Abstract
The ladder algorithms presented in Chap. 7 were based on the recursive computation of transversal predictor parameters, which serve as intermediate recursion variables. This type of ladder algorithm employed the Levinson recursion for a conversion between the transversal predictor parameters and the ladder reflection coefficients. Although the ladder reflection coefficients are known to have a lower variance than the transversal predictor parameters, this advantage is compensated by the Levinson recursion, which requires a high dynamic range for the computation of the intermediate transversal predictor parameters. In fact, the intermediate transversal predictor parameters are unbounded quantities, i.e., they may attain large values, depending on the data. This makes the fixed-point implementation of Levinson type algorithms quite a difficult task.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chapter 8
J. LeRoux, C. Gueguen: A fixed-point computation of partial correlation coefficients. IEEE Trans. ASSP 25, 257–259 (1977)
A. Cumani: On a covariance lattice algorithm for linear prediction. Proc. IEEE Int. Conf. on ASSP, Paris (1982) pp. 651–654
J. Makhoul: Stable and efficient lattice methods for linear prediction. IEEE Trans. ASSP 25, 423–428 (1977)
P. Strobach: Pure order recursive least-squares ladder algorithms. IEEE Trans. ASSP 34, 880–897 (1986)
P. Strobach: A new approach to the least-squares ladder estimation algorithm. Proc. IASTED Int. Symp. Appl. Signal Proc. Digital Filtering, Paris (1985) pp. 37–40
J. Sokat, P. Strobach: A new class of pure order recursive ladder algorithms. Proc. IEEE Int. Workshop on Digital Signal Processing, Stanford Sierra Lodge, Tahoe, CA (1988)
J. Sokat: The split generalized LeRoux-Gueguen algorithm for least-squares problems. Proc. Int. Symp. on Signals, Systems, and Electronics, URSI, Erlangen (Sept. 1989) to appear
P. Strobach: Efficient covariance ladder algorithms for finite arithmetic applications. Signal Processing 13, 29–70 (1987)
N. Levinson: The Wiener RMS (root-mean-square) error criterion in filter design and prediction. J. Math. Phys. 25, 261–278 (1947)
J. Durbin: The fitting of time series models. Rev. Int. Stat. 28, 233–244 (1960)
J. Heinhold: Einführung in die Höhere Mathematik (Carl Hanser, München 1976)
J.P. Burg: Maximum Entropy Spectral Analysis. Ph.D. Dissertation, Stanford University, Stanford, CA (1975)
J.D. Markel, A.H. Gray: Linear Prediction of Speech, Communications and Cybernetics, Vol. 12 (Springer, Berlin, Heidelberg 1976)
U. Grenander, G. Szegö: Toeplitz Forms and Their Applications (California Press, Berkeley, CA 1958)
P. Delsarte, Y. Genin: On the splitting of classical algorithms in linear prediction theory. IEEE Trans. ASSP 35, 645–653 (1987)
H. Krishna: New split Levinson, Schur, and lattice algorithms for digital signal processing. IEEE Int. Conf. on ASSP, New York (1988) pp. 1640–1642
I. Schur (1917): Über Potenzreihen die im Innern des Einheitskreises beschränkt sind. J. Reine Angew. Math. 147, 205–232; ibid. 148, 122–145 (1917)
P. Strobach: A fast recursive approach to FIR system identification. Proc. EUSIPCO-86, The Hague (1986) pp. 1055–1058
P. Strobach: Recursive covariance ladder algorithms for ARMA system identification. IEEE Trans. ASSP 36, 560–580 (1988)
S.Y. Kung, Y.H. Hu: A highly concurrent algorithm and pipelined architecture for solving Toeplitz systems. IEEE Trans. ASSP 31, 66–76 (1983)
I.C. You, Y.H. Hu, W.S. Feng: A novel implementation of pipelined Toeplitz system solver. Proc. IEEE 74, 1463–1464 (1986)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Strobach, P. (1990). Covariance Ladder Algorithms. In: Linear Prediction Theory. Springer Series in Information Sciences, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75206-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-75206-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-75208-7
Online ISBN: 978-3-642-75206-3
eBook Packages: Springer Book Archive