Journal ArticleDOI
Fixed point error analysis of the normalized ladder algorithm
Claude Samson,V. Reddy +1 more
TLDR
In this article, the fixed point error performance of the normalized ladder algorithm, for autoregressive system identification, assuming rounding arithmetic, was analyzed and a simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage was derived.Abstract:
An attempt is made to analyze the fixed point error performance of the normalized ladder algorithm, for autoregressive system identification, assuming rounding arithmetic. A preliminary simulation study of this algorithm has shown that the bias in the estimated reflection coefficients is much more predominant than the variance of the error in the estimate. The study, therefore, is directed to find a model for predicting the bias in the estimated reflection coefficients. The analysis shows that the roundoff errors associated with the square root operations in one of the algorithm equations are mainly responsible for the bias in the estimated reflection coefficients. These errors arise because of the normalization procedure that makes the quantities under the square root operations very close to one. Two main results are presented in the paper. 1) A simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage is derived. 2) A recursive relation for the average error, arising from the finite precision arithmetic in the squared residuals, is derived. This relation illustrates how the errors made in one stage affect the errors in the succeeding stages. Simulations are performed to check the theoretical models. The experimental results agree very closely with the theoretical predictions.read more
Citations
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Journal ArticleDOI
Numerically stable fast transversal filters for recursive least squares adaptive filtering
Dirk Slock,Thomas Kailath +1 more
TL;DR: A solution is proposed to the long-standing problem of the numerical instability of fast recursive least squares transversal filter (FTF) algorithms with exponential weighting, an important class of algorithms for adaptive filtering.
Journal ArticleDOI
Paper: Error propagation properties of recursive least-squares adaptation algorithms
Stefan Ljung,Lennart Ljung +1 more
TL;DR: This work investigates how an error that is introduced at an arbitrary point in the algorithm propagates and it is shown that conventional LS algorithms are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially.
Journal ArticleDOI
Gradient-based variable forgetting factor RLS algorithm in time-varying environments
Shu-Hung Leung,C. F. So +1 more
TL;DR: A new control mechanism for the variable forgetting factor (VFF) of the recursive least square (RLS) adaptive algorithm is presented, which is basically a gradient-based method of which the gradient is derived from an improved mean square error analysis of RLS.
Journal ArticleDOI
Computationally Efficient Subspace-Based Method for Two-Dimensional Direction Estimation With L-Shaped Array
TL;DR: The effectiveness of proposed method and the theoretical analysis are verified through numerical examples, and it is shown that the proposed CODE method performs well at low signal-to-noise ratio (SNR) and with a small number of snapshots.
Journal ArticleDOI
Propagation of uncertainty in a discrete Fourier transform algorithm
TL;DR: The problem of evaluating the uncertainty that characterises discrete Fourier transform output data is dealt with, using a method based on a ‘white box’ theoretical approach, which can be particularly useful for any designer and user of DFT-based instruments.
References
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Journal ArticleDOI
Recursive least squares ladder estimation algorithms
TL;DR: A Hilbert space approach to the derivations of magnitude normalized signal and gain recursions is presented and normalized forms are expected to have even better numerical properties than the unnormalized versions.
Journal ArticleDOI
Effects of finite register length in digital filtering and the fast Fourier transform
Alan V. Oppenheim,C. Weinstein +1 more
TL;DR: The groundwork is set through a discussion of the relationship between the binary representation of numbers and truncation or rounding, and a formulation of a statistical model for arithmetic roundoff, to illustrate techniques of working with particular models.
Journal ArticleDOI
Effect of finite word length on the accuracy of digital filters--a review
TL;DR: The calculation of the statistical mean-squared error at the output of the filter is discussed in detail and some of the approaches used in investigating them are reviewed.
Proceedings ArticleDOI
An adaptive lattice structure for noise-cancelling applications
TL;DR: An adaptive filter structure which may be used in multi-channel noise-cancelling applications that incorporates a lattice filter framework, rather than tapped-delay-lines, which offers advantages in adaptive convergence rate which cannot be achieved with tapped- delay-lines.
Journal ArticleDOI
Application of Least Squares Lattice Algorithms to Adaptive Equalization
E. Satorius,J. Pack +1 more
TL;DR: This paper shows how the least squares lattice algorithms, recently introduced by Morf and Lee, can be adapted to the equalizer adjustment algorithm, which has a number of desirable features which should prove useful in many applications.