that Combining, (14), (15), and the input vector partition , we get (19) where the vector corresponds to the last elements of and is expressed as (20) Clearly, is the th-order a priori backward error vector, and consequently, can be interpreted as the th-order normalized a priori backward error vector. In addition, the nesting of vectors in (19) indicates that the th -element block of (16) corresponds to the th-order normalized a priori backward error vector for From (14), (16), and the input vector partition , we also obtain (21) where (22) is the th-order a priori normalized forward error vector.…”

Section: Block Multichannel Fast Qrd Algorithmmentioning

confidence: 99%

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Multichannel fast QRD-LS adaptive filtering: new technique and algorithms

Rontogiannis

1998

IEEE Trans. Signal Process.

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Abstract-In this paper, a direct, unified approach for deriving fast multichannel QR decompostion (QRD) least squares (LS) adaptive algorithms is introduced. The starting point of the new methodology is the efficient update of the Cholesky factor of the input data correlation matrix. Using the new technique, two novel fast multichannel algorithms are developed. Both algorithms comprise scalar operations only and are based exclusively on numerically robust orthogonal Givens rotations. The first algorithm assumes channels of equal orders and processes them all simultaneously. It is highly modular and provides enhanced pipelinability, with no increase in computational complexity, when compared with other algorithms of the same category. The second multichannel algorithm deals with the general case of channels with different number of delay elements and processes each channel separately. A modification of the algorithm leads to a scheme that can be implemented on a very regular systolic architecture. Moreover, both schemes offer substantially reduced computational complexity compared not only with the first algorithm but also with previously derived multichannel fast QRD schemes. Experimental results in two specific application setups as well as simulations in a finite precision environment are also included.

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Section: Discussionmentioning

confidence: 99%

Section: Block Multichannel Fast Qrd Algorithmmentioning

confidence: 99%

Section: Block Multichannel Fast Qrd Algorithmmentioning

confidence: 99%

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Multichannel fast QRD-LS adaptive filtering: new technique and algorithms

Rontogiannis

1998

IEEE Trans. Signal Process.

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“…The computational complexity of a fast RLS transversal ARMA filter can also be expressed in order of p k and q k [50]. When the fast Fourier transform (FFT) is utilized in implementing the Periodogram method, the required number of operations, which is the total number of real additions(subtractions) and multiplications(divisions) is C FFT (N) = 4N log 2 N, where N is the number of signal samples and is a power of 2 [51].…”

Section: Computational Complexitymentioning

confidence: 99%

Adaptive multichannel sequential lattice prediction filtering method for ARMA spectrum estimation in subbands

Ozden

2013

EURASIP J. Adv. Signal Process.

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A multichannel characterization for autoregressive moving average (ARMA) spectrum estimation in subbands is considered in this article. The fullband ARMA spectrum estimation can be realized in two-channels as a special form of this characterization. A complete orthogonalization of input multichannel data is accomplished using a modified form of sequential processing multichannel lattice stages. Matrix operations are avoided, only scalar operations are used, and a multichannel ARMA prediction filter with a highly modular and suitable structure for VLSI implementations is achieved. Lattice reflection coefficients for autoregressive (AR) and moving average (MA) parts are simultaneously computed. These coefficients are then converted to process parameters using a newly developed Levinson-Durbin type multichannel conversion algorithm. Hence, a novel method for spectrum estimation in subbands as well as in fullband is developed. The computational complexity is given in terms of model order parameters, and comparisons with the complexities of nonparametric methods are provided. In addition, the performance is visually and statistically compared against those of the nonparametric methods under both stationary and nonstationary conditions.

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Fast algorithm of chandrasekhar type for ARMA model identification

Brella

Longchamp

1992

Automatica

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A fast ARMA transversal RLS filter algorithm

Cited by 17 publications

References 11 publications

Multichannel fast QRD-LS adaptive filtering: new technique and algorithms

Multichannel fast QRD-LS adaptive filtering: new technique and algorithms

Adaptive multichannel sequential lattice prediction filtering method for ARMA spectrum estimation in subbands

Fast algorithm of chandrasekhar type for ARMA model identification

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