Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.
About 89 papers for “Levinson recursion”
Franke, J., Heidelberg Univ. (Germany). Sonderforschungsbereich 123 - Stochastische Mathematische Modelle, Deutsche Forschungsgemeinschaft (DFG), Bonn (Germany) · OpenGrey (Institut de l'Information Scientifique et Technique) · 1985
Cited by 0
J�rgen Franke · Biometrika · 1985
We discuss an algorithm which allows for recursive-in-order calculation of the parameters of autoregressive-moving average processes. The proposed procedure generalizes the recursion of Levinson (1946) and Durbin (1960), which applies in the pure autoregressive case. We use ideas similar to the multivariate autoregressive case. Our results suggest how estimation procedures for autoregressive-moving average parameters, which include an automatic choice of model order, for example, the one proposed by Hannan & Rissanen (1982), may be made computationally more efficient.
Cited by 41
Manuel Duarte Ortigueira, António Serralheiro · IET Control Theory and Applications · 2006
The modelling of fractional linear systems through ARMA models is addressed. To perform this study, a new recursive algorithm for impulse response ARMA modelling is presented. This is a general algorithm that allows the recursive construction of ARMA models from the impulse response sequence. This algorithm does not need an exact order specification, as it gives some insights into the correct orders. It is applied to modelling fractional linear systems described by fractional powers of the backward difference and the bilinear transformations. The analysis of the results leads to propose suitable models for those systems.
Cited by 13
Tom Doan · RePEc: Research Papers in Economics
Uses the Durbin-Levinson recursion to estimate the coefficients in a sequence of autoregressive representations for a stationary series.
Cited by 0
Manuel D. Ortigueira, António J. Serralheiro · 2008
Cited by 0
W. Scott Dunbar · Proceedings of the IEEE · 1981
An in-place Levinson update algorithm is presented which requires less storage than update algorithms in some published programs. The algorithm may be easily implemented in a program which employs a Levinson recursion.
Cited by 2
2004
This chapter includes the following topics: Normal Equations Levinson–Durbin Recursion
Cited by 0
K. S. Sim, Mei Shyan Lim, Z. X. Yeap · Journal of Microscopy · 2016
A new technique to quantify signal-to-noise ratio (SNR) value of the scanning electron microscope (SEM) images is proposed. This technique is known as autocorrelation Levinson-Durbin recursion (ACLDR) model. To test the performance of this technique, the SEM image is corrupted with noise. The autocorrelation function of the original image and the noisy image are formed. The signal spectrum based on the autocorrelation function of image is formed. ACLDR is then used as an SNR estimator to quantify the signal spectrum of noisy image. The SNR values of the original image and the quantified image are calculated. The ACLDR is then compared with the three existing techniques, which are nearest neighbourhood, first-order linear interpolation and nearest neighbourhood combined with first-order linear interpolation. It is shown that ACLDR model is able to achieve higher accuracy in SNR estimation.
Cited by 2
Paul Shaman · Integers · 2009
Abstract The Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson–Durbin sequence is also defined, and we note that binomial coefficients constitute a special case of such a sequence. Generalized Levinson–Durbin sequences obey formulas which generalize relations satisfied by binomial coefficients. Some of these results are extended to vector stationary processes.
Cited by 0
Brian D. O. Anderson, Ah Chung Tsoi · 1982
The prime concern of this paper is to describe procedures for computing the polynomial defining a backward autoregressive recursion from the polynomial defining a forward autoregressive recursion without necessarily using a Levinson-Wiggins-Robinson type of algorithm. Two distinct procedures are given, one involving the computation of covariance data, the other not.
Cited by 0
José J. López, Alberto González · Electronics Letters · 2000
A computationally efficient implementation of the Levinson algorithm in two steps that dramatically reduces the computational cost is presented. The algorithm uses the generalised Levinson recursion for block matrices as a first step and the Gohberg-Semencul formula as a second step, saving ~75% in terms of the computational cost for a typical two-channel deconvolution problem.
Cited by 7
Jangkung Raharjo, Syamsul Rizal, Jaspar Hasudungan · International Review of Electrical Engineering (IREE) · 2023
Forecasting energy consumption is essential for planning electricity provision by both central and local governments, as well as electricity providers. This research sought to adapt Levinson recursion, previously utilized in speech signal prediction, for predicting electrical energy consumption in the household sector. By employing Levinson’s algorithm to derive autocorrelation from historical data, the study contrasted the method's efficacy across various orders of Levinson Recursion. The 22nd order emerged as the most optimal, with an approximate error rate of 3.67%. Although the method showed a pronounced sensitivity to fluctuations in historical data, making it suitable for short-term forecasts, the noticeable fluctuation in the energy consumption prediction graph warrants further research, especially given that the current method has mainly been applied to concise signal predictions.
