Documentation Help Center. Estimate the correlation function. Discard the correlation values at negative lags. Use the Levinson-Durbin recursion to estimate the model coefficients. Verify that the prediction error corresponds to the variance of the input. Estimate the reflection coefficients for a 16th-order model.

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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 and Durbin , which applies in the pure autoregressive case. We use ideas similar to the multivariate autoregressive case. Most users should sign in with their email address. If you originally registered with a username please use that to sign in. To purchase short term access, please sign in to your Oxford Academic account above.

Don't already have an Oxford Academic account? Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account. Sign In. Advanced Search. Search Menu. Article Navigation. Close mobile search navigation Article Navigation. Volume Article Contents Abstract. A Levinson-Durbin recursion for autoregressive-moving average processes J.

Department of Mathematics, University of Frankfurt. Oxford Academic. Google Scholar. Cite Cite J. Select Format Select format. Permissions Icon Permissions. Abstract We discuss an algorithm which allows for recursive-in-order calculation of the parameters of autoregressive-moving average processes. Issue Section:. You do not currently have access to this article. Download all figures.

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An extended Levinson-Durbin algorithm and its application in mixed excitation linear prediction

Traditional Levinson-Durbin algorithm is one of the methods to solve the Yule-Walker equations conducted by the ten order linear prediction model. Taking the iteration step of traditional Levinson-Durbin algorithm as 1, an extended algorithm with any positive integer iteration step which is no larger than the order of Teoplitz matrix is proposed. The extended algorithm considers interaction between the adjacent subtracts. The perceptual evaluation of speech quality mean opinion score of nasal syllable is improved in some degree. Linear predictive coding has been widely used in low-bit-rate speech coders. Desired results are achieved by the use of an all-pole model in this algorithm to simulate the vocal tract in producing voiced sounds. However, as the nasal cavity opens and the end of the vocal tract branches during nasal sound production, a pole-zero or higher-order all-pole model is necessary to model the vocal tract.


Levinson recursion

Levinson recursion or Levinson—Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix. The Levinson—Durbin algorithm was proposed first by Norman Levinson in , improved by James Durbin in , and subsequently improved to 4 n 2 and then 3 n 2 multiplications by W. Trench and S. Zohar, respectively. Other methods to process data include Schur decomposition and Cholesky decomposition. In comparison to these, Levinson recursion particularly split Levinson recursion tends to be faster computationally, but more sensitive to computational inaccuracies like round-off errors.


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