Self-regressive model (AR models) _ Speech signal processing

Turn from: http://geodesy.blog.sohu.com/273714573.html
1. autoregressive Model definition Autoregressive model (autoregressive models) is the process of using its own regression variables, that is to describe the linear regression model of random variables at a later time by using the linear combination of random variables in the earlier periods [1], which is a common form in the Time-series [2].



2. AR models of State-space forms (ar-process in State spaces form) AR model can be written in the form of the status space model [4] [5] [6], so that:



3. AR model can be solved by the form of Yule-walker equation [3]. Considering the P-order AR model, the AR feature polynomial and the corresponding AR characteristic equation are given.






4. AR Model Example



References [1] R. Shumway  and D. Stoffer, time Series analysis and its applications with R examples, third ed.: SPR Inger, 2011. [2] A. cowpertwait P. P., introductory time Series with R:springer, 2009. [3] J. Cryer and K. Chan, time Series analysis with with and applications in R (Second Edition): Springer, 2008. [4] M. Wildi, "an A Intro duction to the state space Mo dels," 2013. [5] J. Durbin and S. J. Koopman, Time Series analysis by state space Methods:second Edition:oup Oxford, 2012. [6] J. Commandeur and S. J. Koopman, an Introduction to the state spaces time Series Analysis:oup Oxford, 2007.