Cited by 0
Izumi Hanazaki, Tsuyoshi Nakajima, Kageo Akizuki · Transactions of the Society of Instrument and Control Engineers · 1985
Burg's algorithm and forward-backward linear prediction algorithm (FBLP algorithm) are effective for short data records in autoregrresive spectrum analysis. But Burg's algorithm has several problems, including spectral line splitting and biases in frequency estimates. Burg's algorithm minimizes the sum of the forward and backward prediction powers subject to the constraint that the AR parameter estimates satisfy the Levinson recursion. The constraint causes the problems, but ensures the stable prediction filter. While FBLP algorithm minimizes it with respect to all AR paramters. This algorithm is the procedure in which the Levinson recursion constraint is removed, and includes less biases in frequency estimates and absence of spectral line splitting, however cannot guarantee the stable prediction filter.In this paper, we propose a new algorithm possessing the advantage of Burg's algorithm and improving the estimates and show that spectral line splitting cannot be observed by using this algorithm.
Cited by 1Open access
Martine Collaud Coen, Elisabeth Andrews, Diego Aliaga et al. · 2017
To obtain a statistically estimation of the diurnal cycles of a time series x(t), the following steps were applied for each month of the year: 1) We calculate the auto-correlation function (ACF) and the partial auto-correlation function (PACF) with the Levinson-Durbin recursion function of matlab (see Fig. S1 a and b).
Cited by 1Open access
David Burshtein, E. Weinstein · IEEE Transactions on Acoustics Speech and Signal Processing · 1987
We present a computationally efficient method of calculating confidence intervals for the maximum entropy (ME) or autoregressive (AR) spectrum, based on new theoretical considerations. The method is consistent with the well-known asymptotic results, and it can be incorporated under certain assumptions into the Levinson-Durbin recursion. The method is also extended to ME wavenumber estimation.
Cited by 28
John A. Zelano, Ronald M. Mackintosh, Joy Hirsch · 2003
Heart-rate variability was examined with a recently developed microcomputer system in a number of patients with varied metabolic states. Power spectral density was computed in each case using standard FFT and the Levinson recursion algorithms. Reproducible spectral analyses were obtained for all patients. No difference in interpretation was observed between Levinson and standard FFT algorithms. Therefore, in spite of the inherent better definition of autoregressive modeling for spectral computation, the fast FFT algorithm yields equivalent results. The new system provides wide functional versatility for users interested in heart rate variability studies.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cited by 0
Bruce R. Musicus · IEEE Transactions on Acoustics Speech and Signal Processing · 1985
We derive a fast algorithm for calculating the Capon maximum likelihood method (MLM) power spectrum estimate when given uniformly spaced samples of the correlation function. This algorithm computes a weighted correlation of the predictor coefficients found by running Levinson recursion. The Fourier transform of the result gives the MLM spectrum. This approach also suggests an interesting new comparison between MLM and MEM.
Cited by 81
Milton J. Porsani · Geophysics · 1996
Abstract Two recursive algorithms for designing discrete Wiener filters for wavelets of different phase characteristics are the Simpson and the Manolakis recursions. Both procedures are efficient; however, both recursions work with a prefixed length filter. Two fast algorithms to design discrete Wiener filters in lag and length coordinates are presented. The recursion methods of Levinson and Manolakis are combined to generate two fast algorithms that calculate the value for the minimized total squared error (MTSE) corresponding to spiking and shaping filters. For a spiking filter of length n and a wavelet of m data points, 5mn + 5/2n2 + 3/2n operations are required to obtain the (m + n −1) × n map of the MTSEs, (one operation is defined here as one multiplication and one addition). For a shaping filter, 4mn + 3/2(n2 + n) operations are required to obtain the corresponding m × n map. These algorithms may be seen as a Levinson recursion on two variables, length j of the filter and lag k, for the desired signal. Numerical examples for spiking and shaping filters are presented.
Cited by 4
Dirk Slock, T. Kailath · 2005
In this paper, the correspondence between the efficient Split-Levinson algorithm and linear-phase filtering is exploited. Least-squares estimation subject to a linear-phase constraint leads to a persynnnetric sample covariance matrix in the normal equations. We introduce a new orthogonal- ization scheme for the data vectors. This scheme is appropriate for problems with the structure of a liticar-phase constraint. The symmetric linear-phase prediction polynomials effecting this orthogonaligmtion procedure obey a thrcetemn recursion, as in the Split-Levinson algorithin, with the addition of an extra term involving the Kalman gain. As a byproduct, the predictor polynoinial of the Forward-Backward Prediction Method (FBPM) can be recovered from the linear-pliase polynomial, paralleling a similar relationship in the Split-Levinson algorithm. Finally, we also describe how the batch-processing fast LS algorithm can be converted into a time-recursive solution. This yields a fast lattice algorithin for solving the corresponding RLS problems. The multichannel prewindowing formulation is considered.
Cited by 0
Pan, J., Levine, William S. · Digital Repository at the University of Maryland (University of Maryland College Park) · 1992
A Levinson-type recursion for a class of non-Teoplitz systems of linear equations is demonstrated. A complete solution is expressed as a linear combination of a partial solution and three auxiliary solutions. The class of systems possesses a special structure in that the coefficient matrices can be partitioned into four block Teoplitz submatrices. The number of multiplications and additions required to compute an n- dimensional solution if O(n2). The recursion is then applied to multichannel IIR filtering. Specifically, a lattice structure is established for linear minimum mean square error predictors having independently and arbitrarily specified numbers of poles and zeros. Next the recursion is used to develop a fast time and order recursive algorithm for ARX system identification, producing parameter estimates of family of ARX models. The algorithm preserves consistency of the well-known recursive least-squares algorithm.
Cited by 0Open access